diff --git a/.clang-format b/.clang-format new file mode 100644 index 0000000..59dd36e --- /dev/null +++ b/.clang-format @@ -0,0 +1,39 @@ +--- +Language: Cpp +BasedOnStyle: LLVM +AccessModifierOffset: -4 +AlignOperands: false +AlignTrailingComments: false +AlwaysBreakTemplateDeclarations: Yes +BraceWrapping: + AfterCaseLabel: true + AfterClass: true + AfterControlStatement: true + AfterEnum: true + AfterFunction: true + AfterNamespace: true + AfterStruct: true + AfterUnion: true + AfterExternBlock: false + BeforeCatch: true + BeforeElse: true + SplitEmptyFunction: true + SplitEmptyRecord: true + SplitEmptyNamespace: true +BreakBeforeBraces: Custom +BreakConstructorInitializers: AfterColon +ColumnLimit: 500 +Cpp11BracedListStyle: false +IncludeCategories: + - Regex: '^<.*' + Priority: 1 + - Regex: '^".*' + Priority: 2 + - Regex: '.*' + Priority: 3 +IncludeIsMainRegex: '([-_](test|unittest))?$' +IndentWidth: 4 +MaxEmptyLinesToKeep: 2 +NamespaceIndentation: All +TabWidth: 4 +... diff --git a/.gitignore b/.gitignore index d244352..0626272 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,37 @@ -* -!FastNoise.cpp -!FastNoise.h -!LICENSE -!*.md +*.swp +*.*~ +project.lock.json +.DS_Store +*.pyc +nupkg/ + +# Visual Studio Code +.vscode + +# Rider +.idea + +# User-specific files +*.suo +*.user +*.userosscache +*.sln.docstates + +# Build results +[Dd]ebug/ +[Dd]ebugPublic/ +[Rr]elease/ +[Rr]eleases/ +x64/ +x86/ +build/ +bld/ +[Bb]in/ +[Oo]bj/ +[Oo]ut/ +msbuild.log +msbuild.err +msbuild.wrn + +# Visual Studio 2015 +.vs/ \ No newline at end of file diff --git a/C/FastNoiseLite.h b/C/FastNoiseLite.h new file mode 100644 index 0000000..0a60e96 --- /dev/null +++ b/C/FastNoiseLite.h @@ -0,0 +1,2427 @@ +// MIT License +// +// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com) +// Copyright(c) 2020 Contributors +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files(the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions : +// +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +// +// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll +// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo +// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd +// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx +// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx +// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd +// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo +// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo +// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo +// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo +// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo +// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo +// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl +// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c +// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c +// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc +// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll +// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo +// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd +// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk +// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000 +// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX +// +// VERSION: 1.0 +// https://github.com/Auburn/FastNoise + +// In *one* C or C++ file, use #define FNL_IMPL to generate implementation + +// Switch between using floats or doubles for input position +typedef float FNLfloat; +//typedef double FNLfloat; + +#if defined(__cplusplus) +extern "C" { +#endif + +#include +#include +#include + +// Enums +typedef enum +{ + FNL_NOISE_OPENSIMPLEX2, + FNL_NOISE_OPENSIMPLEX2S, + FNL_NOISE_CELLULAR, + FNL_NOISE_PERLIN, + FNL_NOISE_VALUE_CUBIC, + FNL_NOISE_VALUE +} fnl_noise_type; + +typedef enum +{ + FNL_ROTATION_NONE, + FNL_ROTATION_IMPROVE_XY_PLANES, + FNL_ROTATION_IMPROVE_XZ_PLANES +} fnl_rotation_type_3d; + +typedef enum +{ + FNL_FRACTAL_NONE, + FNL_FRACTAL_FBM, + FNL_FRACTAL_RIDGED, + FNL_FRACTAL_PINGPONG, + FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE, + FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT +} fnl_fractal_type; + +typedef enum +{ + FNL_CELLULAR_DISTANCE_EUCLIDEAN, + FNL_CELLULAR_DISTANCE_EUCLIDEANSQ, + FNL_CELLULAR_DISTANCE_MANHATTAN, + FNL_CELLULAR_DISTANCE_HYBRID +} fnl_cellular_distance_func; + +typedef enum +{ + FNL_CELLULAR_RETURN_VALUE_CELLVALUE, + FNL_CELLULAR_RETURN_VALUE_DISTANCE, + FNL_CELLULAR_RETURN_VALUE_DISTANCE2, + FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD, + FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB, + FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL, + FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV, +} fnl_cellular_return_type; + +typedef enum +{ + FNL_DOMAIN_WARP_OPENSIMPLEX2, + FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED, + FNL_DOMAIN_WARP_BASICGRID +} fnl_domain_warp_type; + +/** + * Structure containing entire noise system state. + * @note Must only be created using fnlCreateState(optional: seed). To ensure defaults are set. + */ +typedef struct fnl_state +{ + /** + * Seed used for all noise types. + * @remark Default: 1337 + */ + int seed; + + /** + * The frequency for all noise types. + * @remark Default: 0.01 + */ + float frequency; + + /** + * The noise algorithm to be used by GetNoise(...). + * @remark Default: FNL_NOISE_OPENSIMPLEX2 + */ + fnl_noise_type noise_type; + + /** + * Sets noise rotation type for 3D. + * @remark Default: FNL_ROTATION_NONE + */ + fnl_rotation_type_3d rotation_type_3d; + + /** + * The method used for combining octaves for all fractal noise types. + * @remark Default: None + * @remark FNL_FRACTAL_DOMAIN_WARP_... only effects fnlDomainWarp... + */ + fnl_fractal_type fractal_type; + + /** + * The octave count for all fractal noise types. + * @remark Default: 3 + */ + int octaves; + + /** + * The octave lacunarity for all fractal noise types. + * @remark Default: 2.0 + */ + float lacunarity; + + /** + * The octave gain for all fractal noise types. + * @remark Default: 0.5 + */ + float gain; + + /** + * The octave weighting for all none Domaain Warp fractal types. + * @remark Default: 0.0 + * @remark + */ + float weighted_strength; + + /** + * The strength of the fractal ping pong effect. + * @remark Default: 2.0 + */ + float ping_pong_strength; + + /** + * The distance function used in cellular noise calculations. + * @remark Default: FNL_CELLULAR_FUNC_DISTANCE + */ + fnl_cellular_distance_func cellular_distance_func; + + /** + * The cellular return type from cellular noise calculations. + * @remark Default: FNL_CELLULAR_RETURN_VALUE_EUCLIEANSQ + */ + fnl_cellular_return_type cellular_return_type; + + /** + * The maximum distance a cellular point can move from it's grid position. + * @remark Default: 1.0 + * @note Setting this higher than 1 will cause artifacts. + */ + float cellular_jitter_mod; + + /** + * The warp algorithm when using fnlDomainWarp... + * @remark Default: OpenSimplex2 + */ + fnl_domain_warp_type domain_warp_type; + + /** + * The maximum warp distance from original position when using fnlDomainWarp... + * @remark Default: 1.0 + */ + float domain_warp_amp; +} fnl_state; + +/** + * Creates a noise state with default values. + * @param seed Optionally set the state seed. + */ +fnl_state fnlCreateState(int seed = 1337); + +/** + * 2D noise at given position using the state settings + * @returns Noise output bounded between -1 and 1. + */ +float fnlGetNoise2D(fnl_state *state, FNLfloat x, FNLfloat y); + +/** + * 3D noise at given position using the state settings + * @returns Noise output bounded between -1 and 1. + */ +float fnlGetNoise3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z); + +/** + * 2D warps the input position using current domain warp settings. + * + * Example usage with fnlGetNoise2D: + * ``` + * fnlDomainWarp2D(&state, &x, &y); + * noise = fnlGetNoise2D(&state, x, y); + * ``` + */ +void fnlDomainWarp2D(fnl_state *state, FNLfloat *x, FNLfloat *y); + +/** + * 3D warps the input position using current domain warp settings. + * + * Example usage with fnlGetNoise3D: + * ``` + * fnlDomainWarp3D(&state, &x, &y, &z); + * noise = fnlGetNoise3D(&state, x, y, z); + * ``` + */ +void fnlDomainWarp3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z); + +// ==================== +// Below this line is the implementation +// ==================== + +#if defined(FNL_IMPL) + +// Constants + +static const float GRADIENTS_2D[] = +{ + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f, + -0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f, +}; + +static const float RAND_VECS_2D[] = +{ + -0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f, + -0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, -0.892300288f, -0.4514423508f, -0.379844434f, -0.9250503802f, -0.9951650832f, 0.0982163789f, 0.7724397808f, -0.6350880136f, 0.7573283322f, -0.6530343002f, -0.9928004525f, -0.119780055f, + -0.0532665713f, 0.9985803285f, 0.9754253726f, -0.2203300762f, -0.7665018163f, 0.6422421394f, 0.991636706f, 0.1290606184f, -0.994696838f, 0.1028503788f, -0.5379205513f, -0.84299554f, 0.5022815471f, -0.8647041387f, 0.4559821461f, -0.8899889226f, + -0.8659131224f, -0.5001944266f, 0.0879458407f, -0.9961252577f, -0.5051684983f, 0.8630207346f, 0.7753185226f, -0.6315704146f, -0.6921944612f, 0.7217110418f, -0.5191659449f, -0.8546734591f, 0.8978622882f, -0.4402764035f, -0.1706774107f, 0.9853269617f, + -0.9353430106f, -0.3537420705f, -0.9992404798f, 0.03896746794f, -0.2882064021f, -0.9575683108f, -0.9663811329f, 0.2571137995f, -0.8759714238f, -0.4823630009f, -0.8303123018f, -0.5572983775f, 0.05110133755f, -0.9986934731f, -0.8558373281f, -0.5172450752f, + 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-0.9988770922f, -0.047376731f, -0.1250179027f, 0.992154486f, -0.8280133617f, 0.560708367f, 0.9324863769f, -0.3612051451f, 0.6394653183f, 0.7688199442f, -0.01623847064f, -0.9998681473f, -0.9955014666f, -0.09474613458f, -0.81453315f, 0.580117012f, + 0.4037327978f, -0.9148769469f, 0.9944263371f, 0.1054336766f, -0.1624711654f, 0.9867132919f, -0.9949487814f, -0.100383875f, -0.6995302564f, 0.7146029809f, 0.5263414922f, -0.85027327f, -0.5395221479f, 0.841971408f, 0.6579370318f, 0.7530729462f, + 0.01426758847f, -0.9998982128f, -0.6734383991f, 0.7392433447f, 0.639412098f, -0.7688642071f, 0.9211571421f, 0.3891908523f, -0.146637214f, -0.9891903394f, -0.782318098f, 0.6228791163f, -0.5039610839f, -0.8637263605f, -0.7743120191f, -0.6328039957f, +}; + +static const float GRADIENTS_3D[] = +{ + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 1, 1, 0, 0, 0,-1, 1, 0, -1, 1, 0, 0, 0,-1,-1, 0 +}; + +static const float RAND_VECS_3D[] = +{ + -0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, -0.2739291014f, 0, 0.7217578935f, 0.6226212466f, -0.3023380997f, 0, 0.565683137f, -0.8208298145f, -0.0790000257f, 0, 0.760049034f, -0.5555979497f, -0.3370999617f, 0, 0.3713945616f, 0.5011264475f, 0.7816254623f, 0, -0.1277062463f, -0.4254438999f, -0.8959289049f, 0, 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-0.8044887315f, 0.5827524187f, 0, + -0.7870349638f, 0.03447489231f, 0.6159443543f, 0, -0.2015596421f, 0.6859872284f, 0.6991389226f, 0, -0.08581082512f, -0.10920836f, -0.9903080513f, 0, 0.5532693395f, 0.7325250401f, -0.396610771f, 0, -0.1842489331f, -0.9777375055f, -0.1004076743f, 0, 0.0775473789f, -0.9111505856f, 0.4047110257f, 0, 0.1399838409f, 0.7601631212f, -0.6344734459f, 0, 0.4484419361f, -0.845289248f, 0.2904925424f, 0 +}; + +// Utilities + +static inline float _fnlFastMin(float x, float y) { return x < y ? x : y; } + +static inline float _fnlFastMax(float x, float y) { return x > y ? x : y; } + +static inline float _fnlFastAbs(float f) { return f < 0 ? -f : f; } + +static inline float _fnlCasti32Tof32(int i) +{ + union + { + float f; + int32_t i; + } u; + u.i = i; + return u.f; +} + +static inline int _fnlCastf32Toi32(float f) +{ + union + { + float f; + int32_t i; + } u; + u.f = f; + return u.i; +} + +static inline float _fnlInvSqrt(float a) +{ + float xhalf = 0.5f * a; + a = _fnlCasti32Tof32(0x5f3759df - (_fnlCastf32Toi32(a) >> 1)); + a = a * (1.5f - xhalf * a * a); + return a; +} + +// NOTE: If your language does not support this method (seen above), then simply use the native sqrt function. +static inline float _fnlFastSqrt(float a) { return a * _fnlInvSqrt(a); } + +static inline int _fnlFastFloor(FNLfloat f) { return (f >= 0 ? (int)f : (int)f - 1); } + +static inline int _fnlFastRound(FNLfloat f) { return (f >= 0) ? (int)(f + 0.5f) : (int)(f - 0.5f); } + +static inline float _fnlLerp(float a, float b, float t) { return a + t * (b - a); } + +static inline float _fnlInterpHermite(float t) { return t * t * (3 - 2 * t); } + +static inline float _fnlInterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); } + +static inline float _fnlCubicLerp(float a, float b, float c, float d, float t) +{ + float p = (d - c) - (a - b); + return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b; +} + +static inline float _fnlPingPong(float t) +{ + t -= (int)(t * 0.5f) * 2; + return t < 1 ? t : 2 - t; +} + +static float _fnlCalculateFractalBounding(fnl_state *state) +{ + float gain = _fnlFastAbs(state->gain); + float amp = gain; + float ampFractal = 1.0f; + for (int i = 1; i < state->octaves; i++) + { + ampFractal += amp; + amp *= gain; + } + return 1.0f / ampFractal; +} + +// Hashing + +static const int PRIME_X = 501125321; +static const int PRIME_Y = 1136930381; +static const int PRIME_Z = 1720413743; + +static inline int _fnlHash2D(int seed, int xPrimed, int yPrimed) +{ + int hash = seed ^ xPrimed ^ yPrimed; + + hash *= 0x27d4eb2d; + return hash; +} + +static inline int _fnlHash3D(int seed, int xPrimed, int yPrimed, int zPrimed) +{ + int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed; + + hash *= 0x27d4eb2d; + return hash; +} + +static inline float _fnlValCoord2D(int seed, int xPrimed, int yPrimed) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); +} + +static inline float _fnlValCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); +} + +static inline float _fnlGradCoord2D(int seed, int xPrimed, int yPrimed, float xd, float yd) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + hash ^= hash >> 15; + hash &= 127 << 1; + return xd * GRADIENTS_2D[hash] + yd * GRADIENTS_2D[hash | 1]; +} + +static inline float _fnlGradCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + hash ^= hash >> 15; + hash &= 63 << 2; + return xd * GRADIENTS_3D[hash] + yd * GRADIENTS_3D[hash | 1] + zd * GRADIENTS_3D[hash | 2]; +} + +static inline void _fnlGradCoordOut2D(int seed, int xPrimed, int yPrimed, float *xo, float *yo) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed) & (255 << 1); + + *xo = RAND_VECS_2D[hash]; + *yo = RAND_VECS_2D[hash | 1]; +} + +static inline void _fnlGradCoordOut3D(int seed, int xPrimed, int yPrimed, int zPrimed, float *xo, float *yo, float *zo) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed) & (255 << 2); + + *xo = RAND_VECS_3D[hash]; + *yo = RAND_VECS_3D[hash | 1]; + *zo = RAND_VECS_3D[hash | 2]; +} + +static inline void _fnlGradCoordDual2D(int seed, int xPrimed, int yPrimed, float xd, float yd, float *xo, float *yo) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + + float xg = GRADIENTS_2D[index1]; + float yg = GRADIENTS_2D[index1 | 1]; + float value = xd * xg + yd * yg; + + float xgo = RAND_VECS_2D[index2]; + float ygo = RAND_VECS_2D[index2 | 1]; + + *xo = value * xgo; + *yo = value * ygo; +} + +static inline void _fnlGradCoordDual3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, float *xo, float *yo, float *zo) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int index1 = hash & (63 << 2); + int index2 = (hash >> 6) & (255 << 2); + + float xg = GRADIENTS_3D[index1]; + float yg = GRADIENTS_3D[index1 | 1]; + float zg = GRADIENTS_3D[index1 | 2]; + float value = xd * xg + yd * yg + zd * zg; + + float xgo = RAND_VECS_3D[index2]; + float ygo = RAND_VECS_3D[index2 | 1]; + float zgo = RAND_VECS_3D[index2 | 2]; + + *xo = value * xgo; + *yo = value * ygo; + *zo = value * zgo; +} + +// Generic Noise Gen + +static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleCellular2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleCellular3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); + +static float _fnlGenNoiseSingle2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y) +{ + switch (state->noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + return _fnlSingleSimplex2D(seed, x, y); + case FNL_NOISE_OPENSIMPLEX2S: + return _fnlSingleOpenSimplex2S2D(seed, x, y); + case FNL_NOISE_CELLULAR: + return _fnlSingleCellular2D(state, seed, x, y); + case FNL_NOISE_PERLIN: + return _fnlSinglePerlin2D(seed, x, y); + case FNL_NOISE_VALUE_CUBIC: + return _fnlSingleValueCubic2D(seed, x, y); + case FNL_NOISE_VALUE: + return _fnlSingleValue2D(seed, x, y); + default: + return 0; + } +} + +static float _fnlGenNoiseSingle3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + switch (state->noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + return _fnlSingleOpenSimplex23D(seed, x, y, z); + case FNL_NOISE_OPENSIMPLEX2S: + return _fnlSingleOpenSimplex2S3D(seed, x, y, z); + case FNL_NOISE_CELLULAR: + return _fnlSingleCellular3D(state, seed, x, y, z); + case FNL_NOISE_PERLIN: + return _fnlSinglePerlin3D(seed, x, y, z); + case FNL_NOISE_VALUE_CUBIC: + return _fnlSingleValueCubic3D(seed, x, y, z); + case FNL_NOISE_VALUE: + return _fnlSingleValue3D(seed, x, y, z); + default: + return 0; + } +} + +// Noise Coordinate Transforms (frequency, and possible skew or rotation) + +static void _fnlTransformNoiseCoordinate2D(fnl_state *state, FNLfloat *x, FNLfloat *y) +{ + *x *= state->frequency; + *y *= state->frequency; + + switch (state->noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + case FNL_NOISE_OPENSIMPLEX2S: + { + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat F2 = 0.5f * (SQRT3 - 1); + FNLfloat t = (*x + *y) * F2; + *x += t; + *y += t; + } + break; + default: + break; + } +} + +static void _fnlTransformNoiseCoordinate3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z) +{ + *x *= state->frequency; + *y *= state->frequency; + *z *= state->frequency; + + switch (state->rotation_type_3d) + { + case FNL_ROTATION_IMPROVE_XY_PLANES: + { + FNLfloat xy = *x + *y; + FNLfloat s2 = xy * -(FNLfloat)0.211324865405187; + *z *= (FNLfloat)0.577350269189626; + *x += s2 - *z; + *y = *y + s2 - *z; + *z += xy * (FNLfloat)0.577350269189626; + } + break; + case FNL_ROTATION_IMPROVE_XZ_PLANES: + { + FNLfloat xz = *x + *z; + FNLfloat s2 = xz * -(FNLfloat)0.211324865405187; + *y *= (FNLfloat)0.577350269189626; + *x += s2 - *y; + *z += s2 - *y; + *y += xz * (FNLfloat)0.577350269189626; + } + break; + default: + switch (state->noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + case FNL_NOISE_OPENSIMPLEX2S: + { + const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + FNLfloat r = (*x + *y + *z) * R3; // Rotation, not skew + *x = r - *x; + *y = r - *y; + *z = r - *z; + } + break; + default: + break; + } + } +} + +// Domain Warp Coordinate Transforms + +static void _fnlTransformDomainWarpCoordinate2D(fnl_state *state, FNLfloat *x, FNLfloat *y) +{ + switch (state->domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + { + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat F2 = 0.5f * (SQRT3 - 1); + FNLfloat t = (*x + *y) * F2; + *x += t; + *y += t; + } + break; + default: + break; + } +} + +static void _fnlTransformDomainWarpCoordinate3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z) +{ + switch (state->rotation_type_3d) + { + case FNL_ROTATION_IMPROVE_XY_PLANES: + { + FNLfloat xy = *x + *y; + FNLfloat s2 = xy * -(FNLfloat)0.211324865405187; + *z *= (FNLfloat)0.577350269189626; + *x += s2 - *z; + *y = *y + s2 - *z; + *z += xy * (FNLfloat)0.577350269189626; + } + break; + case FNL_ROTATION_IMPROVE_XZ_PLANES: + { + FNLfloat xz = *x + *z; + FNLfloat s2 = xz * -(FNLfloat)0.211324865405187; + *y *= (FNLfloat)0.577350269189626; + *x += s2 - *y; + *z += s2 - *y; + *y += xz * (FNLfloat)0.577350269189626; + } + break; + default: + switch (state->domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + { + const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + FNLfloat r = (*x + *y + *z) * R3; // Rotation, not skew + *x = r - *x; + *y = r - *y; + *z = r - *z; + } + break; + default: + break; + } + } +} + +// Fractal FBm +static float _fnlGenFractalFBM2D(fnl_state *state, FNLfloat x, FNLfloat y) +{ + int seed = state->seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state->octaves; i++) + { + float noise = _fnlGenNoiseSingle2D(state, seed++, x, y); + sum += noise * amp; + amp *= _fnlLerp(1.0f, _fnlFastMin(noise + 1, 2) * 0.5f, state->weighted_strength); + + x *= state->lacunarity; + y *= state->lacunarity; + amp *= state->gain; + } + + return sum; +} + +static float _fnlGenFractalFBM3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int seed = state->seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state->octaves; i++) + { + float noise = _fnlGenNoiseSingle3D(state, seed++, x, y, z); + sum += noise * amp; + amp *= _fnlLerp(1.0f, (noise + 1) * 0.5f, state->weighted_strength); + + x *= state->lacunarity; + y *= state->lacunarity; + z *= state->lacunarity; + amp *= state->gain; + } + + return sum; +} + +// Fractal Ridged + +static float _fnlGenFractalRidged2D(fnl_state *state, FNLfloat x, FNLfloat y) +{ + int seed = state->seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state->octaves; i++) + { + float noise = _fnlFastAbs(_fnlGenNoiseSingle2D(state, seed++, x, y)); + sum += (noise * -2 + 1) * amp; + amp *= _fnlLerp(1.0f, 1 - noise, state->weighted_strength); + + x *= state->lacunarity; + y *= state->lacunarity; + amp *= state->gain; + } + + return sum; +} + +static float _fnlGenFractalRidged3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int seed = state->seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state->octaves; i++) + { + float noise = _fnlFastAbs(_fnlGenNoiseSingle3D(state, seed++, x, y, z)); + sum += (noise * -2 + 1) * amp; + amp *= _fnlLerp(1.0f, 1 - noise, state->weighted_strength); + + x *= state->lacunarity; + y *= state->lacunarity; + z *= state->lacunarity; + amp *= state->gain; + } + + return sum; +} + +// Fractal PingPong + +static float _fnlGenFractalPingPong2D(fnl_state *state, FNLfloat x, FNLfloat y) +{ + int seed = state->seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state->octaves; i++) + { + float noise = _fnlPingPong((_fnlGenNoiseSingle2D(state, seed++, x, y) + 1) * state->ping_pong_strength); + sum += (noise - 0.5f) * 2 * amp; + amp *= _fnlLerp(1.0f, noise, state->weighted_strength); + + x *= state->lacunarity; + y *= state->lacunarity; + amp *= state->gain; + } + + return sum; +} + +static float _fnlGenFractalPingPong3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int seed = state->seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state->octaves; i++) + { + float noise = _fnlPingPong((_fnlGenNoiseSingle3D(state, seed++, x, y, z) + 1) * state->ping_pong_strength); + sum += (noise - 0.5f) * 2 * amp; + amp *= _fnlLerp(1.0f, noise, state->weighted_strength); + + x *= state->lacunarity; + y *= state->lacunarity; + z *= state->lacunarity; + amp *= state->gain; + } + + return sum; +} + +// Simplex/OpenSimplex2 Noise + +static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y) +{ + // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex. + + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PRIME_X; + j *= PRIME_Y; + + float n0, n1, n2; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a <= 0) + n0 = 0; + else + { + n0 = (a * a) * (a * a) * _fnlGradCoord2D(seed, i, j, x0, y0); + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c <= 0) + n2 = 0; + else + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + n2 = (c * c) * (c * c) * _fnlGradCoord2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2); + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) + n1 = 0; + else + { + n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x1, y1); + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) + n1 = 0; + else + { + n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i + PRIME_X, j, x1, y1); + } + } + + return (n0 + n1 + n2) * 99.83685446303647f; +} + +static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + // 3D OpenSimplex2 case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = _fnlFastRound(x); + int j = _fnlFastRound(y); + int k = _fnlFastRound(z); + float x0 = (float)(x - i); + float y0 = (float)(y - j); + float z0 = (float)(z - k); + + int xNSign = (int)(-1.0f - x0) | 1; + int yNSign = (int)(-1.0f - y0) | 1; + int zNSign = (int)(-1.0f - z0) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PRIME_X; + j *= PRIME_Y; + k *= PRIME_Z; + + float value = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; l < 2; l++) + { + if (a > 0) + { + value += (a * a) * (a * a) * _fnlGradCoord3D(seed, i, j, k, x0, y0, z0); + } + + float b = a + 1; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b -= xNSign * 2 * x1; + i1 -= xNSign * PRIME_X; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b -= yNSign * 2 * y1; + j1 -= yNSign * PRIME_Y; + } + else + { + z1 += zNSign; + b -= zNSign * 2 * z1; + k1 -= zNSign * PRIME_Z; + } + + if (b > 0) + { + value += (b * b) * (b * b) * _fnlGradCoord3D(seed, i1, j1, k1, x1, y1, z1); + } + + if (l == 1) + break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PRIME_X; + j += (yNSign >> 1) & PRIME_Y; + k += (zNSign >> 1) & PRIME_Z; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + return value * 32.69428253173828125f; +} + +// OpenSimplex2S Noise + +static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y) +{ + // 2D OpenSimplex2S case is a modified 2D simplex noise. + + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + i *= PRIME_X; + j *= PRIME_Y; + int i1 = i + PRIME_X; + int j1 = j + PRIME_Y; + + float t = (xi + yi) * (float)G2; + float x0 = xi - t; + float y0 = yi - t; + + float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0; + float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord2D(seed, i, j, x0, y0); + + float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0); + float x1 = x0 - (float)(1 - 2 * G2); + float y1 = y0 - (float)(1 - 2 * G2); + value += (a1 * a1) * (a1 * a1) * _fnlGradCoord2D(seed, i1, j1, x1, y1); + + // Nested conditionals were faster than compact bit logic/arithmetic. + float xmyi = xi - yi; + if (t > G2) + { + if (xi + xmyi > 1) + { + float x2 = x0 + (float)(3 * G2 - 2); + float y2 = y0 + (float)(3 * G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i + (PRIME_X << 1), j + PRIME_Y, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x2, y2); + } + } + + if (yi - xmyi > 1) + { + float x3 = x0 + (float)(3 * G2 - 1); + float y3 = y0 + (float)(3 * G2 - 2); + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * _fnlGradCoord2D(seed, i + PRIME_X, j + (PRIME_Y << 1), x3, y3); + } + } + else + { + float x3 = x0 + (float)(G2 - 1); + float y3 = y0 + (float)G2; + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * _fnlGradCoord2D(seed, i + PRIME_X, j, x3, y3); + } + } + } + else + { + if (xi + xmyi < 0) + { + float x2 = x0 + (float)(1 - G2); + float y2 = y0 - (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i - PRIME_X, j, x2, y2); + } + } + else + { + float x2 = x0 + (float)(G2 - 1); + float y2 = y0 + (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i + PRIME_X, j, x2, y2); + } + } + + if (yi < xmyi) + { + float x2 = x0 - (float)G2; + float y2 = y0 - (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i, j - PRIME_Y, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x2, y2); + } + } + } + + return value * 18.24196194486065f; +} + +static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + // 3D OpenSimplex2S case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + int k = _fnlFastFloor(z); + float xi = (float)(x - i); + float yi = (float)(y - j); + float zi = (float)(z - k); + + i *= PRIME_X; + j *= PRIME_Y; + k *= PRIME_Z; + int seed2 = seed + 1293373; + + int xNMask = (int)(-0.5f - xi); + int yNMask = (int)(-0.5f - yi); + int zNMask = (int)(-0.5f - zi); + + float x0 = xi + xNMask; + float y0 = yi + yNMask; + float z0 = zi + zNMask; + float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0; + float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x0, y0, z0); + + float x1 = xi - 0.5f; + float y1 = yi - 0.5f; + float z1 = zi - 0.5f; + float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1; + value += (a1 * a1) * (a1 * a1) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + PRIME_Y, k + PRIME_Z, x1, y1, z1); + + float xAFlipMask0 = ((xNMask | 1) << 1) * x1; + float yAFlipMask0 = ((yNMask | 1) << 1) * y1; + float zAFlipMask0 = ((zNMask | 1) << 1) * z1; + float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f; + float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f; + float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f; + + bool skip5 = false; + float a2 = xAFlipMask0 + a0; + if (a2 > 0) + { + float x2 = x0 - (xNMask | 1); + float y2 = y0; + float z2 = z0; + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord3D(seed, + i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x2, y2, z2); + } + else + { + float a3 = yAFlipMask0 + zAFlipMask0 + a0; + if (a3 > 0) + { + float x3 = x0; + float y3 = y0 - (yNMask | 1); + float z3 = z0 - (zNMask | 1); + value += (a3 * a3) * (a3 * a3) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x3, y3, z3); + } + + float a4 = xAFlipMask1 + a1; + if (a4 > 0) + { + float x4 = (xNMask | 1) + x1; + float y4 = y1; + float z4 = z1; + value += (a4 * a4) * (a4 * a4) * _fnlGradCoord3D(seed2, + i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + PRIME_Z, x4, y4, z4); + skip5 = true; + } + } + + bool skip9 = false; + float a6 = yAFlipMask0 + a0; + if (a6 > 0) + { + float x6 = x0; + float y6 = y0 - (yNMask | 1); + float z6 = z0; + value += (a6 * a6) * (a6 * a6) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x6, y6, z6); + } + else + { + float a7 = xAFlipMask0 + zAFlipMask0 + a0; + if (a7 > 0) + { + float x7 = x0 - (xNMask | 1); + float y7 = y0; + float z7 = z0 - (zNMask | 1); + value += (a7 * a7) * (a7 * a7) * _fnlGradCoord3D(seed, + i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x7, y7, z7); + } + + float a8 = yAFlipMask1 + a1; + if (a8 > 0) + { + float x8 = x1; + float y8 = (yNMask | 1) + y1; + float z8 = z1; + value += (a8 * a8) * (a8 * a8) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, x8, y8, z8); + skip9 = true; + } + } + + bool skipD = false; + float aA = zAFlipMask0 + a0; + if (aA > 0) + { + float xA = x0; + float yA = y0; + float zA = z0 - (zNMask | 1); + value += (aA * aA) * (aA * aA) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), xA, yA, zA); + } + else + { + float aB = xAFlipMask0 + yAFlipMask0 + a0; + if (aB > 0) + { + float xB = x0 - (xNMask | 1); + float yB = y0 - (yNMask | 1); + float zB = z0; + value += (aB * aB) * (aB * aB) * _fnlGradCoord3D(seed, + i + (~xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), xB, yB, zB); + } + + float aC = zAFlipMask1 + a1; + if (aC > 0) + { + float xC = x1; + float yC = y1; + float zC = (zNMask | 1) + z1; + value += (aC * aC) * (aC * aC) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), xC, yC, zC); + skipD = true; + } + } + + if (!skip5) + { + float a5 = yAFlipMask1 + zAFlipMask1 + a1; + if (a5 > 0) + { + float x5 = x1; + float y5 = (yNMask | 1) + y1; + float z5 = (zNMask | 1) + z1; + value += (a5 * a5) * (a5 * a5) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + (zNMask & (PRIME_Z << 1)), x5, y5, z5); + } + } + + if (!skip9) + { + float a9 = xAFlipMask1 + zAFlipMask1 + a1; + if (a9 > 0) + { + float x9 = (xNMask | 1) + x1; + float y9 = y1; + float z9 = (zNMask | 1) + z1; + value += (a9 * a9) * (a9 * a9) * _fnlGradCoord3D(seed2, + i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), x9, y9, z9); + } + } + + if (!skipD) + { + float aD = xAFlipMask1 + yAFlipMask1 + a1; + if (aD > 0) + { + float xD = (xNMask | 1) + x1; + float yD = (yNMask | 1) + y1; + float zD = z1; + value += (aD * aD) * (aD * aD) * _fnlGradCoord3D(seed2, + i + (xNMask & (PRIME_X << 1)), j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, xD, yD, zD); + } + } + + return value * 9.046026385208288f; +} + +// Cellular Noise + +static float _fnlSingleCellular2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y) +{ + int xr = _fnlFastRound(x); + int yr = _fnlFastRound(y); + + float distance0 = FLT_MAX; + float distance1 = FLT_MAX; + int closestHash = 0; + + float cellularJitter = 0.5f * state->cellular_jitter_mod; + + int xPrimed = (xr - 1) * PRIME_X; + int yPrimedBase = (yr - 1) * PRIME_Y; + + switch (state->cellular_distance_func) + { + default: + case FNL_CELLULAR_DISTANCE_EUCLIDEAN: + case FNL_CELLULAR_DISTANCE_EUCLIDEANSQ: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY; + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + case FNL_CELLULAR_DISTANCE_MANHATTAN: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter; + + float newDistance = _fnlFastAbs(vecX) + _fnlFastAbs(vecY); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + case FNL_CELLULAR_DISTANCE_HYBRID: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter; + + float newDistance = (_fnlFastAbs(vecX) + _fnlFastAbs(vecY)) + (vecX * vecX + vecY * vecY); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + + if (state->cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN && state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE) + { + distance0 = _fnlFastSqrt(distance0); + if (state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE2) + distance1 = _fnlFastSqrt(distance1); + } + + switch (state->cellular_return_type) + { + case FNL_CELLULAR_RETURN_VALUE_CELLVALUE: + return closestHash * (1 / 2147483648.0f); + case FNL_CELLULAR_RETURN_VALUE_DISTANCE: + return distance0 - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2: + return distance1 - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD: + return (distance1 + distance0) * 0.5f - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB: + return distance1 - distance0 - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL: + return distance1 * distance0 * 0.5f - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV: + return distance0 / distance1 - 1; + default: + return 0; + } +} + +static float _fnlSingleCellular3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int xr = _fnlFastRound(x); + int yr = _fnlFastRound(y); + int zr = _fnlFastRound(z); + + float distance0 = FLT_MAX; + float distance1 = FLT_MAX; + int closestHash = 0; + + float cellularJitter = 0.39614353f * state->cellular_jitter_mod; + + int xPrimed = (xr - 1) * PRIME_X; + int yPrimedBase = (yr - 1) * PRIME_Y; + int zPrimedBase = (zr - 1) * PRIME_Z; + + switch (state->cellular_distance_func) + { + default: + case FNL_CELLULAR_DISTANCE_EUCLIDEAN: + case FNL_CELLULAR_DISTANCE_EUCLIDEANSQ: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PRIME_Z; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + case FNL_CELLULAR_DISTANCE_MANHATTAN: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter; + + float newDistance = _fnlFastAbs(vecX) + _fnlFastAbs(vecY) + _fnlFastAbs(vecZ); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PRIME_Z; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + case FNL_CELLULAR_DISTANCE_HYBRID: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter; + + float newDistance = (_fnlFastAbs(vecX) + _fnlFastAbs(vecY) + _fnlFastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PRIME_Z; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + + if (state->cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN && state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE) + { + distance0 = _fnlFastSqrt(distance0); + if (state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE2) + distance1 = _fnlFastSqrt(distance1); + } + + switch (state->cellular_return_type) + { + case FNL_CELLULAR_RETURN_VALUE_CELLVALUE: + return closestHash * (1 / 2147483648.0f); + case FNL_CELLULAR_RETURN_VALUE_DISTANCE: + return distance0 - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2: + return distance1 - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD: + return (distance1 + distance0) * 0.5f - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB: + return distance1 - distance0 - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL: + return distance1 * distance0 * 0.5f - 1; + case FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV: + return distance0 / distance1 - 1; + default: + return 0; + } +} + +// Perlin Noise + +static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + + float xs = _fnlInterpQuintic(xd0); + float ys = _fnlInterpQuintic(yd0); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + + float xf0 = _fnlLerp(_fnlGradCoord2D(seed, x0, y0, xd0, yd0), _fnlGradCoord2D(seed, x1, y0, xd1, yd0), xs); + float xf1 = _fnlLerp(_fnlGradCoord2D(seed, x0, y1, xd0, yd1), _fnlGradCoord2D(seed, x1, y1, xd1, yd1), xs); + + return _fnlLerp(xf0, xf1, ys) * 1.4247691104677813f; +} + +static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + int z0 = _fnlFastFloor(z); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float zd0 = (float)(z - z0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + float zd1 = zd0 - 1; + + float xs = _fnlInterpQuintic(xd0); + float ys = _fnlInterpQuintic(yd0); + float zs = _fnlInterpQuintic(zd0); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + z0 *= PRIME_Z; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + int z1 = z0 + PRIME_Z; + + float xf00 = _fnlLerp(_fnlGradCoord3D(seed, x0, y0, z0, xd0, yd0, zd0), _fnlGradCoord3D(seed, x1, y0, z0, xd1, yd0, zd0), xs); + float xf10 = _fnlLerp(_fnlGradCoord3D(seed, x0, y1, z0, xd0, yd1, zd0), _fnlGradCoord3D(seed, x1, y1, z0, xd1, yd1, zd0), xs); + float xf01 = _fnlLerp(_fnlGradCoord3D(seed, x0, y0, z1, xd0, yd0, zd1), _fnlGradCoord3D(seed, x1, y0, z1, xd1, yd0, zd1), xs); + float xf11 = _fnlLerp(_fnlGradCoord3D(seed, x0, y1, z1, xd0, yd1, zd1), _fnlGradCoord3D(seed, x1, y1, z1, xd1, yd1, zd1), xs); + + float yf0 = _fnlLerp(xf00, xf10, ys); + float yf1 = _fnlLerp(xf01, xf11, ys); + + return _fnlLerp(yf0, yf1, zs) * 0.964921414852142333984375f; +} + +// Value Cubic + +static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y) +{ + int x1 = _fnlFastFloor(x); + int y1 = _fnlFastFloor(y); + + float xs = x - (float)x1; + float ys = y - (float)y1; + + x1 *= PRIME_X; + y1 *= PRIME_Y; + + int x0 = x1 - PRIME_X; + int y0 = y1 - PRIME_Y; + int x2 = x1 + PRIME_X; + int y2 = y1 + PRIME_Y; + int x3 = x1 + PRIME_X * 2; + int y3 = y1 + PRIME_Y * 2; + + return _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y0), _fnlValCoord2D(seed, x1, y0), _fnlValCoord2D(seed, x2, y0), _fnlValCoord2D(seed, x3, y0), + xs), + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y1), _fnlValCoord2D(seed, x1, y1), _fnlValCoord2D(seed, x2, y1), _fnlValCoord2D(seed, x3, y1), + xs), + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y2), _fnlValCoord2D(seed, x1, y2), _fnlValCoord2D(seed, x2, y2), _fnlValCoord2D(seed, x3, y2), + xs), + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y3), _fnlValCoord2D(seed, x1, y3), _fnlValCoord2D(seed, x2, y3), _fnlValCoord2D(seed, x3, y3), + xs), + ys) * (1 / (1.5f * 1.5f)); +} + +static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int x1 = _fnlFastFloor(x); + int y1 = _fnlFastFloor(y); + int z1 = _fnlFastFloor(z); + + float xs = x - (float)x1; + float ys = y - (float)y1; + float zs = z - (float)z1; + + x1 *= PRIME_X; + y1 *= PRIME_Y; + z1 *= PRIME_Z; + + int x0 = x1 - PRIME_X; + int y0 = y1 - PRIME_Y; + int z0 = z1 - PRIME_Z; + int x2 = x1 + PRIME_X; + int y2 = y1 + PRIME_Y; + int z2 = z1 + PRIME_Z; + int x3 = x1 + PRIME_X * 2; + int y3 = y1 + PRIME_Y * 2; + int z3 = z1 + PRIME_Z * 2; + + return _fnlCubicLerp( + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z0), _fnlValCoord3D(seed, x1, y0, z0), _fnlValCoord3D(seed, x2, y0, z0), _fnlValCoord3D(seed, x3, y0, z0), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z0), _fnlValCoord3D(seed, x1, y1, z0), _fnlValCoord3D(seed, x2, y1, z0), _fnlValCoord3D(seed, x3, y1, z0), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z0), _fnlValCoord3D(seed, x1, y2, z0), _fnlValCoord3D(seed, x2, y2, z0), _fnlValCoord3D(seed, x3, y2, z0), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z0), _fnlValCoord3D(seed, x1, y3, z0), _fnlValCoord3D(seed, x2, y3, z0), _fnlValCoord3D(seed, x3, y3, z0), xs), + ys), + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z1), _fnlValCoord3D(seed, x1, y0, z1), _fnlValCoord3D(seed, x2, y0, z1), _fnlValCoord3D(seed, x3, y0, z1), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z1), _fnlValCoord3D(seed, x1, y1, z1), _fnlValCoord3D(seed, x2, y1, z1), _fnlValCoord3D(seed, x3, y1, z1), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z1), _fnlValCoord3D(seed, x1, y2, z1), _fnlValCoord3D(seed, x2, y2, z1), _fnlValCoord3D(seed, x3, y2, z1), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z1), _fnlValCoord3D(seed, x1, y3, z1), _fnlValCoord3D(seed, x2, y3, z1), _fnlValCoord3D(seed, x3, y3, z1), xs), + ys), + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z2), _fnlValCoord3D(seed, x1, y0, z2), _fnlValCoord3D(seed, x2, y0, z2), _fnlValCoord3D(seed, x3, y0, z2), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z2), _fnlValCoord3D(seed, x1, y1, z2), _fnlValCoord3D(seed, x2, y1, z2), _fnlValCoord3D(seed, x3, y1, z2), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z2), _fnlValCoord3D(seed, x1, y2, z2), _fnlValCoord3D(seed, x2, y2, z2), _fnlValCoord3D(seed, x3, y2, z2), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z2), _fnlValCoord3D(seed, x1, y3, z2), _fnlValCoord3D(seed, x2, y3, z2), _fnlValCoord3D(seed, x3, y3, z2), xs), + ys), + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z3), _fnlValCoord3D(seed, x1, y0, z3), _fnlValCoord3D(seed, x2, y0, z3), _fnlValCoord3D(seed, x3, y0, z3), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z3), _fnlValCoord3D(seed, x1, y1, z3), _fnlValCoord3D(seed, x2, y1, z3), _fnlValCoord3D(seed, x3, y1, z3), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z3), _fnlValCoord3D(seed, x1, y2, z3), _fnlValCoord3D(seed, x2, y2, z3), _fnlValCoord3D(seed, x3, y2, z3), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z3), _fnlValCoord3D(seed, x1, y3, z3), _fnlValCoord3D(seed, x2, y3, z3), _fnlValCoord3D(seed, x3, y3, z3), xs), + ys), + zs) * (1 / 1.5f * 1.5f * 1.5f); +} + +// Value noise + +static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + + float xs = _fnlInterpHermite((float)(x - x0)); + float ys = _fnlInterpHermite((float)(y - y0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + + float xf0 = _fnlLerp(_fnlValCoord2D(seed, x0, y0), _fnlValCoord2D(seed, x1, y0), xs); + float xf1 = _fnlLerp(_fnlValCoord2D(seed, x0, y1), _fnlValCoord2D(seed, x1, y1), xs); + + return _fnlLerp(xf0, xf1, ys); +} + +static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + int z0 = _fnlFastFloor(z); + + float xs = _fnlInterpHermite((float)(x - x0)); + float ys = _fnlInterpHermite((float)(y - y0)); + float zs = _fnlInterpHermite((float)(z - z0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + z0 *= PRIME_Z; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + int z1 = z0 + PRIME_Z; + + float xf00 = _fnlLerp(_fnlValCoord3D(seed, x0, y0, z0), _fnlValCoord3D(seed, x1, y0, z0), xs); + float xf10 = _fnlLerp(_fnlValCoord3D(seed, x0, y1, z0), _fnlValCoord3D(seed, x1, y1, z0), xs); + float xf01 = _fnlLerp(_fnlValCoord3D(seed, x0, y0, z1), _fnlValCoord3D(seed, x1, y0, z1), xs); + float xf11 = _fnlLerp(_fnlValCoord3D(seed, x0, y1, z1), _fnlValCoord3D(seed, x1, y1, z1), xs); + + float yf0 = _fnlLerp(xf00, xf10, ys); + float yf1 = _fnlLerp(xf01, xf11, ys); + + return _fnlLerp(yf0, yf1, zs); +} + +// Domain Warp + +// Forward declare +static void _fnlSingleDomainWarpBasicGrid2D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xp, FNLfloat *yp); +static void _fnlSingleDomainWarpBasicGrid3D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xp, FNLfloat *yp, FNLfloat *zp); +static void _fnlSingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xr, FNLfloat *yr, bool outGradOnly); +static void _fnlSingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xr, FNLfloat *yr, FNLfloat *zr, bool outGradOnly); + +static inline void _fnlDoSingleDomainWarp2D(fnl_state *state, int seed, float amp, float freq, FNLfloat x, FNLfloat y, FNLfloat *xp, FNLfloat *yp) +{ + switch (state->domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + _fnlSingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, xp, yp, false); + break; + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + _fnlSingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, xp, yp, true); + break; + case FNL_DOMAIN_WARP_BASICGRID: + _fnlSingleDomainWarpBasicGrid2D(seed, amp, freq, x, y, xp, yp); + break; + } +} + +static inline void _fnlDoSingleDomainWarp3D(fnl_state *state, int seed, float amp, float freq, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xp, FNLfloat *yp, FNLfloat *zp) +{ + switch (state->domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + _fnlSingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, xp, yp, zp, false); + break; + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + _fnlSingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, xp, yp, zp, true); + break; + case FNL_DOMAIN_WARP_BASICGRID: + _fnlSingleDomainWarpBasicGrid3D(seed, amp, freq, x, y, z, xp, yp, zp); + break; + } +} + +// Domain Warp Single Wrapper + +static void _fnlDomainWarpSingle2D(fnl_state *state, FNLfloat *x, FNLfloat *y) +{ + int seed = state->seed; + float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state->frequency; + + FNLfloat xs = *x; + FNLfloat ys = *y; + _fnlTransformDomainWarpCoordinate2D(state, &xs, &ys); + + _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y); +} + +static void _fnlDomainWarpSingle3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z) +{ + int seed = state->seed; + float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state->frequency; + + FNLfloat xs = *x; + FNLfloat ys = *y; + FNLfloat zs = *z; + _fnlTransformDomainWarpCoordinate3D(state, &xs, &ys, &zs); + + _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z); +} + +// Domain Warp Fractal Progressive + +static void _fnlDomainWarpFractalProgressive2D(fnl_state *state, FNLfloat *x, FNLfloat *y) +{ + int seed = state->seed; + float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state->frequency; + + for (int i = 0; i < state->octaves; i++) + { + FNLfloat xs = *x; + FNLfloat ys = *y; + _fnlTransformDomainWarpCoordinate2D(state, &xs, &ys); + + _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y); + + seed++; + amp *= state->gain; + freq *= state->lacunarity; + } +} + +static void _fnlDomainWarpFractalProgressive3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z) +{ + int seed = state->seed; + float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state->frequency; + + for (int i = 0; i < state->octaves; i++) + { + FNLfloat xs = *x; + FNLfloat ys = *y; + FNLfloat zs = *z; + _fnlTransformDomainWarpCoordinate3D(state, &xs, &ys, &zs); + + _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z); + + seed++; + amp *= state->gain; + freq *= state->lacunarity; + } +} + +// Domain Warp Fractal Independent + +static void _fnlDomainWarpFractalIndependent2D(fnl_state *state, FNLfloat *x, FNLfloat *y) +{ + FNLfloat xs = *x; + FNLfloat ys = *y; + _fnlTransformDomainWarpCoordinate2D(state, &xs, &ys); + + int seed = state->seed; + float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state->frequency; + + for (int i = 0; i < state->octaves; i++) + { + _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y); + + seed++; + amp *= state->gain; + freq *= state->lacunarity; + } +} + +static void _fnlDomainWarpFractalIndependent3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z) +{ + FNLfloat xs = *x; + FNLfloat ys = *y; + FNLfloat zs = *z; + _fnlTransformDomainWarpCoordinate3D(state, &xs, &ys, &zs); + + int seed = state->seed; + float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state->frequency; + + for (int i = 0; i < state->octaves; i++) + { + _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z); + + seed++; + amp *= state->gain; + freq *= state->lacunarity; + } +} + +// Domain Warp Basic Grid + +static void _fnlSingleDomainWarpBasicGrid2D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xp, FNLfloat *yp) +{ + FNLfloat xf = x * frequency; + FNLfloat yf = y * frequency; + + int x0 = _fnlFastFloor(xf); + int y0 = _fnlFastFloor(yf); + + float xs = _fnlInterpHermite((float)(xf - x0)); + float ys = _fnlInterpHermite((float)(yf - y0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + + int idx0 = _fnlHash2D(seed, x0, y0) & (255 << 1); + int idx1 = _fnlHash2D(seed, x1, y0) & (255 << 1); + + float lx0x = _fnlLerp(RAND_VECS_2D[idx0], RAND_VECS_2D[idx1], xs); + float ly0x = _fnlLerp(RAND_VECS_2D[idx0 | 1], RAND_VECS_2D[idx1 | 1], xs); + + idx0 = _fnlHash2D(seed, x0, y1) & (255 << 1); + idx1 = _fnlHash2D(seed, x1, y1) & (255 << 1); + + float lx1x = _fnlLerp(RAND_VECS_2D[idx0], RAND_VECS_2D[idx1], xs); + float ly1x = _fnlLerp(RAND_VECS_2D[idx0 | 1], RAND_VECS_2D[idx1 | 1], xs); + + *xp += _fnlLerp(lx0x, lx1x, ys) * warpAmp; + *yp += _fnlLerp(ly0x, ly1x, ys) * warpAmp; +} + +static void _fnlSingleDomainWarpBasicGrid3D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xp, FNLfloat *yp, FNLfloat *zp) +{ + FNLfloat xf = x * frequency; + FNLfloat yf = y * frequency; + FNLfloat zf = z * frequency; + + int x0 = _fnlFastFloor(xf); + int y0 = _fnlFastFloor(yf); + int z0 = _fnlFastFloor(zf); + + float xs = _fnlInterpHermite((float)(xf - x0)); + float ys = _fnlInterpHermite((float)(yf - y0)); + float zs = _fnlInterpHermite((float)(zf - z0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + z0 *= PRIME_Z; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + int z1 = z0 + PRIME_Z; + + int idx0 = _fnlHash3D(seed, x0, y0, z0) & (255 << 2); + int idx1 = _fnlHash3D(seed, x1, y0, z0) & (255 << 2); + + float lx0x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + float ly0x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + float lz0x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + idx0 = _fnlHash3D(seed, x0, y1, z0) & (255 << 2); + idx1 = _fnlHash3D(seed, x1, y1, z0) & (255 << 2); + + float lx1x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + float ly1x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + float lz1x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + float lx0y = _fnlLerp(lx0x, lx1x, ys); + float ly0y = _fnlLerp(ly0x, ly1x, ys); + float lz0y = _fnlLerp(lz0x, lz1x, ys); + + idx0 = _fnlHash3D(seed, x0, y0, z1) & (255 << 2); + idx1 = _fnlHash3D(seed, x1, y0, z1) & (255 << 2); + + lx0x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + ly0x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + lz0x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + idx0 = _fnlHash3D(seed, x0, y1, z1) & (255 << 2); + idx1 = _fnlHash3D(seed, x1, y1, z1) & (255 << 2); + + lx1x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + ly1x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + lz1x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + *xp += _fnlLerp(lx0y, _fnlLerp(lx0x, lx1x, ys), zs) * warpAmp; + *yp += _fnlLerp(ly0y, _fnlLerp(ly0x, ly1x, ys), zs) * warpAmp; + *zp += _fnlLerp(lz0y, _fnlLerp(lz0x, lz1x, ys), zs) * warpAmp; +} + +// Domain Warp Simplex/OpenSimplex2 + +static void _fnlSingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xr, FNLfloat *yr, bool outGradOnly) +{ + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + x *= frequency; + y *= frequency; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PRIME_X; + j *= PRIME_Y; + + float vx, vy; + vx = vy = 0; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i, j, &xo, &yo); + else + _fnlGradCoordDual2D(seed, i, j, x0, y0, &xo, &yo); + vx += aaaa * xo; + vy += aaaa * yo; + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c > 0) + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + float cccc = (c * c) * (c * c); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i + PRIME_X, j + PRIME_Y, &xo, &yo); + else + _fnlGradCoordDual2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2, &xo, &yo); + vx += cccc * xo; + vy += cccc * yo; + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i, j + PRIME_Y, &xo, &yo); + else + _fnlGradCoordDual2D(seed, i, j + PRIME_Y, x1, y1, &xo, &yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i + PRIME_X, j, &xo, &yo); + else + _fnlGradCoordDual2D(seed, i + PRIME_X, j, x1, y1, &xo, &yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + + *xr += vx * warpAmp; + *yr += vy * warpAmp; +} + +static void _fnlSingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xr, FNLfloat *yr, FNLfloat *zr, bool outGradOnly) +{ + x *= frequency; + y *= frequency; + z *= frequency; + + /* + * --- Rotation moved to TransformDomainWarpCoordinate method --- + * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = _fnlFastRound(x); + int j = _fnlFastRound(y); + int k = _fnlFastRound(z); + float x0 = (float)x - i; + float y0 = (float)y - j; + float z0 = (float)z - k; + + int xNSign = (int)(-x0 - 1.0f) | 1; + int yNSign = (int)(-y0 - 1.0f) | 1; + int zNSign = (int)(-z0 - 1.0f) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PRIME_X; + j *= PRIME_Y; + k *= PRIME_Z; + + float vx, vy, vz; + vx = vy = vz = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; l < 2; l++) + { + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo, zo; + if (outGradOnly) + _fnlGradCoordOut3D(seed, i, j, k, &xo, &yo, &zo); + else + _fnlGradCoordDual3D(seed, i, j, k, x0, y0, z0, &xo, &yo, &zo); + vx += aaaa * xo; + vy += aaaa * yo; + vz += aaaa * zo; + } + + float b = a + 1; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b -= xNSign * 2 * x1; + i1 -= xNSign * PRIME_X; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b -= yNSign * 2 * y1; + j1 -= yNSign * PRIME_Y; + } + else + { + z1 += zNSign; + b -= zNSign * 2 * z1; + k1 -= zNSign * PRIME_Z; + } + + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo, zo; + if (outGradOnly) + _fnlGradCoordOut3D(seed, i1, j1, k1, &xo, &yo, &zo); + else + _fnlGradCoordDual3D(seed, i1, j1, k1, x1, y1, z1, &xo, &yo, &zo); + vx += bbbb * xo; + vy += bbbb * yo; + vz += bbbb * zo; + } + + if (l == 1) + break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PRIME_X; + j += (yNSign >> 1) & PRIME_Y; + k += (zNSign >> 1) & PRIME_Z; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + *xr += vx * warpAmp; + *yr += vy * warpAmp; + *zr += vz * warpAmp; +} + +// ==================== +// Public API +// ==================== + +fnl_state fnlCreateState(int seed) +{ + fnl_state newState; + newState.seed = seed; + newState.frequency = 0.01f; + newState.noise_type = FNL_NOISE_OPENSIMPLEX2; + newState.rotation_type_3d = FNL_ROTATION_NONE; + newState.fractal_type = FNL_FRACTAL_NONE; + newState.octaves = 3; + newState.lacunarity = 2.0f; + newState.gain = 0.5f; + newState.weighted_strength = 0.0f; + newState.ping_pong_strength = 2.0f; + newState.cellular_distance_func = FNL_CELLULAR_DISTANCE_EUCLIDEANSQ; + newState.cellular_return_type = FNL_CELLULAR_RETURN_VALUE_DISTANCE; + newState.cellular_jitter_mod = 1.0f; + newState.domain_warp_amp = 30.0f; + newState.domain_warp_type = FNL_DOMAIN_WARP_OPENSIMPLEX2; + return newState; +} + +float fnlGetNoise2D(fnl_state *state, FNLfloat x, FNLfloat y) +{ + _fnlTransformNoiseCoordinate2D(state, &x, &y); + + switch (state->fractal_type) + { + default: + return _fnlGenNoiseSingle2D(state, state->seed, x, y); + case FNL_FRACTAL_FBM: + return _fnlGenFractalFBM2D(state, x, y); + case FNL_FRACTAL_RIDGED: + return _fnlGenFractalRidged2D(state, x, y); + case FNL_FRACTAL_PINGPONG: + return _fnlGenFractalPingPong2D(state, x, y); + } +} + +float fnlGetNoise3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + _fnlTransformNoiseCoordinate3D(state, &x, &y, &z); + + // Select a noise type + switch (state->fractal_type) + { + default: + return _fnlGenNoiseSingle3D(state, state->seed, x, y, z); + case FNL_FRACTAL_FBM: + return _fnlGenFractalFBM3D(state, x, y, z); + case FNL_FRACTAL_RIDGED: + return _fnlGenFractalRidged3D(state, x, y, z); + case FNL_FRACTAL_PINGPONG: + return _fnlGenFractalPingPong3D(state, x, y, z); + } +} + +void fnlDomainWarp2D(fnl_state *state, FNLfloat *x, FNLfloat *y) +{ + switch (state->fractal_type) + { + default: + _fnlDomainWarpSingle2D(state, x, y); + break; + case FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE: + _fnlDomainWarpFractalProgressive2D(state, x, y); + break; + case FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT: + _fnlDomainWarpFractalIndependent2D(state, x, y); + break; + } +} + +void fnlDomainWarp3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z) +{ + switch (state->fractal_type) + { + default: + _fnlDomainWarpSingle3D(state, x, y, z); + break; + case FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE: + _fnlDomainWarpFractalProgressive3D(state, x, y, z); + break; + case FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT: + _fnlDomainWarpFractalIndependent3D(state, x, y, z); + break; + } +} + +#endif // FNL_IMPL + +#if defined(__cplusplus) +} +#endif diff --git a/CSharp/FastNoiseLite.cs b/CSharp/FastNoiseLite.cs new file mode 100644 index 0000000..e376c6d --- /dev/null +++ b/CSharp/FastNoiseLite.cs @@ -0,0 +1,2506 @@ +// MIT License +// +// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com) +// Copyright(c) 2020 Contributors +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files(the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions : +// +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +// +// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll +// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo +// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd +// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx +// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx +// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd +// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo +// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo +// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo +// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo +// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo +// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo +// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl +// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c +// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c +// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc +// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll +// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo +// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd +// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk +// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000 +// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX +// +// VERSION: 1.0 +// https://github.com/Auburn/FastNoise + +using System; +using System.Runtime.CompilerServices; + +// Switch between using floats or doubles for input position +using FNLfloat = System.Single; +//using FNLfloat = System.Double; + +public class FastNoiseLite +{ + private const short INLINE = 256; // MethodImplOptions.AggressiveInlining; + private const short OPTIMISE = 512; // MethodImplOptions.AggressiveOptimization; + + public enum NoiseType + { + OpenSimplex2, + OpenSimplex2S, + Cellular, + Perlin, + ValueCubic, + Value + }; + + public enum RotationType3D + { + None, + ImproveXYPlanes, + ImproveXZPlanes + }; + + public enum FractalType + { + None, + FBm, + Ridged, + PingPong, + DomainWarpProgressive, + DomainWarpIndependent + }; + + public enum CellularDistanceFunction + { + Euclidean, + EuclideanSq, + Manhattan, + Hybrid + }; + + public enum CellularReturnType + { + CellValue, + Distance, + Distance2, + Distance2Add, + Distance2Sub, + Distance2Mul, + Distance2Div + }; + + public enum DomainWarpType + { + OpenSimplex2, + OpenSimplex2Reduced, + BasicGrid + }; + + private enum TransformType3D + { + None, + ImproveXYPlanes, + ImproveXZPlanes, + DefaultOpenSimplex2 + }; + + private int mSeed = 1337; + private float mFrequency = 0.01f; + private NoiseType mNoiseType = NoiseType.OpenSimplex2; + private RotationType3D mRotationType3D = RotationType3D.None; + private TransformType3D mTransformType3D = TransformType3D.DefaultOpenSimplex2; + + private FractalType mFractalType = FractalType.None; + private int mOctaves = 3; + private float mLacunarity = 2.0f; + private float mGain = 0.5f; + private float mWeightedStrength = 0.0f; + private float mPingPongStength = 2.0f; + + private float mFractalBounding = 1 / 1.75f; + + private CellularDistanceFunction mCellularDistanceFunction = CellularDistanceFunction.EuclideanSq; + private CellularReturnType mCellularReturnType = CellularReturnType.Distance; + private float mCellularJitterModifier = 1.0f; + + private DomainWarpType mDomainWarpType = DomainWarpType.OpenSimplex2; + private TransformType3D mWarpTransformType3D = TransformType3D.DefaultOpenSimplex2; + private float mDomainWarpAmp = 1.0f; + + /// + /// Create new FastNoise object with optional seed + /// + public FastNoiseLite(int seed = 1337) + { + SetSeed(seed); + } + + /// + /// Sets seed used for all noise types + /// + /// + /// Default: 1337 + /// + public void SetSeed(int seed) { mSeed = seed; } + + /// + /// Sets frequency for all noise types + /// + /// + /// Default: 0.01 + /// + public void SetFrequency(float frequency) { mFrequency = frequency; } + + /// + /// Sets noise algorithm used for GetNoise(...) + /// + /// + /// Default: OpenSimplex2 + /// + public void SetNoiseType(NoiseType noiseType) + { + mNoiseType = noiseType; + UpdateTransformType3D(); + } + + /// + /// Sets domain rotation type for 3D Noise and 3D DomainWarp. + /// Can aid in reducing directional artifacts when sampling a 2D plane in 3D + /// + /// + /// Default: None + /// + public void SetRotationType3D(RotationType3D rotationType3D) + { + mRotationType3D = rotationType3D; + UpdateTransformType3D(); + UpdateWarpTransformType3D(); + } + + /// + /// Sets method for combining octaves in all fractal noise types + /// + /// + /// Default: None + /// Note: FractalType.DomainWarp... only affects DomainWarp(...) + /// + public void SetFractalType(FractalType fractalType) { mFractalType = fractalType; } + + /// + /// Sets octave count for all fractal noise types + /// + /// + /// Default: 3 + /// + public void SetFractalOctaves(int octaves) + { + mOctaves = octaves; + CalculateFractalBounding(); + } + + /// + /// Sets octave lacunarity for all fractal noise types + /// + /// + /// Default: 2.0 + /// + public void SetFractalLacunarity(float lacunarity) { mLacunarity = lacunarity; } + + /// + /// Sets octave gain for all fractal noise types + /// + /// + /// Default: 0.5 + /// + public void SetFractalGain(float gain) + { + mGain = gain; + CalculateFractalBounding(); + } + + /// + /// Sets octave weighting for all none DomainWarp fratal types + /// + /// + /// Default: 0.0 + /// Note: Keep between 0...1 to maintain -1...1 output bounding + /// + public void SetFractalWeightedStrength(float weightedStrength) { mWeightedStrength = weightedStrength; } + + /// + /// Sets strength of the fractal ping pong effect + /// + /// + /// Default: 2.0 + /// + public void SetFractalPingPongStrength(float pingPongStrength) { mPingPongStength = pingPongStrength; } + + + /// + /// Sets distance function used in cellular noise calculations + /// + /// + /// Default: Distance + /// + public void SetCellularDistanceFunction(CellularDistanceFunction cellularDistanceFunction) { mCellularDistanceFunction = cellularDistanceFunction; } + + /// + /// Sets return type from cellular noise calculations + /// + /// + /// Default: EuclideanSq + /// + public void SetCellularReturnType(CellularReturnType cellularReturnType) { mCellularReturnType = cellularReturnType; } + + /// + /// Sets the maximum distance a cellular point can move from it's grid position + /// + /// + /// Default: 1.0 + /// Note: Setting this higher than 1 will cause artifacts + /// + public void SetCellularJitter(float cellularJitter) { mCellularJitterModifier = cellularJitter; } + + + /// + /// Sets the warp algorithm when using DomainWarp(...) + /// + /// + /// Default: OpenSimplex2 + /// + public void SetDomainWarpType(DomainWarpType domainWarpType) + { + mDomainWarpType = domainWarpType; + UpdateWarpTransformType3D(); + } + + + /// + /// Sets the maximum warp distance from original position when using DomainWarp(...) + /// + /// + /// Default: 1.0 + /// + public void SetDomainWarpAmp(float domainWarpAmp) { mDomainWarpAmp = domainWarpAmp; } + + + /// + /// 2D noise at given position using current settings + /// + /// + /// Noise output bounded between -1...1 + /// + [MethodImpl(OPTIMISE)] + public float GetNoise(FNLfloat x, FNLfloat y) + { + TransformNoiseCoordinate(ref x, ref y); + + switch (mFractalType) + { + default: + return GenNoiseSingle(mSeed, x, y); + case FractalType.FBm: + return GenFractalFBm(x, y); + case FractalType.Ridged: + return GenFractalRidged(x, y); + case FractalType.PingPong: + return GenFractalPingPong(x, y); + } + } + + /// + /// 3D noise at given position using current settings + /// + /// + /// Noise output bounded between -1...1 + /// + [MethodImpl(OPTIMISE)] + public float GetNoise(FNLfloat x, FNLfloat y, FNLfloat z) + { + TransformNoiseCoordinate(ref x, ref y, ref z); + + switch (mFractalType) + { + default: + return GenNoiseSingle(mSeed, x, y, z); + case FractalType.FBm: + return GenFractalFBm(x, y, z); + case FractalType.Ridged: + return GenFractalRidged(x, y, z); + case FractalType.PingPong: + return GenFractalPingPong(x, y, z); + } + } + + + /// + /// 2D warps the input position using current domain warp settings + /// + /// + /// Example usage with GetNoise + /// DomainWarp(ref x, ref y) + /// noise = GetNoise(x, y) + /// + [MethodImpl(OPTIMISE)] + public void DomainWarp(ref FNLfloat x, ref FNLfloat y) + { + switch (mFractalType) + { + default: + DomainWarpSingle(ref x, ref y); + break; + case FractalType.DomainWarpProgressive: + DomainWarpFractalProgressive(ref x, ref y); + break; + case FractalType.DomainWarpIndependent: + DomainWarpFractalIndependent(ref x, ref y); + break; + } + } + + /// + /// 3D warps the input position using current domain warp settings + /// + /// + /// Example usage with GetNoise + /// DomainWarp(ref x, ref y, ref z) + /// noise = GetNoise(x, y, z) + /// + [MethodImpl(OPTIMISE)] + public void DomainWarp(ref FNLfloat x, ref FNLfloat y, ref FNLfloat z) + { + switch (mFractalType) + { + default: + DomainWarpSingle(ref x, ref y, ref z); + break; + case FractalType.DomainWarpProgressive: + DomainWarpFractalProgressive(ref x, ref y, ref z); + break; + case FractalType.DomainWarpIndependent: + DomainWarpFractalIndependent(ref x, ref y, ref z); + break; + } + } + + + private static readonly float[] Gradients2D = + { + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f, + -0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f, + }; + + private static readonly float[] RandVecs2D = + { + -0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f, + -0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, -0.892300288f, -0.4514423508f, -0.379844434f, -0.9250503802f, -0.9951650832f, 0.0982163789f, 0.7724397808f, -0.6350880136f, 0.7573283322f, -0.6530343002f, -0.9928004525f, -0.119780055f, + -0.0532665713f, 0.9985803285f, 0.9754253726f, -0.2203300762f, -0.7665018163f, 0.6422421394f, 0.991636706f, 0.1290606184f, -0.994696838f, 0.1028503788f, -0.5379205513f, -0.84299554f, 0.5022815471f, -0.8647041387f, 0.4559821461f, -0.8899889226f, + -0.8659131224f, -0.5001944266f, 0.0879458407f, -0.9961252577f, -0.5051684983f, 0.8630207346f, 0.7753185226f, -0.6315704146f, -0.6921944612f, 0.7217110418f, -0.5191659449f, -0.8546734591f, 0.8978622882f, -0.4402764035f, -0.1706774107f, 0.9853269617f, + -0.9353430106f, -0.3537420705f, -0.9992404798f, 0.03896746794f, -0.2882064021f, -0.9575683108f, -0.9663811329f, 0.2571137995f, -0.8759714238f, -0.4823630009f, -0.8303123018f, -0.5572983775f, 0.05110133755f, -0.9986934731f, -0.8558373281f, -0.5172450752f, + 0.09887025282f, 0.9951003332f, 0.9189016087f, 0.3944867976f, -0.2439375892f, -0.9697909324f, -0.8121409387f, -0.5834613061f, -0.9910431363f, 0.1335421355f, 0.8492423985f, -0.5280031709f, -0.9717838994f, -0.2358729591f, 0.9949457207f, 0.1004142068f, + 0.6241065508f, -0.7813392434f, 0.662910307f, 0.7486988212f, -0.7197418176f, 0.6942418282f, -0.8143370775f, -0.5803922158f, 0.104521054f, -0.9945226741f, -0.1065926113f, -0.9943027784f, 0.445799684f, -0.8951327509f, 0.105547406f, 0.9944142724f, + -0.992790267f, 0.1198644477f, -0.8334366408f, 0.552615025f, 0.9115561563f, -0.4111755999f, 0.8285544909f, -0.5599084351f, 0.7217097654f, -0.6921957921f, 0.4940492677f, -0.8694339084f, -0.3652321272f, -0.9309164803f, -0.9696606758f, 0.2444548501f, + 0.08925509731f, -0.996008799f, 0.5354071276f, -0.8445941083f, -0.1053576186f, 0.9944343981f, -0.9890284586f, 0.1477251101f, 0.004856104961f, 0.9999882091f, 0.9885598478f, 0.1508291331f, 0.9286129562f, -0.3710498316f, -0.5832393863f, -0.8123003252f, + 0.3015207509f, 0.9534596146f, -0.9575110528f, 0.2883965738f, 0.9715802154f, -0.2367105511f, 0.229981792f, 0.9731949318f, 0.955763816f, -0.2941352207f, 0.740956116f, 0.6715534485f, -0.9971513787f, -0.07542630764f, 0.6905710663f, -0.7232645452f, + -0.290713703f, -0.9568100872f, 0.5912777791f, -0.8064679708f, -0.9454592212f, -0.325740481f, 0.6664455681f, 0.74555369f, 0.6236134912f, 0.7817328275f, 0.9126993851f, -0.4086316587f, -0.8191762011f, 0.5735419353f, -0.8812745759f, -0.4726046147f, + 0.9953313627f, 0.09651672651f, 0.9855650846f, -0.1692969699f, -0.8495980887f, 0.5274306472f, 0.6174853946f, -0.7865823463f, 0.8508156371f, 0.52546432f, 0.9985032451f, -0.05469249926f, 0.1971371563f, -0.9803759185f, 0.6607855748f, -0.7505747292f, + -0.03097494063f, 0.9995201614f, -0.6731660801f, 0.739491331f, -0.7195018362f, -0.6944905383f, 0.9727511689f, 0.2318515979f, 0.9997059088f, -0.0242506907f, 0.4421787429f, -0.8969269532f, 0.9981350961f, -0.061043673f, -0.9173660799f, -0.3980445648f, + -0.8150056635f, -0.5794529907f, -0.8789331304f, 0.4769450202f, 0.0158605829f, 0.999874213f, -0.8095464474f, 0.5870558317f, -0.9165898907f, -0.3998286786f, -0.8023542565f, 0.5968480938f, -0.5176737917f, 0.8555780767f, -0.8154407307f, -0.5788405779f, + 0.4022010347f, -0.9155513791f, -0.9052556868f, -0.4248672045f, 0.7317445619f, 0.6815789728f, -0.5647632201f, -0.8252529947f, -0.8403276335f, -0.5420788397f, -0.9314281527f, 0.363925262f, 0.5238198472f, 0.8518290719f, 0.7432803869f, -0.6689800195f, + -0.985371561f, -0.1704197369f, 0.4601468731f, 0.88784281f, 0.825855404f, 0.5638819483f, 0.6182366099f, 0.7859920446f, 0.8331502863f, -0.553046653f, 0.1500307506f, 0.9886813308f, -0.662330369f, -0.7492119075f, -0.668598664f, 0.743623444f, + 0.7025606278f, 0.7116238924f, -0.5419389763f, -0.8404178401f, -0.3388616456f, 0.9408362159f, 0.8331530315f, 0.5530425174f, -0.2989720662f, -0.9542618632f, 0.2638522993f, 0.9645630949f, 0.124108739f, -0.9922686234f, -0.7282649308f, -0.6852956957f, + 0.6962500149f, 0.7177993569f, -0.9183535368f, 0.3957610156f, -0.6326102274f, -0.7744703352f, -0.9331891859f, -0.359385508f, -0.1153779357f, -0.9933216659f, 0.9514974788f, -0.3076565421f, -0.08987977445f, -0.9959526224f, 0.6678496916f, 0.7442961705f, + 0.7952400393f, -0.6062947138f, -0.6462007402f, -0.7631674805f, -0.2733598753f, 0.9619118351f, 0.9669590226f, -0.254931851f, -0.9792894595f, 0.2024651934f, -0.5369502995f, -0.8436138784f, -0.270036471f, -0.9628500944f, -0.6400277131f, 0.7683518247f, + -0.7854537493f, -0.6189203566f, 0.06005905383f, -0.9981948257f, -0.02455770378f, 0.9996984141f, -0.65983623f, 0.751409442f, -0.6253894466f, -0.7803127835f, -0.6210408851f, -0.7837781695f, 0.8348888491f, 0.5504185768f, -0.1592275245f, 0.9872419133f, + 0.8367622488f, 0.5475663786f, -0.8675753916f, -0.4973056806f, -0.2022662628f, -0.9793305667f, 0.9399189937f, 0.3413975472f, 0.9877404807f, -0.1561049093f, -0.9034455656f, 0.4287028224f, 0.1269804218f, -0.9919052235f, -0.3819600854f, 0.924178821f, + 0.9754625894f, 0.2201652486f, -0.3204015856f, -0.9472818081f, -0.9874760884f, 0.1577687387f, 0.02535348474f, -0.9996785487f, 0.4835130794f, -0.8753371362f, -0.2850799925f, -0.9585037287f, -0.06805516006f, -0.99768156f, -0.7885244045f, -0.6150034663f, + 0.3185392127f, -0.9479096845f, 0.8880043089f, 0.4598351306f, 0.6476921488f, -0.7619021462f, 0.9820241299f, 0.1887554194f, 0.9357275128f, -0.3527237187f, -0.8894895414f, 0.4569555293f, 0.7922791302f, 0.6101588153f, 0.7483818261f, 0.6632681526f, + -0.7288929755f, -0.6846276581f, 0.8729032783f, -0.4878932944f, 0.8288345784f, 0.5594937369f, 0.08074567077f, 0.9967347374f, 0.9799148216f, -0.1994165048f, -0.580730673f, -0.8140957471f, -0.4700049791f, -0.8826637636f, 0.2409492979f, 0.9705377045f, + 0.9437816757f, -0.3305694308f, -0.8927998638f, -0.4504535528f, -0.8069622304f, 0.5906030467f, 0.06258973166f, 0.9980393407f, -0.9312597469f, 0.3643559849f, 0.5777449785f, 0.8162173362f, -0.3360095855f, -0.941858566f, 0.697932075f, -0.7161639607f, + -0.002008157227f, -0.9999979837f, -0.1827294312f, -0.9831632392f, -0.6523911722f, 0.7578824173f, -0.4302626911f, -0.9027037258f, -0.9985126289f, -0.05452091251f, -0.01028102172f, -0.9999471489f, -0.4946071129f, 0.8691166802f, -0.2999350194f, 0.9539596344f, + 0.8165471961f, 0.5772786819f, 0.2697460475f, 0.962931498f, -0.7306287391f, -0.6827749597f, -0.7590952064f, -0.6509796216f, -0.907053853f, 0.4210146171f, -0.5104861064f, -0.8598860013f, 0.8613350597f, 0.5080373165f, 0.5007881595f, -0.8655698812f, + -0.654158152f, 0.7563577938f, -0.8382755311f, -0.545246856f, 0.6940070834f, 0.7199681717f, 0.06950936031f, 0.9975812994f, 0.1702942185f, -0.9853932612f, 0.2695973274f, 0.9629731466f, 0.5519612192f, -0.8338697815f, 0.225657487f, -0.9742067022f, + 0.4215262855f, -0.9068161835f, 0.4881873305f, -0.8727388672f, -0.3683854996f, -0.9296731273f, -0.9825390578f, 0.1860564427f, 0.81256471f, 0.5828709909f, 0.3196460933f, -0.9475370046f, 0.9570913859f, 0.2897862643f, -0.6876655497f, -0.7260276109f, + -0.9988770922f, -0.047376731f, -0.1250179027f, 0.992154486f, -0.8280133617f, 0.560708367f, 0.9324863769f, -0.3612051451f, 0.6394653183f, 0.7688199442f, -0.01623847064f, -0.9998681473f, -0.9955014666f, -0.09474613458f, -0.81453315f, 0.580117012f, + 0.4037327978f, -0.9148769469f, 0.9944263371f, 0.1054336766f, -0.1624711654f, 0.9867132919f, -0.9949487814f, -0.100383875f, -0.6995302564f, 0.7146029809f, 0.5263414922f, -0.85027327f, -0.5395221479f, 0.841971408f, 0.6579370318f, 0.7530729462f, + 0.01426758847f, -0.9998982128f, -0.6734383991f, 0.7392433447f, 0.639412098f, -0.7688642071f, 0.9211571421f, 0.3891908523f, -0.146637214f, -0.9891903394f, -0.782318098f, 0.6228791163f, -0.5039610839f, -0.8637263605f, -0.7743120191f, -0.6328039957f, + }; + + private static readonly float[] Gradients3D = + { + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 1, 1, 0, 0, 0,-1, 1, 0, -1, 1, 0, 0, 0,-1,-1, 0 + }; + + private static readonly float[] RandVecs3D = + { + -0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, -0.2739291014f, 0, 0.7217578935f, 0.6226212466f, -0.3023380997f, 0, 0.565683137f, -0.8208298145f, -0.0790000257f, 0, 0.760049034f, -0.5555979497f, -0.3370999617f, 0, 0.3713945616f, 0.5011264475f, 0.7816254623f, 0, -0.1277062463f, -0.4254438999f, -0.8959289049f, 0, -0.2881560924f, -0.5815838982f, 0.7607405838f, 0, + 0.5849561111f, -0.662820239f, -0.4674352136f, 0, 0.3307171178f, 0.0391653737f, 0.94291689f, 0, 0.8712121778f, -0.4113374369f, -0.2679381538f, 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-0.4371373164f, 0.5188422971f, 0, + 0.9985120116f, 0.04659011161f, -0.02833944577f, 0, -0.3727687496f, -0.9082481361f, 0.1900757285f, 0, 0.91737377f, -0.3483642108f, 0.1925298489f, 0, 0.2714911074f, 0.4147529736f, -0.8684886582f, 0, 0.5131763485f, -0.7116334161f, 0.4798207128f, 0, -0.8737353606f, 0.18886992f, -0.4482350644f, 0, 0.8460043821f, -0.3725217914f, 0.3814499973f, 0, 0.8978727456f, -0.1780209141f, -0.4026575304f, 0, + 0.2178065647f, -0.9698322841f, -0.1094789531f, 0, -0.1518031304f, -0.7788918132f, -0.6085091231f, 0, -0.2600384876f, -0.4755398075f, -0.8403819825f, 0, 0.572313509f, -0.7474340931f, -0.3373418503f, 0, -0.7174141009f, 0.1699017182f, -0.6756111411f, 0, -0.684180784f, 0.02145707593f, -0.7289967412f, 0, -0.2007447902f, 0.06555605789f, -0.9774476623f, 0, -0.1148803697f, -0.8044887315f, 0.5827524187f, 0, + -0.7870349638f, 0.03447489231f, 0.6159443543f, 0, -0.2015596421f, 0.6859872284f, 0.6991389226f, 0, -0.08581082512f, -0.10920836f, -0.9903080513f, 0, 0.5532693395f, 0.7325250401f, -0.396610771f, 0, -0.1842489331f, -0.9777375055f, -0.1004076743f, 0, 0.0775473789f, -0.9111505856f, 0.4047110257f, 0, 0.1399838409f, 0.7601631212f, -0.6344734459f, 0, 0.4484419361f, -0.845289248f, 0.2904925424f, 0 + }; + + + [MethodImpl(INLINE)] + private static float FastMin(float a, float b) { return a < b ? a : b; } + + [MethodImpl(INLINE)] + private static float FastMax(float a, float b) { return a > b ? a : b; } + + [MethodImpl(INLINE)] + private static float FastAbs(float f) { return f < 0 ? -f : f; } + + [MethodImpl(INLINE)] + private static float FastSqrt(float f) { return (float)Math.Sqrt(f); } + + [MethodImpl(INLINE)] + private static int FastFloor(FNLfloat f) { return f >= 0 ? (int)f : (int)f - 1; } + + [MethodImpl(INLINE)] + private static int FastRound(FNLfloat f) { return f >= 0 ? (int)(f + 0.5f) : (int)(f - 0.5f); } + + [MethodImpl(INLINE)] + private static float Lerp(float a, float b, float t) { return a + t * (b - a); } + + [MethodImpl(INLINE)] + private static float InterpHermite(float t) { return t * t * (3 - 2 * t); } + + [MethodImpl(INLINE)] + private static float InterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); } + + [MethodImpl(INLINE)] + private static float CubicLerp(float a, float b, float c, float d, float t) + { + float p = (d - c) - (a - b); + return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b; + } + + [MethodImpl(INLINE)] + private static float PingPong(float t) + { + t -= (int)(t * 0.5f) * 2; + return t < 1 ? t : 2 - t; + } + + private void CalculateFractalBounding() + { + float gain = FastAbs(mGain); + float amp = gain; + float ampFractal = 1.0f; + for (int i = 1; i < mOctaves; i++) + { + ampFractal += amp; + amp *= gain; + } + mFractalBounding = 1 / ampFractal; + } + + // Hashing + private const int PrimeX = 501125321; + private const int PrimeY = 1136930381; + private const int PrimeZ = 1720413743; + + [MethodImpl(INLINE)] + private static int Hash(int seed, int xPrimed, int yPrimed) + { + int hash = seed ^ xPrimed ^ yPrimed; + + hash *= 0x27d4eb2d; + return hash; + } + + [MethodImpl(INLINE)] + private static int Hash(int seed, int xPrimed, int yPrimed, int zPrimed) + { + int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed; + + hash *= 0x27d4eb2d; + return hash; + } + + [MethodImpl(INLINE)] + private static float ValCoord(int seed, int xPrimed, int yPrimed) + { + int hash = Hash(seed, xPrimed, yPrimed); + + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); + } + + [MethodImpl(INLINE)] + private static float ValCoord(int seed, int xPrimed, int yPrimed, int zPrimed) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); + } + + [MethodImpl(INLINE)] + private static float GradCoord(int seed, int xPrimed, int yPrimed, float xd, float yd) + { + int hash = Hash(seed, xPrimed, yPrimed); + hash ^= hash >> 15; + hash &= 127 << 1; + + float xg = Gradients2D[hash]; + float yg = Gradients2D[hash | 1]; + + return xd * xg + yd * yg; + } + + [MethodImpl(INLINE)] + private static float GradCoord(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + hash ^= hash >> 15; + hash &= 63 << 2; + + float xg = Gradients3D[hash]; + float yg = Gradients3D[hash | 1]; + float zg = Gradients3D[hash | 2]; + + return xd * xg + yd * yg + zd * zg; + } + + [MethodImpl(INLINE)] + private static void GradCoordOut(int seed, int xPrimed, int yPrimed, out float xo, out float yo) + { + int hash = Hash(seed, xPrimed, yPrimed) & (255 << 1); + + xo = RandVecs2D[hash]; + yo = RandVecs2D[hash | 1]; + } + + [MethodImpl(INLINE)] + private static void GradCoordOut(int seed, int xPrimed, int yPrimed, int zPrimed, out float xo, out float yo, out float zo) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed) & (255 << 2); + + xo = RandVecs3D[hash]; + yo = RandVecs3D[hash | 1]; + zo = RandVecs3D[hash | 2]; + } + + [MethodImpl(INLINE)] + private static void GradCoordDual(int seed, int xPrimed, int yPrimed, float xd, float yd, out float xo, out float yo) + { + int hash = Hash(seed, xPrimed, yPrimed); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + + float xg = Gradients2D[index1]; + float yg = Gradients2D[index1 | 1]; + float value = xd * xg + yd * yg; + + float xgo = RandVecs2D[index2]; + float ygo = RandVecs2D[index2 | 1]; + + xo = value * xgo; + yo = value * ygo; + } + + [MethodImpl(INLINE)] + private static void GradCoordDual(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, out float xo, out float yo, out float zo) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int index1 = hash & (63 << 2); + int index2 = (hash >> 6) & (255 << 2); + + float xg = Gradients3D[index1]; + float yg = Gradients3D[index1 | 1]; + float zg = Gradients3D[index1 | 2]; + float value = xd * xg + yd * yg + zd * zg; + + float xgo = RandVecs3D[index2]; + float ygo = RandVecs3D[index2 | 1]; + float zgo = RandVecs3D[index2 | 2]; + + xo = value * xgo; + yo = value * ygo; + zo = value * zgo; + } + + + // Generic noise gen + + private float GenNoiseSingle(int seed, FNLfloat x, FNLfloat y) + { + switch (mNoiseType) + { + case NoiseType.OpenSimplex2: + return SingleSimplex(seed, x, y); + case NoiseType.OpenSimplex2S: + return SingleOpenSimplex2S(seed, x, y); + case NoiseType.Cellular: + return SingleCellular(seed, x, y); + case NoiseType.Perlin: + return SinglePerlin(seed, x, y); + case NoiseType.ValueCubic: + return SingleValueCubic(seed, x, y); + case NoiseType.Value: + return SingleValue(seed, x, y); + default: + return 0; + } + } + + private float GenNoiseSingle(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + switch (mNoiseType) + { + case NoiseType.OpenSimplex2: + return SingleOpenSimplex2(seed, x, y, z); + case NoiseType.OpenSimplex2S: + return SingleOpenSimplex2S(seed, x, y, z); + case NoiseType.Cellular: + return SingleCellular(seed, x, y, z); + case NoiseType.Perlin: + return SinglePerlin(seed, x, y, z); + case NoiseType.ValueCubic: + return SingleValueCubic(seed, x, y, z); + case NoiseType.Value: + return SingleValue(seed, x, y, z); + default: + return 0; + } + } + + + // Noise Coordinate Transforms (frequency, and possible skew or rotation) + + [MethodImpl(INLINE)] + private void TransformNoiseCoordinate(ref FNLfloat x, ref FNLfloat y) + { + x *= mFrequency; + y *= mFrequency; + + switch (mNoiseType) + { + case NoiseType.OpenSimplex2: + case NoiseType.OpenSimplex2S: + { + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat F2 = 0.5f * (SQRT3 - 1); + FNLfloat t = (x + y) * F2; + x += t; + y += t; + } + break; + default: + break; + } + } + + [MethodImpl(INLINE)] + private void TransformNoiseCoordinate(ref FNLfloat x, ref FNLfloat y, ref FNLfloat z) + { + x *= mFrequency; + y *= mFrequency; + z *= mFrequency; + + switch (mTransformType3D) + { + case TransformType3D.ImproveXYPlanes: + { + FNLfloat xy = x + y; + FNLfloat s2 = xy * -(FNLfloat)0.211324865405187; + z *= (FNLfloat)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (FNLfloat)0.577350269189626; + } + break; + case TransformType3D.ImproveXZPlanes: + { + FNLfloat xz = x + z; + FNLfloat s2 = xz * -(FNLfloat)0.211324865405187; + y *= (FNLfloat)0.577350269189626; + x += s2 - y; + z += s2 - y; + y += xz * (FNLfloat)0.577350269189626; + } + break; + case TransformType3D.DefaultOpenSimplex2: + { + const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + FNLfloat r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + } + + private void UpdateTransformType3D() + { + switch (mRotationType3D) + { + case RotationType3D.ImproveXYPlanes: + mTransformType3D = TransformType3D.ImproveXYPlanes; + break; + case RotationType3D.ImproveXZPlanes: + mTransformType3D = TransformType3D.ImproveXZPlanes; + break; + default: + switch (mNoiseType) + { + case NoiseType.OpenSimplex2: + case NoiseType.OpenSimplex2S: + mTransformType3D = TransformType3D.DefaultOpenSimplex2; + break; + default: + mTransformType3D = TransformType3D.None; + break; + } + break; + } + } + + + // Domain Warp Coordinate Transforms + + [MethodImpl(INLINE)] + private void TransformDomainWarpCoordinate(ref FNLfloat x, ref FNLfloat y) + { + switch (mDomainWarpType) + { + case DomainWarpType.OpenSimplex2: + case DomainWarpType.OpenSimplex2Reduced: + { + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat F2 = 0.5f * (SQRT3 - 1); + FNLfloat t = (x + y) * F2; + x += t; y += t; + } + break; + default: + break; + } + } + + [MethodImpl(INLINE)] + private void TransformDomainWarpCoordinate(ref FNLfloat x, ref FNLfloat y, ref FNLfloat z) + { + switch (mWarpTransformType3D) + { + case TransformType3D.ImproveXYPlanes: + { + FNLfloat xy = x + y; + FNLfloat s2 = xy * -(FNLfloat)0.211324865405187; + z *= (FNLfloat)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (FNLfloat)0.577350269189626; + } + break; + case TransformType3D.ImproveXZPlanes: + { + FNLfloat xz = x + z; + FNLfloat s2 = xz * -(FNLfloat)0.211324865405187; + y *= (FNLfloat)0.577350269189626; + x += s2 - y; z += s2 - y; + y += xz * (FNLfloat)0.577350269189626; + } + break; + case TransformType3D.DefaultOpenSimplex2: + { + const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + FNLfloat r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + } + + private void UpdateWarpTransformType3D() + { + switch (mRotationType3D) + { + case RotationType3D.ImproveXYPlanes: + mWarpTransformType3D = TransformType3D.ImproveXYPlanes; + break; + case RotationType3D.ImproveXZPlanes: + mWarpTransformType3D = TransformType3D.ImproveXZPlanes; + break; + default: + switch (mDomainWarpType) + { + case DomainWarpType.OpenSimplex2: + case DomainWarpType.OpenSimplex2Reduced: + mWarpTransformType3D = TransformType3D.DefaultOpenSimplex2; + break; + default: + mWarpTransformType3D = TransformType3D.None; + break; + } + break; + } + } + + + // Fractal FBm + + private float GenFractalFBm(FNLfloat x, FNLfloat y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = GenNoiseSingle(seed++, x, y); + sum += noise * amp; + amp *= Lerp(1.0f, FastMin(noise + 1, 2) * 0.5f, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + private float GenFractalFBm(FNLfloat x, FNLfloat y, FNLfloat z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = GenNoiseSingle(seed++, x, y, z); + sum += noise * amp; + amp *= Lerp(1.0f, (noise + 1) * 0.5f, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Fractal Ridged + + private float GenFractalRidged(FNLfloat x, FNLfloat y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = FastAbs(GenNoiseSingle(seed++, x, y)); + sum += (noise * -2 + 1) * amp; + amp *= Lerp(1.0f, 1 - noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + private float GenFractalRidged(FNLfloat x, FNLfloat y, FNLfloat z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = FastAbs(GenNoiseSingle(seed++, x, y, z)); + sum += (noise * -2 + 1) * amp; + amp *= Lerp(1.0f, 1 - noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Fractal PingPong + + private float GenFractalPingPong(FNLfloat x, FNLfloat y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = PingPong((GenNoiseSingle(seed++, x, y) + 1) * mPingPongStength); + sum += (noise - 0.5f) * 2 * amp; + amp *= Lerp(1.0f, noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + private float GenFractalPingPong(FNLfloat x, FNLfloat y, FNLfloat z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = PingPong((GenNoiseSingle(seed++, x, y, z) + 1) * mPingPongStength); + sum += (noise - 0.5f) * 2 * amp; + amp *= Lerp(1.0f, noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Simplex/OpenSimplex2 Noise + + private float SingleSimplex(int seed, FNLfloat x, FNLfloat y) + { + // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex. + + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNfloat F2 = 0.5f * (SQRT3 - 1); + * FNfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PrimeX; + j *= PrimeY; + + float n0, n1, n2; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a <= 0) n0 = 0; + else + { + n0 = (a * a) * (a * a) * GradCoord(seed, i, j, x0, y0); + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c <= 0) n2 = 0; + else + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + n2 = (c * c) * (c * c) * GradCoord(seed, i + PrimeX, j + PrimeY, x2, y2); + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) n1 = 0; + else + { + n1 = (b * b) * (b * b) * GradCoord(seed, i, j + PrimeY, x1, y1); + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) n1 = 0; + else + { + n1 = (b * b) * (b * b) * GradCoord(seed, i + PrimeX, j, x1, y1); + } + } + + return (n0 + n1 + n2) * 99.83685446303647f; + } + + private float SingleOpenSimplex2(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + // 3D OpenSimplex2 case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNfloat R3 = (FNfloat)(2.0 / 3.0); + * FNfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastRound(x); + int j = FastRound(y); + int k = FastRound(z); + float x0 = (float)(x - i); + float y0 = (float)(y - j); + float z0 = (float)(z - k); + + int xNSign = (int)(-1.0f - x0) | 1; + int yNSign = (int)(-1.0f - y0) | 1; + int zNSign = (int)(-1.0f - z0) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + + float value = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; ; l++) + { + if (a > 0) + { + value += (a * a) * (a * a) * GradCoord(seed, i, j, k, x0, y0, z0); + } + + if (ax0 >= ay0 && ax0 >= az0) + { + float b = a + ax0 + ax0; + if (b > 1) { + b -= 1; + value += (b * b) * (b * b) * GradCoord(seed, i - xNSign * PrimeX, j, k, x0 + xNSign, y0, z0); + } + } + else if (ay0 > ax0 && ay0 >= az0) + { + float b = a + ay0 + ay0; + if (b > 1) + { + b -= 1; + value += (b * b) * (b * b) * GradCoord(seed, i, j - yNSign * PrimeY, k, x0, y0 + yNSign, z0); + } + } + else + { + float b = a + az0 + az0; + if (b > 1) + { + b -= 1; + value += (b * b) * (b * b) * GradCoord(seed, i, j, k - zNSign * PrimeZ, x0, y0, z0 + zNSign); + } + } + + if (l == 1) break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PrimeX; + j += (yNSign >> 1) & PrimeY; + k += (zNSign >> 1) & PrimeZ; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + return value * 32.69428253173828125f; + } + + + // OpenSimplex2S Noise + + private float SingleOpenSimplex2S(int seed, FNLfloat x, FNLfloat y) + { + // 2D OpenSimplex2S case is a modified 2D simplex noise. + + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNfloat F2 = 0.5f * (SQRT3 - 1); + * FNfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + i *= PrimeX; + j *= PrimeY; + int i1 = i + PrimeX; + int j1 = j + PrimeY; + + float t = (xi + yi) * (float)G2; + float x0 = xi - t; + float y0 = yi - t; + + float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0; + float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, i, j, x0, y0); + + float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0); + float x1 = x0 - (float)(1 - 2 * G2); + float y1 = y0 - (float)(1 - 2 * G2); + value += (a1 * a1) * (a1 * a1) * GradCoord(seed, i1, j1, x1, y1); + + // Nested conditionals were faster than compact bit logic/arithmetic. + float xmyi = xi - yi; + if (t > G2) + { + if (xi + xmyi > 1) + { + float x2 = x0 + (float)(3 * G2 - 2); + float y2 = y0 + (float)(3 * G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + (PrimeX << 1), j + PrimeY, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2); + } + } + + if (yi - xmyi > 1) + { + float x3 = x0 + (float)(3 * G2 - 1); + float y3 = y0 + (float)(3 * G2 - 2); + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j + (PrimeY << 1), x3, y3); + } + } + else + { + float x3 = x0 + (float)(G2 - 1); + float y3 = y0 + (float)G2; + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j, x3, y3); + } + } + } + else + { + if (xi + xmyi < 0) + { + float x2 = x0 + (float)(1 - G2); + float y2 = y0 - (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i - PrimeX, j, x2, y2); + } + } + else + { + float x2 = x0 + (float)(G2 - 1); + float y2 = y0 + (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + PrimeX, j, x2, y2); + } + } + + if (yi < xmyi) + { + float x2 = x0 - (float)G2; + float y2 = y0 - (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j - PrimeY, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2); + } + } + } + + return value * 18.24196194486065f; + } + + private float SingleOpenSimplex2S(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + // 3D OpenSimplex2S case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNfloat R3 = (FNfloat)(2.0 / 3.0); + * FNfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + int k = FastFloor(z); + float xi = (float)(x - i); + float yi = (float)(y - j); + float zi = (float)(z - k); + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + int seed2 = seed + 1293373; + + int xNMask = (int)(-0.5f - xi); + int yNMask = (int)(-0.5f - yi); + int zNMask = (int)(-0.5f - zi); + + float x0 = xi + xNMask; + float y0 = yi + yNMask; + float z0 = zi + zNMask; + float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0; + float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, + i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x0, y0, z0); + + float x1 = xi - 0.5f; + float y1 = yi - 0.5f; + float z1 = zi - 0.5f; + float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1; + value += (a1 * a1) * (a1 * a1) * GradCoord(seed2, + i + PrimeX, j + PrimeY, k + PrimeZ, x1, y1, z1); + + float xAFlipMask0 = ((xNMask | 1) << 1) * x1; + float yAFlipMask0 = ((yNMask | 1) << 1) * y1; + float zAFlipMask0 = ((zNMask | 1) << 1) * z1; + float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f; + float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f; + float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f; + + bool skip5 = false; + float a2 = xAFlipMask0 + a0; + if (a2 > 0) + { + float x2 = x0 - (xNMask | 1); + float y2 = y0; + float z2 = z0; + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x2, y2, z2); + } + else + { + float a3 = yAFlipMask0 + zAFlipMask0 + a0; + if (a3 > 0) + { + float x3 = x0; + float y3 = y0 - (yNMask | 1); + float z3 = z0 - (zNMask | 1); + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, + i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (~zNMask & PrimeZ), x3, y3, z3); + } + + float a4 = xAFlipMask1 + a1; + if (a4 > 0) + { + float x4 = (xNMask | 1) + x1; + float y4 = y1; + float z4 = z1; + value += (a4 * a4) * (a4 * a4) * GradCoord(seed2, + i + (xNMask & (PrimeX * 2)), j + PrimeY, k + PrimeZ, x4, y4, z4); + skip5 = true; + } + } + + bool skip9 = false; + float a6 = yAFlipMask0 + a0; + if (a6 > 0) + { + float x6 = x0; + float y6 = y0 - (yNMask | 1); + float z6 = z0; + value += (a6 * a6) * (a6 * a6) * GradCoord(seed, + i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), x6, y6, z6); + } + else + { + float a7 = xAFlipMask0 + zAFlipMask0 + a0; + if (a7 > 0) + { + float x7 = x0 - (xNMask | 1); + float y7 = y0; + float z7 = z0 - (zNMask | 1); + value += (a7 * a7) * (a7 * a7) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), x7, y7, z7); + } + + float a8 = yAFlipMask1 + a1; + if (a8 > 0) + { + float x8 = x1; + float y8 = (yNMask | 1) + y1; + float z8 = z1; + value += (a8 * a8) * (a8 * a8) * GradCoord(seed2, + i + PrimeX, j + (yNMask & (PrimeY << 1)), k + PrimeZ, x8, y8, z8); + skip9 = true; + } + } + + bool skipD = false; + float aA = zAFlipMask0 + a0; + if (aA > 0) + { + float xA = x0; + float yA = y0; + float zA = z0 - (zNMask | 1); + value += (aA * aA) * (aA * aA) * GradCoord(seed, + i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), xA, yA, zA); + } + else + { + float aB = xAFlipMask0 + yAFlipMask0 + a0; + if (aB > 0) + { + float xB = x0 - (xNMask | 1); + float yB = y0 - (yNMask | 1); + float zB = z0; + value += (aB * aB) * (aB * aB) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), xB, yB, zB); + } + + float aC = zAFlipMask1 + a1; + if (aC > 0) + { + float xC = x1; + float yC = y1; + float zC = (zNMask | 1) + z1; + value += (aC * aC) * (aC * aC) * GradCoord(seed2, + i + PrimeX, j + PrimeY, k + (zNMask & (PrimeZ << 1)), xC, yC, zC); + skipD = true; + } + } + + if (!skip5) + { + float a5 = yAFlipMask1 + zAFlipMask1 + a1; + if (a5 > 0) + { + float x5 = x1; + float y5 = (yNMask | 1) + y1; + float z5 = (zNMask | 1) + z1; + value += (a5 * a5) * (a5 * a5) * GradCoord(seed2, + i + PrimeX, j + (yNMask & (PrimeY << 1)), k + (zNMask & (PrimeZ << 1)), x5, y5, z5); + } + } + + if (!skip9) + { + float a9 = xAFlipMask1 + zAFlipMask1 + a1; + if (a9 > 0) + { + float x9 = (xNMask | 1) + x1; + float y9 = y1; + float z9 = (zNMask | 1) + z1; + value += (a9 * a9) * (a9 * a9) * GradCoord(seed2, + i + (xNMask & (PrimeX * 2)), j + PrimeY, k + (zNMask & (PrimeZ << 1)), x9, y9, z9); + } + } + + if (!skipD) + { + float aD = xAFlipMask1 + yAFlipMask1 + a1; + if (aD > 0) + { + float xD = (xNMask | 1) + x1; + float yD = (yNMask | 1) + y1; + float zD = z1; + value += (aD * aD) * (aD * aD) * GradCoord(seed2, + i + (xNMask & (PrimeX << 1)), j + (yNMask & (PrimeY << 1)), k + PrimeZ, xD, yD, zD); + } + } + + return value * 9.046026385208288f; + } + + + // Cellular Noise + + private float SingleCellular(int seed, FNLfloat x, FNLfloat y) + { + int xr = FastRound(x); + int yr = FastRound(y); + + float distance0 = float.MaxValue; + float distance1 = float.MaxValue; + int closestHash = 0; + + float cellularJitter = 0.43701595f * mCellularJitterModifier; + + int xPrimed = (xr - 1) * PrimeX; + int yPrimedBase = (yr - 1) * PrimeY; + + switch (mCellularDistanceFunction) + { + default: + case CellularDistanceFunction.Euclidean: + case CellularDistanceFunction.EuclideanSq: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY; + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction.Manhattan: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = FastAbs(vecX) + FastAbs(vecY); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction.Hybrid: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = (FastAbs(vecX) + FastAbs(vecY)) + (vecX * vecX + vecY * vecY); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + } + + if (mCellularDistanceFunction == CellularDistanceFunction.Euclidean && mCellularReturnType >= CellularReturnType.Distance) + { + distance0 = FastSqrt(distance0); + + if (mCellularReturnType >= CellularReturnType.Distance2) + { + distance1 = FastSqrt(distance1); + } + } + + switch (mCellularReturnType) + { + case CellularReturnType.CellValue: + return closestHash * (1 / 2147483648.0f); + case CellularReturnType.Distance: + return distance0 - 1; + case CellularReturnType.Distance2: + return distance1 - 1; + case CellularReturnType.Distance2Add: + return (distance1 + distance0) * 0.5f - 1; + case CellularReturnType.Distance2Sub: + return distance1 - distance0 - 1; + case CellularReturnType.Distance2Mul: + return distance1 * distance0 * 0.5f - 1; + case CellularReturnType.Distance2Div: + return distance0 / distance1 - 1; + default: + return 0; + } + } + + private float SingleCellular(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + int xr = FastRound(x); + int yr = FastRound(y); + int zr = FastRound(z); + + float distance0 = float.MaxValue; + float distance1 = float.MaxValue; + int closestHash = 0; + + float cellularJitter = 0.39614353f * mCellularJitterModifier; + + int xPrimed = (xr - 1) * PrimeX; + int yPrimedBase = (yr - 1) * PrimeY; + int zPrimedBase = (zr - 1) * PrimeZ; + + switch (mCellularDistanceFunction) + { + case CellularDistanceFunction.Euclidean: + case CellularDistanceFunction.EuclideanSq: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction.Manhattan: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction.Hybrid: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = (FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + default: + break; + } + + if (mCellularDistanceFunction == CellularDistanceFunction.Euclidean && mCellularReturnType >= CellularReturnType.Distance) + { + distance0 = FastSqrt(distance0); + + if (mCellularReturnType >= CellularReturnType.Distance2) + { + distance1 = FastSqrt(distance1); + } + } + + switch (mCellularReturnType) + { + case CellularReturnType.CellValue: + return closestHash * (1 / 2147483648.0f); + case CellularReturnType.Distance: + return distance0 - 1; + case CellularReturnType.Distance2: + return distance1 - 1; + case CellularReturnType.Distance2Add: + return (distance1 + distance0) * 0.5f - 1; + case CellularReturnType.Distance2Sub: + return distance1 - distance0 - 1; + case CellularReturnType.Distance2Mul: + return distance1 * distance0 * 0.5f - 1; + case CellularReturnType.Distance2Div: + return distance0 / distance1 - 1; + default: + return 0; + } + } + + + // Perlin Noise + + private float SinglePerlin(int seed, FNLfloat x, FNLfloat y) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + + float xs = InterpQuintic(xd0); + float ys = InterpQuintic(yd0); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + float xf0 = Lerp(GradCoord(seed, x0, y0, xd0, yd0), GradCoord(seed, x1, y0, xd1, yd0), xs); + float xf1 = Lerp(GradCoord(seed, x0, y1, xd0, yd1), GradCoord(seed, x1, y1, xd1, yd1), xs); + + return Lerp(xf0, xf1, ys) * 1.4247691104677813f; + } + + private float SinglePerlin(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + int z0 = FastFloor(z); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float zd0 = (float)(z - z0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + float zd1 = zd0 - 1; + + float xs = InterpQuintic(xd0); + float ys = InterpQuintic(yd0); + float zs = InterpQuintic(zd0); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + float xf00 = Lerp(GradCoord(seed, x0, y0, z0, xd0, yd0, zd0), GradCoord(seed, x1, y0, z0, xd1, yd0, zd0), xs); + float xf10 = Lerp(GradCoord(seed, x0, y1, z0, xd0, yd1, zd0), GradCoord(seed, x1, y1, z0, xd1, yd1, zd0), xs); + float xf01 = Lerp(GradCoord(seed, x0, y0, z1, xd0, yd0, zd1), GradCoord(seed, x1, y0, z1, xd1, yd0, zd1), xs); + float xf11 = Lerp(GradCoord(seed, x0, y1, z1, xd0, yd1, zd1), GradCoord(seed, x1, y1, z1, xd1, yd1, zd1), xs); + + float yf0 = Lerp(xf00, xf10, ys); + float yf1 = Lerp(xf01, xf11, ys); + + return Lerp(yf0, yf1, zs) * 0.964921414852142333984375f; + } + + + // Value Cubic Noise + + private float SingleValueCubic(int seed, FNLfloat x, FNLfloat y) + { + int x1 = FastFloor(x); + int y1 = FastFloor(y); + + float xs = (float)(x - x1); + float ys = (float)(y - y1); + + x1 *= PrimeX; + y1 *= PrimeY; + int x0 = x1 - PrimeX; + int y0 = y1 - PrimeY; + int x2 = x1 + PrimeX; + int y2 = y1 + PrimeY; + int x3 = x1 + unchecked(PrimeX * 2); + int y3 = y1 + unchecked(PrimeY * 2); + + return CubicLerp( + CubicLerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), ValCoord(seed, x2, y0), ValCoord(seed, x3, y0), + xs), + CubicLerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), ValCoord(seed, x2, y1), ValCoord(seed, x3, y1), + xs), + CubicLerp(ValCoord(seed, x0, y2), ValCoord(seed, x1, y2), ValCoord(seed, x2, y2), ValCoord(seed, x3, y2), + xs), + CubicLerp(ValCoord(seed, x0, y3), ValCoord(seed, x1, y3), ValCoord(seed, x2, y3), ValCoord(seed, x3, y3), + xs), + ys) * (1 / (1.5f * 1.5f)); + } + + private float SingleValueCubic(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + int x1 = FastFloor(x); + int y1 = FastFloor(y); + int z1 = FastFloor(z); + + float xs = (float)(x - x1); + float ys = (float)(y - y1); + float zs = (float)(z - z1); + + x1 *= PrimeX; + y1 *= PrimeY; + z1 *= PrimeZ; + + int x0 = x1 - PrimeX; + int y0 = y1 - PrimeY; + int z0 = z1 - PrimeZ; + int x2 = x1 + PrimeX; + int y2 = y1 + PrimeY; + int z2 = z1 + PrimeZ; + int x3 = x1 + unchecked(PrimeX * 2); + int y3 = y1 + unchecked(PrimeY * 2); + int z3 = z1 + unchecked(PrimeZ * 2); + + + return CubicLerp( + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), ValCoord(seed, x2, y0, z0), ValCoord(seed, x3, y0, z0), xs), + CubicLerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), ValCoord(seed, x2, y1, z0), ValCoord(seed, x3, y1, z0), xs), + CubicLerp(ValCoord(seed, x0, y2, z0), ValCoord(seed, x1, y2, z0), ValCoord(seed, x2, y2, z0), ValCoord(seed, x3, y2, z0), xs), + CubicLerp(ValCoord(seed, x0, y3, z0), ValCoord(seed, x1, y3, z0), ValCoord(seed, x2, y3, z0), ValCoord(seed, x3, y3, z0), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), ValCoord(seed, x2, y0, z1), ValCoord(seed, x3, y0, z1), xs), + CubicLerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), ValCoord(seed, x2, y1, z1), ValCoord(seed, x3, y1, z1), xs), + CubicLerp(ValCoord(seed, x0, y2, z1), ValCoord(seed, x1, y2, z1), ValCoord(seed, x2, y2, z1), ValCoord(seed, x3, y2, z1), xs), + CubicLerp(ValCoord(seed, x0, y3, z1), ValCoord(seed, x1, y3, z1), ValCoord(seed, x2, y3, z1), ValCoord(seed, x3, y3, z1), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z2), ValCoord(seed, x1, y0, z2), ValCoord(seed, x2, y0, z2), ValCoord(seed, x3, y0, z2), xs), + CubicLerp(ValCoord(seed, x0, y1, z2), ValCoord(seed, x1, y1, z2), ValCoord(seed, x2, y1, z2), ValCoord(seed, x3, y1, z2), xs), + CubicLerp(ValCoord(seed, x0, y2, z2), ValCoord(seed, x1, y2, z2), ValCoord(seed, x2, y2, z2), ValCoord(seed, x3, y2, z2), xs), + CubicLerp(ValCoord(seed, x0, y3, z2), ValCoord(seed, x1, y3, z2), ValCoord(seed, x2, y3, z2), ValCoord(seed, x3, y3, z2), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z3), ValCoord(seed, x1, y0, z3), ValCoord(seed, x2, y0, z3), ValCoord(seed, x3, y0, z3), xs), + CubicLerp(ValCoord(seed, x0, y1, z3), ValCoord(seed, x1, y1, z3), ValCoord(seed, x2, y1, z3), ValCoord(seed, x3, y1, z3), xs), + CubicLerp(ValCoord(seed, x0, y2, z3), ValCoord(seed, x1, y2, z3), ValCoord(seed, x2, y2, z3), ValCoord(seed, x3, y2, z3), xs), + CubicLerp(ValCoord(seed, x0, y3, z3), ValCoord(seed, x1, y3, z3), ValCoord(seed, x2, y3, z3), ValCoord(seed, x3, y3, z3), xs), + ys), + zs) * (1 / (1.5f * 1.5f * 1.5f)); + } + + + // Value Noise + + private float SingleValue(int seed, FNLfloat x, FNLfloat y) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + + float xs = InterpHermite((float)(x - x0)); + float ys = InterpHermite((float)(y - y0)); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + float xf0 = Lerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), xs); + float xf1 = Lerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), xs); + + return Lerp(xf0, xf1, ys); + } + + private float SingleValue(int seed, FNLfloat x, FNLfloat y, FNLfloat z) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + int z0 = FastFloor(z); + + float xs = InterpHermite((float)(x - x0)); + float ys = InterpHermite((float)(y - y0)); + float zs = InterpHermite((float)(z - z0)); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + float xf00 = Lerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), xs); + float xf10 = Lerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), xs); + float xf01 = Lerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), xs); + float xf11 = Lerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), xs); + + float yf0 = Lerp(xf00, xf10, ys); + float yf1 = Lerp(xf01, xf11, ys); + + return Lerp(yf0, yf1, zs); + } + + + // Domain Warp + + private void DoSingleDomainWarp(int seed, float amp, float freq, FNLfloat x, FNLfloat y, ref FNLfloat xr, ref FNLfloat yr) + { + switch (mDomainWarpType) + { + case DomainWarpType.OpenSimplex2: + SingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, ref xr, ref yr, false); + break; + case DomainWarpType.OpenSimplex2Reduced: + SingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, ref xr, ref yr, true); + break; + case DomainWarpType.BasicGrid: + SingleDomainWarpBasicGrid(seed, amp, freq, x, y, ref xr, ref yr); + break; + } + } + + private void DoSingleDomainWarp(int seed, float amp, float freq, FNLfloat x, FNLfloat y, FNLfloat z, ref FNLfloat xr, ref FNLfloat yr, ref FNLfloat zr) + { + switch (mDomainWarpType) + { + case DomainWarpType.OpenSimplex2: + SingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, ref xr, ref yr, ref zr, false); + break; + case DomainWarpType.OpenSimplex2Reduced: + SingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, ref xr, ref yr, ref zr, true); + break; + case DomainWarpType.BasicGrid: + SingleDomainWarpBasicGrid(seed, amp, freq, x, y, z, ref xr, ref yr, ref zr); + break; + } + } + + + // Domain Warp Single Wrapper + + private void DomainWarpSingle(ref FNLfloat x, ref FNLfloat y) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + FNLfloat xs = x; + FNLfloat ys = y; + TransformDomainWarpCoordinate(ref xs, ref ys); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, ref x, ref y); + } + + private void DomainWarpSingle(ref FNLfloat x, ref FNLfloat y, ref FNLfloat z) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + FNLfloat xs = x; + FNLfloat ys = y; + FNLfloat zs = z; + TransformDomainWarpCoordinate(ref xs, ref ys, ref zs); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, ref x, ref y, ref z); + } + + + // Domain Warp Fractal Progressive + + private void DomainWarpFractalProgressive(ref FNLfloat x, ref FNLfloat y) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + FNLfloat xs = x; + FNLfloat ys = y; + TransformDomainWarpCoordinate(ref xs, ref ys); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, ref x, ref y); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + private void DomainWarpFractalProgressive(ref FNLfloat x, ref FNLfloat y, ref FNLfloat z) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + FNLfloat xs = x; + FNLfloat ys = y; + FNLfloat zs = z; + TransformDomainWarpCoordinate(ref xs, ref ys, ref zs); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, ref x, ref y, ref z); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + + // Domain Warp Fractal Independant + private void DomainWarpFractalIndependent(ref FNLfloat x, ref FNLfloat y) + { + FNLfloat xs = x; + FNLfloat ys = y; + TransformDomainWarpCoordinate(ref xs, ref ys); + + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + DoSingleDomainWarp(seed, amp, freq, xs, ys, ref x, ref y); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + private void DomainWarpFractalIndependent(ref FNLfloat x, ref FNLfloat y, ref FNLfloat z) + { + FNLfloat xs = x; + FNLfloat ys = y; + FNLfloat zs = z; + TransformDomainWarpCoordinate(ref xs, ref ys, ref zs); + + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, ref x, ref y, ref z); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + + // Domain Warp Basic Grid + + private void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, ref FNLfloat xr, ref FNLfloat yr) + { + FNLfloat xf = x * frequency; + FNLfloat yf = y * frequency; + + int x0 = FastFloor(xf); + int y0 = FastFloor(yf); + + float xs = InterpHermite((float)(xf - x0)); + float ys = InterpHermite((float)(yf - y0)); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + int hash0 = Hash(seed, x0, y0) & (255 << 1); + int hash1 = Hash(seed, x1, y0) & (255 << 1); + + float lx0x = Lerp(RandVecs2D[hash0], RandVecs2D[hash1], xs); + float ly0x = Lerp(RandVecs2D[hash0 | 1], RandVecs2D[hash1 | 1], xs); + + hash0 = Hash(seed, x0, y1) & (255 << 1); + hash1 = Hash(seed, x1, y1) & (255 << 1); + + float lx1x = Lerp(RandVecs2D[hash0], RandVecs2D[hash1], xs); + float ly1x = Lerp(RandVecs2D[hash0 | 1], RandVecs2D[hash1 | 1], xs); + + xr += Lerp(lx0x, lx1x, ys) * warpAmp; + yr += Lerp(ly0x, ly1x, ys) * warpAmp; + } + + private void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, ref FNLfloat xr, ref FNLfloat yr, ref FNLfloat zr) + { + FNLfloat xf = x * frequency; + FNLfloat yf = y * frequency; + FNLfloat zf = z * frequency; + + int x0 = FastFloor(xf); + int y0 = FastFloor(yf); + int z0 = FastFloor(zf); + + float xs = InterpHermite((float)(xf - x0)); + float ys = InterpHermite((float)(yf - y0)); + float zs = InterpHermite((float)(zf - z0)); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + int hash0 = Hash(seed, x0, y0, z0) & (255 << 2); + int hash1 = Hash(seed, x1, y0, z0) & (255 << 2); + + float lx0x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + float ly0x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + float lz0x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + hash0 = Hash(seed, x0, y1, z0) & (255 << 2); + hash1 = Hash(seed, x1, y1, z0) & (255 << 2); + + float lx1x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + float ly1x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + float lz1x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + float lx0y = Lerp(lx0x, lx1x, ys); + float ly0y = Lerp(ly0x, ly1x, ys); + float lz0y = Lerp(lz0x, lz1x, ys); + + hash0 = Hash(seed, x0, y0, z1) & (255 << 2); + hash1 = Hash(seed, x1, y0, z1) & (255 << 2); + + lx0x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + ly0x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + lz0x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + hash0 = Hash(seed, x0, y1, z1) & (255 << 2); + hash1 = Hash(seed, x1, y1, z1) & (255 << 2); + + lx1x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + ly1x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + lz1x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + xr += Lerp(lx0y, Lerp(lx0x, lx1x, ys), zs) * warpAmp; + yr += Lerp(ly0y, Lerp(ly0x, ly1x, ys), zs) * warpAmp; + zr += Lerp(lz0y, Lerp(lz0x, lz1x, ys), zs) * warpAmp; + } + + + // Domain Warp Simplex/OpenSimplex2 + private void SingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, ref FNLfloat xr, ref FNLfloat yr, bool outGradOnly) + { + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + x *= frequency; + y *= frequency; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNfloat F2 = 0.5f * (SQRT3 - 1); + * FNfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PrimeX; + j *= PrimeY; + + float vx, vy; + vx = vy = 0; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i, j, out xo, out yo); + else + GradCoordDual(seed, i, j, x0, y0, out xo, out yo); + vx += aaaa * xo; + vy += aaaa * yo; + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c > 0) + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + float cccc = (c * c) * (c * c); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i + PrimeX, j + PrimeY, out xo, out yo); + else + GradCoordDual(seed, i + PrimeX, j + PrimeY, x2, y2, out xo, out yo); + vx += cccc * xo; + vy += cccc * yo; + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i, j + PrimeY, out xo, out yo); + else + GradCoordDual(seed, i, j + PrimeY, x1, y1, out xo, out yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i + PrimeX, j, out xo, out yo); + else + GradCoordDual(seed, i + PrimeX, j, x1, y1, out xo, out yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + + xr += vx * warpAmp; + yr += vy * warpAmp; + } + + private void SingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, ref FNLfloat xr, ref FNLfloat yr, ref FNLfloat zr, bool outGradOnly) + { + x *= frequency; + y *= frequency; + z *= frequency; + + /* + * --- Rotation moved to TransformDomainWarpCoordinate method --- + * const FNfloat R3 = (FNfloat)(2.0 / 3.0); + * FNfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastRound(x); + int j = FastRound(y); + int k = FastRound(z); + float x0 = (float)x - i; + float y0 = (float)y - j; + float z0 = (float)z - k; + + int xNSign = (int)(-x0 - 1.0f) | 1; + int yNSign = (int)(-y0 - 1.0f) | 1; + int zNSign = (int)(-z0 - 1.0f) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + + float vx, vy, vz; + vx = vy = vz = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; ; l++) + { + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo, zo; + if (outGradOnly) + GradCoordOut(seed, i, j, k, out xo, out yo, out zo); + else + GradCoordDual(seed, i, j, k, x0, y0, z0, out xo, out yo, out zo); + vx += aaaa * xo; + vy += aaaa * yo; + vz += aaaa * zo; + } + + float b = a; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b = b + ax0 + ax0; + i1 -= xNSign * PrimeX; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b = b + ay0 + ay0; + j1 -= yNSign * PrimeY; + } + else + { + z1 += zNSign; + b = b + az0 + az0; + k1 -= zNSign * PrimeZ; + } + + if (b > 1) + { + b -= 1; + float bbbb = (b * b) * (b * b); + float xo, yo, zo; + if (outGradOnly) + GradCoordOut(seed, i1, j1, k1, out xo, out yo, out zo); + else + GradCoordDual(seed, i1, j1, k1, x1, y1, z1, out xo, out yo, out zo); + vx += bbbb * xo; + vy += bbbb * yo; + vz += bbbb * zo; + } + + if (l == 1) break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PrimeX; + j += (yNSign >> 1) & PrimeY; + k += (zNSign >> 1) & PrimeZ; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + xr += vx * warpAmp; + yr += vy * warpAmp; + zr += vz * warpAmp; + } +} \ No newline at end of file diff --git a/Cpp/FastNoiseLite.h b/Cpp/FastNoiseLite.h new file mode 100644 index 0000000..9f082b6 --- /dev/null +++ b/Cpp/FastNoiseLite.h @@ -0,0 +1,2586 @@ +// MIT License +// +// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com) +// Copyright(c) 2020 Contributors +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files(the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions : +// +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +// +// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll +// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo +// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd +// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx +// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx +// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd +// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo +// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo +// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo +// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo +// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo +// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo +// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl +// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c +// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c +// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc +// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll +// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo +// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd +// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk +// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000 +// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX +// +// VERSION: 1.0 +// https://github.com/Auburn/FastNoise + +#ifndef FASTNOISELITE_H +#define FASTNOISELITE_H + +#include + +class FastNoiseLite +{ +public: + enum NoiseType + { + NoiseType_OpenSimplex2, + NoiseType_OpenSimplex2S, + NoiseType_Cellular, + NoiseType_Perlin, + NoiseType_ValueCubic, + NoiseType_Value + }; + + enum RotationType3D + { + RotationType3D_None, + RotationType3D_ImproveXYPlanes, + RotationType3D_ImproveXZPlanes + }; + + enum FractalType + { + FractalType_None, + FractalType_FBm, + FractalType_Ridged, + FractalType_PingPong, + FractalType_DomainWarpProgressive, + FractalType_DomainWarpIndependent + }; + + enum CellularDistanceFunction + { + CellularDistanceFunction_Euclidean, + CellularDistanceFunction_EuclideanSq, + CellularDistanceFunction_Manhattan, + CellularDistanceFunction_Hybrid + }; + + enum CellularReturnType + { + CellularReturnType_CellValue, + CellularReturnType_Distance, + CellularReturnType_Distance2, + CellularReturnType_Distance2Add, + CellularReturnType_Distance2Sub, + CellularReturnType_Distance2Mul, + CellularReturnType_Distance2Div + }; + + enum DomainWarpType + { + DomainWarpType_OpenSimplex2, + DomainWarpType_OpenSimplex2Reduced, + DomainWarpType_BasicGrid + }; + + /// + /// Create new FastNoise object with optional seed + /// + FastNoiseLite(int seed = 1337) + { + mSeed = seed; + mFrequency = 0.01f; + mNoiseType = NoiseType_OpenSimplex2; + mRotationType3D = RotationType3D_None; + mTransformType3D = TransformType3D_DefaultOpenSimplex2; + + mFractalType = FractalType_None; + mOctaves = 3; + mLacunarity = 2.0f; + mGain = 0.5f; + mWeightedStrength = 0.0f; + mPingPongStength = 2.0f; + + mFractalBounding = 1 / 1.75f; + + mCellularDistanceFunction = CellularDistanceFunction_EuclideanSq; + mCellularReturnType = CellularReturnType_Distance; + mCellularJitterModifier = 1.0f; + + mDomainWarpType = DomainWarpType_OpenSimplex2; + mWarpTransformType3D = TransformType3D_DefaultOpenSimplex2; + mDomainWarpAmp = 1.0f; + } + + /// + /// Sets seed used for all noise types + /// + /// + /// Default: 1337 + /// + void SetSeed(int seed) { mSeed = seed; } + + /// + /// Sets frequency for all noise types + /// + /// + /// Default: 0.01 + /// + void SetFrequency(float frequency) { mFrequency = frequency; } + + /// + /// Sets noise algorithm used for GetNoise(...) + /// + /// + /// Default: OpenSimplex2 + /// + void SetNoiseType(NoiseType noiseType) + { + mNoiseType = noiseType; + UpdateTransformType3D(); + } + + /// + /// Sets domain rotation type for 3D Noise and 3D DomainWarp. + /// Can aid in reducing directional artifacts when sampling a 2D plane in 3D + /// + /// + /// Default: None + /// + void SetRotationType3D(RotationType3D rotationType3D) + { + mRotationType3D = rotationType3D; + UpdateTransformType3D(); + UpdateWarpTransformType3D(); + } + + /// + /// Sets method for combining octaves in all fractal noise types + /// + /// + /// Default: None + /// Note: FractalType_DomainWarp... only affects DomainWarp(...) + /// + void SetFractalType(FractalType fractalType) { mFractalType = fractalType; } + + /// + /// Sets octave count for all fractal noise types + /// + /// + /// Default: 3 + /// + void SetFractalOctaves(int octaves) + { + mOctaves = octaves; + CalculateFractalBounding(); + } + + /// + /// Sets octave lacunarity for all fractal noise types + /// + /// + /// Default: 2.0 + /// + void SetFractalLacunarity(float lacunarity) { mLacunarity = lacunarity; } + + /// + /// Sets octave gain for all fractal noise types + /// + /// + /// Default: 0.5 + /// + void SetFractalGain(float gain) + { + mGain = gain; + CalculateFractalBounding(); + } + + /// + /// Sets octave weighting for all none DomainWarp fratal types + /// + /// + /// Default: 0.0 + /// Note: Keep between 0...1 to maintain -1...1 output bounding + /// + void SetFractalWeightedStrength(float weightedStrength) { mWeightedStrength = weightedStrength; } + + /// + /// Sets strength of the fractal ping pong effect + /// + /// + /// Default: 2.0 + /// + void SetFractalPingPongStrength(float pingPongStrength) { mPingPongStength = pingPongStrength; } + + + /// + /// Sets distance function used in cellular noise calculations + /// + /// + /// Default: Distance + /// + void SetCellularDistanceFunction(CellularDistanceFunction cellularDistanceFunction) { mCellularDistanceFunction = cellularDistanceFunction; } + + /// + /// Sets return type from cellular noise calculations + /// + /// + /// Default: EuclideanSq + /// + void SetCellularReturnType(CellularReturnType cellularReturnType) { mCellularReturnType = cellularReturnType; } + + /// + /// Sets the maximum distance a cellular point can move from it's grid position + /// + /// + /// Default: 1.0 + /// Note: Setting this higher than 1 will cause artifacts + /// + void SetCellularJitter(float cellularJitter) { mCellularJitterModifier = cellularJitter; } + + + /// + /// Sets the warp algorithm when using DomainWarp(...) + /// + /// + /// Default: OpenSimplex2 + /// + void SetDomainWarpType(DomainWarpType domainWarpType) + { + mDomainWarpType = domainWarpType; + UpdateWarpTransformType3D(); + } + + + /// + /// Sets the maximum warp distance from original position when using DomainWarp(...) + /// + /// + /// Default: 1.0 + /// + void SetDomainWarpAmp(float domainWarpAmp) { mDomainWarpAmp = domainWarpAmp; } + + + /// + /// 2D noise at given position using current settings + /// + /// + /// Noise output bounded between -1...1 + /// + template + float GetNoise(FNfloat x, FNfloat y) + { + Arguments_must_be_floating_point_values(); + + TransformNoiseCoordinate(x, y); + + switch (mFractalType) + { + default: + return GenNoiseSingle(mSeed, x, y); + case FractalType_FBm: + return GenFractalFBm(x, y); + case FractalType_Ridged: + return GenFractalRidged(x, y); + case FractalType_PingPong: + return GenFractalPingPong(x, y); + } + } + + /// + /// 3D noise at given position using current settings + /// + /// + /// Noise output bounded between -1...1 + /// + template + float GetNoise(FNfloat x, FNfloat y, FNfloat z) + { + Arguments_must_be_floating_point_values(); + + TransformNoiseCoordinate(x, y, z); + + switch (mFractalType) + { + default: + return GenNoiseSingle(mSeed, x, y, z); + case FractalType_FBm: + return GenFractalFBm(x, y, z); + case FractalType_Ridged: + return GenFractalRidged(x, y, z); + case FractalType_PingPong: + return GenFractalPingPong(x, y, z); + } + } + + + /// + /// 2D warps the input position using current domain warp settings + /// + /// + /// Example usage with GetNoise + /// DomainWarp(x, y) + /// noise = GetNoise(x, y) + /// + template + void DomainWarp(FNfloat& x, FNfloat& y) + { + Arguments_must_be_floating_point_values(); + + switch (mFractalType) + { + default: + DomainWarpSingle(x, y); + break; + case FractalType_DomainWarpProgressive: + DomainWarpFractalProgressive(x, y); + break; + case FractalType_DomainWarpIndependent: + DomainWarpFractalIndependent(x, y); + break; + } + } + + /// + /// 3D warps the input position using current domain warp settings + /// + /// + /// Example usage with GetNoise + /// DomainWarp(x, y, z) + /// noise = GetNoise(x, y, z) + /// + template + void DomainWarp(FNfloat& x, FNfloat& y, FNfloat& z) + { + Arguments_must_be_floating_point_values(); + + switch (mFractalType) + { + default: + DomainWarpSingle(x, y, z); + break; + case FractalType_DomainWarpProgressive: + DomainWarpFractalProgressive(x, y, z); + break; + case FractalType_DomainWarpIndependent: + DomainWarpFractalIndependent(x, y, z); + break; + } + } + +private: + template + struct Arguments_must_be_floating_point_values; + + enum TransformType3D + { + TransformType3D_None, + TransformType3D_ImproveXYPlanes, + TransformType3D_ImproveXZPlanes, + TransformType3D_DefaultOpenSimplex2 + }; + + int mSeed; + float mFrequency; + NoiseType mNoiseType; + RotationType3D mRotationType3D; + TransformType3D mTransformType3D; + + FractalType mFractalType; + int mOctaves; + float mLacunarity; + float mGain; + float mWeightedStrength; + float mPingPongStength; + + float mFractalBounding; + + CellularDistanceFunction mCellularDistanceFunction; + CellularReturnType mCellularReturnType; + float mCellularJitterModifier; + + DomainWarpType mDomainWarpType; + TransformType3D mWarpTransformType3D; + float mDomainWarpAmp; + + + template + struct Lookup + { + static const T Gradients2D[]; + static const T Gradients3D[]; + static const T RandVecs2D[]; + static const T RandVecs3D[]; + }; + + static float FastMin(float a, float b) { return a < b ? a : b; } + + static float FastMax(float a, float b) { return a > b ? a : b; } + + static float FastAbs(float f) { return f < 0 ? -f : f; } + + static float FastSqrt(float f) { return sqrtf(f); } + + template + static int FastFloor(FNfloat f) { return f >= 0 ? (int)f : (int)f - 1; } + + template + static int FastRound(FNfloat f) { return f >= 0 ? (int)(f + 0.5f) : (int)(f - 0.5f); } + + static float Lerp(float a, float b, float t) { return a + t * (b - a); } + + static float InterpHermite(float t) { return t * t * (3 - 2 * t); } + + static float InterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); } + + static float CubicLerp(float a, float b, float c, float d, float t) + { + float p = (d - c) - (a - b); + return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b; + } + + static float PingPong(float t) + { + t -= (int)(t * 0.5f) * 2; + return t < 1 ? t : 2 - t; + } + + void CalculateFractalBounding() + { + float gain = FastAbs(mGain); + float amp = gain; + float ampFractal = 1.0f; + for (int i = 1; i < mOctaves; i++) + { + ampFractal += amp; + amp *= gain; + } + mFractalBounding = 1 / ampFractal; + } + + // Hashing + static const int PrimeX = 501125321; + static const int PrimeY = 1136930381; + static const int PrimeZ = 1720413743; + + static int Hash(int seed, int xPrimed, int yPrimed) + { + int hash = seed ^ xPrimed ^ yPrimed; + + hash *= 0x27d4eb2d; + return hash; + } + + + static int Hash(int seed, int xPrimed, int yPrimed, int zPrimed) + { + int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed; + + hash *= 0x27d4eb2d; + return hash; + } + + + static float ValCoord(int seed, int xPrimed, int yPrimed) + { + int hash = Hash(seed, xPrimed, yPrimed); + + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); + } + + + static float ValCoord(int seed, int xPrimed, int yPrimed, int zPrimed) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); + } + + + float GradCoord(int seed, int xPrimed, int yPrimed, float xd, float yd) + { + int hash = Hash(seed, xPrimed, yPrimed); + hash ^= hash >> 15; + hash &= 127 << 1; + + float xg = Lookup::Gradients2D[hash]; + float yg = Lookup::Gradients2D[hash | 1]; + + return xd * xg + yd * yg; + } + + + float GradCoord(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + hash ^= hash >> 15; + hash &= 63 << 2; + + float xg = Lookup::Gradients3D[hash]; + float yg = Lookup::Gradients3D[hash | 1]; + float zg = Lookup::Gradients3D[hash | 2]; + + return xd * xg + yd * yg + zd * zg; + } + + + void GradCoordOut(int seed, int xPrimed, int yPrimed, float& xo, float& yo) + { + int hash = Hash(seed, xPrimed, yPrimed) & (255 << 1); + + xo = Lookup::RandVecs2D[hash]; + yo = Lookup::RandVecs2D[hash | 1]; + } + + + void GradCoordOut(int seed, int xPrimed, int yPrimed, int zPrimed, float& xo, float& yo, float& zo) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed) & (255 << 2); + + xo = Lookup::RandVecs3D[hash]; + yo = Lookup::RandVecs3D[hash | 1]; + zo = Lookup::RandVecs3D[hash | 2]; + } + + + void GradCoordDual(int seed, int xPrimed, int yPrimed, float xd, float yd, float& xo, float& yo) + { + int hash = Hash(seed, xPrimed, yPrimed); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + + float xg = Lookup::Gradients2D[index1]; + float yg = Lookup::Gradients2D[index1 | 1]; + float value = xd * xg + yd * yg; + + float xgo = Lookup::RandVecs2D[index2]; + float ygo = Lookup::RandVecs2D[index2 | 1]; + + xo = value * xgo; + yo = value * ygo; + } + + + void GradCoordDual(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, float& xo, float& yo, float& zo) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int index1 = hash & (63 << 2); + int index2 = (hash >> 6) & (255 << 2); + + float xg = Lookup::Gradients3D[index1]; + float yg = Lookup::Gradients3D[index1 | 1]; + float zg = Lookup::Gradients3D[index1 | 2]; + float value = xd * xg + yd * yg + zd * zg; + + float xgo = Lookup::RandVecs3D[index2]; + float ygo = Lookup::RandVecs3D[index2 | 1]; + float zgo = Lookup::RandVecs3D[index2 | 2]; + + xo = value * xgo; + yo = value * ygo; + zo = value * zgo; + } + + + // Generic noise gen + + template + float GenNoiseSingle(int seed, FNfloat x, FNfloat y) + { + switch (mNoiseType) + { + case NoiseType_OpenSimplex2: + return SingleSimplex(seed, x, y); + case NoiseType_OpenSimplex2S: + return SingleOpenSimplex2S(seed, x, y); + case NoiseType_Cellular: + return SingleCellular(seed, x, y); + case NoiseType_Perlin: + return SinglePerlin(seed, x, y); + case NoiseType_ValueCubic: + return SingleValueCubic(seed, x, y); + case NoiseType_Value: + return SingleValue(seed, x, y); + default: + return 0; + } + } + + template + float GenNoiseSingle(int seed, FNfloat x, FNfloat y, FNfloat z) + { + switch (mNoiseType) + { + case NoiseType_OpenSimplex2: + return SingleOpenSimplex2(seed, x, y, z); + case NoiseType_OpenSimplex2S: + return SingleOpenSimplex2S(seed, x, y, z); + case NoiseType_Cellular: + return SingleCellular(seed, x, y, z); + case NoiseType_Perlin: + return SinglePerlin(seed, x, y, z); + case NoiseType_ValueCubic: + return SingleValueCubic(seed, x, y, z); + case NoiseType_Value: + return SingleValue(seed, x, y, z); + default: + return 0; + } + } + + + // Noise Coordinate Transforms (frequency, and possible skew or rotation) + + template + void TransformNoiseCoordinate(FNfloat& x, FNfloat& y) + { + x *= mFrequency; + y *= mFrequency; + + switch (mNoiseType) + { + case NoiseType_OpenSimplex2: + case NoiseType_OpenSimplex2S: + { + const FNfloat SQRT3 = (FNfloat)1.7320508075688772935274463415059; + const FNfloat F2 = 0.5f * (SQRT3 - 1); + FNfloat t = (x + y) * F2; + x += t; + y += t; + } + break; + default: + break; + } + } + + template + void TransformNoiseCoordinate(FNfloat& x, FNfloat& y, FNfloat& z) + { + x *= mFrequency; + y *= mFrequency; + z *= mFrequency; + + switch (mTransformType3D) + { + case TransformType3D_ImproveXYPlanes: + { + FNfloat xy = x + y; + FNfloat s2 = xy * -(FNfloat)0.211324865405187; + z *= (FNfloat)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (FNfloat)0.577350269189626; + } + break; + case TransformType3D_ImproveXZPlanes: + { + FNfloat xz = x + z; + FNfloat s2 = xz * -(FNfloat)0.211324865405187; + y *= (FNfloat)0.577350269189626; + x += s2 - y; + z += s2 - y; + y += xz * (FNfloat)0.577350269189626; + } + break; + case TransformType3D_DefaultOpenSimplex2: + { + const FNfloat R3 = (FNfloat)(2.0 / 3.0); + FNfloat r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + } + + void UpdateTransformType3D() + { + switch (mRotationType3D) + { + case RotationType3D_ImproveXYPlanes: + mTransformType3D = TransformType3D_ImproveXYPlanes; + break; + case RotationType3D_ImproveXZPlanes: + mTransformType3D = TransformType3D_ImproveXZPlanes; + break; + default: + switch (mNoiseType) + { + case NoiseType_OpenSimplex2: + case NoiseType_OpenSimplex2S: + mTransformType3D = TransformType3D_DefaultOpenSimplex2; + break; + default: + mTransformType3D = TransformType3D_None; + break; + } + break; + } + } + + + // Domain Warp Coordinate Transforms + + template + void TransformDomainWarpCoordinate(FNfloat& x, FNfloat& y) + { + switch (mDomainWarpType) + { + case DomainWarpType_OpenSimplex2: + case DomainWarpType_OpenSimplex2Reduced: + { + const FNfloat SQRT3 = (FNfloat)1.7320508075688772935274463415059; + const FNfloat F2 = 0.5f * (SQRT3 - 1); + FNfloat t = (x + y) * F2; + x += t; + y += t; + } + break; + default: + break; + } + } + + template + void TransformDomainWarpCoordinate(FNfloat& x, FNfloat& y, FNfloat& z) + { + switch (mWarpTransformType3D) + { + case TransformType3D_ImproveXYPlanes: + { + FNfloat xy = x + y; + FNfloat s2 = xy * -(FNfloat)0.211324865405187; + z *= (FNfloat)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (FNfloat)0.577350269189626; + } + break; + case TransformType3D_ImproveXZPlanes: + { + FNfloat xz = x + z; + FNfloat s2 = xz * -(FNfloat)0.211324865405187; + y *= (FNfloat)0.577350269189626; + x += s2 - y; + z += s2 - y; + y += xz * (FNfloat)0.577350269189626; + } + break; + case TransformType3D_DefaultOpenSimplex2: + { + const FNfloat R3 = (FNfloat)(2.0 / 3.0); + FNfloat r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + } + + void UpdateWarpTransformType3D() + { + switch (mRotationType3D) + { + case RotationType3D_ImproveXYPlanes: + mWarpTransformType3D = TransformType3D_ImproveXYPlanes; + break; + case RotationType3D_ImproveXZPlanes: + mWarpTransformType3D = TransformType3D_ImproveXZPlanes; + break; + default: + switch (mDomainWarpType) + { + case DomainWarpType_OpenSimplex2: + case DomainWarpType_OpenSimplex2Reduced: + mWarpTransformType3D = TransformType3D_DefaultOpenSimplex2; + break; + default: + mWarpTransformType3D = TransformType3D_None; + break; + } + break; + } + } + + + // Fractal FBm + + template + float GenFractalFBm(FNfloat x, FNfloat y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = GenNoiseSingle(seed++, x, y); + sum += noise * amp; + amp *= Lerp(1.0f, FastMin(noise + 1, 2) * 0.5f, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + template + float GenFractalFBm(FNfloat x, FNfloat y, FNfloat z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = GenNoiseSingle(seed++, x, y, z); + sum += noise * amp; + amp *= Lerp(1.0f, (noise + 1) * 0.5f, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Fractal Ridged + + template + float GenFractalRidged(FNfloat x, FNfloat y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = FastAbs(GenNoiseSingle(seed++, x, y)); + sum += (noise * -2 + 1) * amp; + amp *= Lerp(1.0f, 1 - noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + template + float GenFractalRidged(FNfloat x, FNfloat y, FNfloat z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = FastAbs(GenNoiseSingle(seed++, x, y, z)); + sum += (noise * -2 + 1) * amp; + amp *= Lerp(1.0f, 1 - noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Fractal PingPong + + template + float GenFractalPingPong(FNfloat x, FNfloat y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = PingPong((GenNoiseSingle(seed++, x, y) + 1) * mPingPongStength); + sum += (noise - 0.5f) * 2 * amp; + amp *= Lerp(1.0f, noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + template + float GenFractalPingPong(FNfloat x, FNfloat y, FNfloat z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = PingPong((GenNoiseSingle(seed++, x, y, z) + 1) * mPingPongStength); + sum += (noise - 0.5f) * 2 * amp; + amp *= Lerp(1.0f, noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Simplex/OpenSimplex2 Noise + + template + float SingleSimplex(int seed, FNfloat x, FNfloat y) + { + // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex. + + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNfloat F2 = 0.5f * (SQRT3 - 1); + * FNfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PrimeX; + j *= PrimeY; + + float n0, n1, n2; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a <= 0) n0 = 0; + else + { + n0 = (a * a) * (a * a) * GradCoord(seed, i, j, x0, y0); + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c <= 0) n2 = 0; + else + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + n2 = (c * c) * (c * c) * GradCoord(seed, i + PrimeX, j + PrimeY, x2, y2); + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) n1 = 0; + else + { + n1 = (b * b) * (b * b) * GradCoord(seed, i, j + PrimeY, x1, y1); + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) n1 = 0; + else + { + n1 = (b * b) * (b * b) * GradCoord(seed, i + PrimeX, j, x1, y1); + } + } + + return (n0 + n1 + n2) * 99.83685446303647f; + } + + template + float SingleOpenSimplex2(int seed, FNfloat x, FNfloat y, FNfloat z) + { + // 3D OpenSimplex2 case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNfloat R3 = (FNfloat)(2.0 / 3.0); + * FNfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastRound(x); + int j = FastRound(y); + int k = FastRound(z); + float x0 = (float)(x - i); + float y0 = (float)(y - j); + float z0 = (float)(z - k); + + int xNSign = (int)(-1.0f - x0) | 1; + int yNSign = (int)(-1.0f - y0) | 1; + int zNSign = (int)(-1.0f - z0) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + + float value = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; l < 2; l++) + { + if (a > 0) + { + value += (a * a) * (a * a) * GradCoord(seed, i, j, k, x0, y0, z0); + } + + float b = a + 1; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b -= xNSign * 2 * x1; + i1 -= xNSign * PrimeX; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b -= yNSign * 2 * y1; + j1 -= yNSign * PrimeY; + } + else + { + z1 += zNSign; + b -= zNSign * 2 * z1; + k1 -= zNSign * PrimeZ; + } + + if (b > 0) + { + value += (b * b) * (b * b) * GradCoord(seed, i1, j1, k1, x1, y1, z1); + } + + if (l == 1) break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PrimeX; + j += (yNSign >> 1) & PrimeY; + k += (zNSign >> 1) & PrimeZ; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + return value * 32.69428253173828125f; + } + + + // OpenSimplex2S Noise + + template + float SingleOpenSimplex2S(int seed, FNfloat x, FNfloat y) + { + // 2D OpenSimplex2S case is a modified 2D simplex noise. + + const FNfloat SQRT3 = (FNfloat)1.7320508075688772935274463415059; + const FNfloat G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNfloat F2 = 0.5f * (SQRT3 - 1); + * FNfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + i *= PrimeX; + j *= PrimeY; + int i1 = i + PrimeX; + int j1 = j + PrimeY; + + float t = (xi + yi) * (float)G2; + float x0 = xi - t; + float y0 = yi - t; + + float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0; + float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, i, j, x0, y0); + + float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0); + float x1 = x0 - (float)(1 - 2 * G2); + float y1 = y0 - (float)(1 - 2 * G2); + value += (a1 * a1) * (a1 * a1) * GradCoord(seed, i1, j1, x1, y1); + + // Nested conditionals were faster than compact bit logic/arithmetic. + float xmyi = xi - yi; + if (t > G2) + { + if (xi + xmyi > 1) + { + float x2 = x0 + (float)(3 * G2 - 2); + float y2 = y0 + (float)(3 * G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + (PrimeX << 1), j + PrimeY, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2); + } + } + + if (yi - xmyi > 1) + { + float x3 = x0 + (float)(3 * G2 - 1); + float y3 = y0 + (float)(3 * G2 - 2); + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j + (PrimeY << 1), x3, y3); + } + } + else + { + float x3 = x0 + (float)(G2 - 1); + float y3 = y0 + (float)G2; + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j, x3, y3); + } + } + } + else + { + if (xi + xmyi < 0) + { + float x2 = x0 + (float)(1 - G2); + float y2 = y0 - (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i - PrimeX, j, x2, y2); + } + } + else + { + float x2 = x0 + (float)(G2 - 1); + float y2 = y0 + (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + PrimeX, j, x2, y2); + } + } + + if (yi < xmyi) + { + float x2 = x0 - (float)G2; + float y2 = y0 - (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j - PrimeY, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2); + } + } + } + + return value * 18.24196194486065f; + } + + template + float SingleOpenSimplex2S(int seed, FNfloat x, FNfloat y, FNfloat z) + { + // 3D OpenSimplex2S case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNfloat R3 = (FNfloat)(2.0 / 3.0); + * FNfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + int k = FastFloor(z); + float xi = (float)(x - i); + float yi = (float)(y - j); + float zi = (float)(z - k); + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + int seed2 = seed + 1293373; + + int xNMask = (int)(-0.5f - xi); + int yNMask = (int)(-0.5f - yi); + int zNMask = (int)(-0.5f - zi); + + float x0 = xi + xNMask; + float y0 = yi + yNMask; + float z0 = zi + zNMask; + float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0; + float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, + i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x0, y0, z0); + + float x1 = xi - 0.5f; + float y1 = yi - 0.5f; + float z1 = zi - 0.5f; + float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1; + value += (a1 * a1) * (a1 * a1) * GradCoord(seed2, + i + PrimeX, j + PrimeY, k + PrimeZ, x1, y1, z1); + + float xAFlipMask0 = ((xNMask | 1) << 1) * x1; + float yAFlipMask0 = ((yNMask | 1) << 1) * y1; + float zAFlipMask0 = ((zNMask | 1) << 1) * z1; + float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f; + float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f; + float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f; + + bool skip5 = false; + float a2 = xAFlipMask0 + a0; + if (a2 > 0) + { + float x2 = x0 - (xNMask | 1); + float y2 = y0; + float z2 = z0; + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x2, y2, z2); + } + else + { + float a3 = yAFlipMask0 + zAFlipMask0 + a0; + if (a3 > 0) + { + float x3 = x0; + float y3 = y0 - (yNMask | 1); + float z3 = z0 - (zNMask | 1); + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, + i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (~zNMask & PrimeZ), x3, y3, z3); + } + + float a4 = xAFlipMask1 + a1; + if (a4 > 0) + { + float x4 = (xNMask | 1) + x1; + float y4 = y1; + float z4 = z1; + value += (a4 * a4) * (a4 * a4) * GradCoord(seed2, + i + (xNMask & (PrimeX * 2)), j + PrimeY, k + PrimeZ, x4, y4, z4); + skip5 = true; + } + } + + bool skip9 = false; + float a6 = yAFlipMask0 + a0; + if (a6 > 0) + { + float x6 = x0; + float y6 = y0 - (yNMask | 1); + float z6 = z0; + value += (a6 * a6) * (a6 * a6) * GradCoord(seed, + i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), x6, y6, z6); + } + else + { + float a7 = xAFlipMask0 + zAFlipMask0 + a0; + if (a7 > 0) + { + float x7 = x0 - (xNMask | 1); + float y7 = y0; + float z7 = z0 - (zNMask | 1); + value += (a7 * a7) * (a7 * a7) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), x7, y7, z7); + } + + float a8 = yAFlipMask1 + a1; + if (a8 > 0) + { + float x8 = x1; + float y8 = (yNMask | 1) + y1; + float z8 = z1; + value += (a8 * a8) * (a8 * a8) * GradCoord(seed2, + i + PrimeX, j + (yNMask & (PrimeY << 1)), k + PrimeZ, x8, y8, z8); + skip9 = true; + } + } + + bool skipD = false; + float aA = zAFlipMask0 + a0; + if (aA > 0) + { + float xA = x0; + float yA = y0; + float zA = z0 - (zNMask | 1); + value += (aA * aA) * (aA * aA) * GradCoord(seed, + i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), xA, yA, zA); + } + else + { + float aB = xAFlipMask0 + yAFlipMask0 + a0; + if (aB > 0) + { + float xB = x0 - (xNMask | 1); + float yB = y0 - (yNMask | 1); + float zB = z0; + value += (aB * aB) * (aB * aB) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), xB, yB, zB); + } + + float aC = zAFlipMask1 + a1; + if (aC > 0) + { + float xC = x1; + float yC = y1; + float zC = (zNMask | 1) + z1; + value += (aC * aC) * (aC * aC) * GradCoord(seed2, + i + PrimeX, j + PrimeY, k + (zNMask & (PrimeZ << 1)), xC, yC, zC); + skipD = true; + } + } + + if (!skip5) + { + float a5 = yAFlipMask1 + zAFlipMask1 + a1; + if (a5 > 0) + { + float x5 = x1; + float y5 = (yNMask | 1) + y1; + float z5 = (zNMask | 1) + z1; + value += (a5 * a5) * (a5 * a5) * GradCoord(seed2, + i + PrimeX, j + (yNMask & (PrimeY << 1)), k + (zNMask & (PrimeZ << 1)), x5, y5, z5); + } + } + + if (!skip9) + { + float a9 = xAFlipMask1 + zAFlipMask1 + a1; + if (a9 > 0) + { + float x9 = (xNMask | 1) + x1; + float y9 = y1; + float z9 = (zNMask | 1) + z1; + value += (a9 * a9) * (a9 * a9) * GradCoord(seed2, + i + (xNMask & (PrimeX * 2)), j + PrimeY, k + (zNMask & (PrimeZ << 1)), x9, y9, z9); + } + } + + if (!skipD) + { + float aD = xAFlipMask1 + yAFlipMask1 + a1; + if (aD > 0) + { + float xD = (xNMask | 1) + x1; + float yD = (yNMask | 1) + y1; + float zD = z1; + value += (aD * aD) * (aD * aD) * GradCoord(seed2, + i + (xNMask & (PrimeX << 1)), j + (yNMask & (PrimeY << 1)), k + PrimeZ, xD, yD, zD); + } + } + + return value * 9.046026385208288f; + } + + + // Cellular Noise + + template + float SingleCellular(int seed, FNfloat x, FNfloat y) + { + int xr = FastRound(x); + int yr = FastRound(y); + + float distance0 = 1e10f; + float distance1 = 1e10f; + int closestHash = 0; + + float cellularJitter = 0.43701595f * mCellularJitterModifier; + + int xPrimed = (xr - 1) * PrimeX; + int yPrimedBase = (yr - 1) * PrimeY; + + switch (mCellularDistanceFunction) + { + default: + case CellularDistanceFunction_Euclidean: + case CellularDistanceFunction_EuclideanSq: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + Lookup::RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + Lookup::RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY; + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction_Manhattan: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + Lookup::RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + Lookup::RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = FastAbs(vecX) + FastAbs(vecY); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction_Hybrid: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + Lookup::RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + Lookup::RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = (FastAbs(vecX) + FastAbs(vecY)) + (vecX * vecX + vecY * vecY); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + } + + if (mCellularDistanceFunction == CellularDistanceFunction_Euclidean && mCellularReturnType >= CellularReturnType_Distance) + { + distance0 = FastSqrt(distance0); + + if (mCellularReturnType >= CellularReturnType_Distance2) + { + distance1 = FastSqrt(distance1); + } + } + + switch (mCellularReturnType) + { + case CellularReturnType_CellValue: + return closestHash * (1 / 2147483648.0f); + case CellularReturnType_Distance: + return distance0 - 1; + case CellularReturnType_Distance2: + return distance1 - 1; + case CellularReturnType_Distance2Add: + return (distance1 + distance0) * 0.5f - 1; + case CellularReturnType_Distance2Sub: + return distance1 - distance0 - 1; + case CellularReturnType_Distance2Mul: + return distance1 * distance0 * 0.5f - 1; + case CellularReturnType_Distance2Div: + return distance0 / distance1 - 1; + default: + return 0; + } + } + + template + float SingleCellular(int seed, FNfloat x, FNfloat y, FNfloat z) + { + int xr = FastRound(x); + int yr = FastRound(y); + int zr = FastRound(z); + + float distance0 = 1e10f; + float distance1 = 1e10f; + int closestHash = 0; + + float cellularJitter = 0.39614353f * mCellularJitterModifier; + + int xPrimed = (xr - 1) * PrimeX; + int yPrimedBase = (yr - 1) * PrimeY; + int zPrimedBase = (zr - 1) * PrimeZ; + + switch (mCellularDistanceFunction) + { + case CellularDistanceFunction_Euclidean: + case CellularDistanceFunction_EuclideanSq: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + Lookup::RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + Lookup::RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + Lookup::RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction_Manhattan: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + Lookup::RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + Lookup::RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + Lookup::RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case CellularDistanceFunction_Hybrid: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + Lookup::RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + Lookup::RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + Lookup::RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = (FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + default: + break; + } + + if (mCellularDistanceFunction == CellularDistanceFunction_Euclidean && mCellularReturnType >= CellularReturnType_Distance) + { + distance0 = FastSqrt(distance0); + + if (mCellularReturnType >= CellularReturnType_Distance2) + { + distance1 = FastSqrt(distance1); + } + } + + switch (mCellularReturnType) + { + case CellularReturnType_CellValue: + return closestHash * (1 / 2147483648.0f); + case CellularReturnType_Distance: + return distance0 - 1; + case CellularReturnType_Distance2: + return distance1 - 1; + case CellularReturnType_Distance2Add: + return (distance1 + distance0) * 0.5f - 1; + case CellularReturnType_Distance2Sub: + return distance1 - distance0 - 1; + case CellularReturnType_Distance2Mul: + return distance1 * distance0 * 0.5f - 1; + case CellularReturnType_Distance2Div: + return distance0 / distance1 - 1; + default: + return 0; + } + } + + + // Perlin Noise + + template + float SinglePerlin(int seed, FNfloat x, FNfloat y) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + + float xs = InterpQuintic(xd0); + float ys = InterpQuintic(yd0); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + float xf0 = Lerp(GradCoord(seed, x0, y0, xd0, yd0), GradCoord(seed, x1, y0, xd1, yd0), xs); + float xf1 = Lerp(GradCoord(seed, x0, y1, xd0, yd1), GradCoord(seed, x1, y1, xd1, yd1), xs); + + return Lerp(xf0, xf1, ys) * 1.4247691104677813f; + } + + template + float SinglePerlin(int seed, FNfloat x, FNfloat y, FNfloat z) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + int z0 = FastFloor(z); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float zd0 = (float)(z - z0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + float zd1 = zd0 - 1; + + float xs = InterpQuintic(xd0); + float ys = InterpQuintic(yd0); + float zs = InterpQuintic(zd0); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + float xf00 = Lerp(GradCoord(seed, x0, y0, z0, xd0, yd0, zd0), GradCoord(seed, x1, y0, z0, xd1, yd0, zd0), xs); + float xf10 = Lerp(GradCoord(seed, x0, y1, z0, xd0, yd1, zd0), GradCoord(seed, x1, y1, z0, xd1, yd1, zd0), xs); + float xf01 = Lerp(GradCoord(seed, x0, y0, z1, xd0, yd0, zd1), GradCoord(seed, x1, y0, z1, xd1, yd0, zd1), xs); + float xf11 = Lerp(GradCoord(seed, x0, y1, z1, xd0, yd1, zd1), GradCoord(seed, x1, y1, z1, xd1, yd1, zd1), xs); + + float yf0 = Lerp(xf00, xf10, ys); + float yf1 = Lerp(xf01, xf11, ys); + + return Lerp(yf0, yf1, zs) * 0.964921414852142333984375f; + } + + + // Value Cubic Noise + + template + float SingleValueCubic(int seed, FNfloat x, FNfloat y) + { + int x1 = FastFloor(x); + int y1 = FastFloor(y); + + float xs = (float)(x - x1); + float ys = (float)(y - y1); + + x1 *= PrimeX; + y1 *= PrimeY; + int x0 = x1 - PrimeX; + int y0 = y1 - PrimeY; + int x2 = x1 + PrimeX; + int y2 = y1 + PrimeY; + int x3 = x1 + (int)((long)PrimeX << 1); + int y3 = y1 + (int)((long)PrimeY << 1); + + return CubicLerp( + CubicLerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), ValCoord(seed, x2, y0), ValCoord(seed, x3, y0), + xs), + CubicLerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), ValCoord(seed, x2, y1), ValCoord(seed, x3, y1), + xs), + CubicLerp(ValCoord(seed, x0, y2), ValCoord(seed, x1, y2), ValCoord(seed, x2, y2), ValCoord(seed, x3, y2), + xs), + CubicLerp(ValCoord(seed, x0, y3), ValCoord(seed, x1, y3), ValCoord(seed, x2, y3), ValCoord(seed, x3, y3), + xs), + ys) * (1 / (1.5f * 1.5f)); + } + + template + float SingleValueCubic(int seed, FNfloat x, FNfloat y, FNfloat z) + { + int x1 = FastFloor(x); + int y1 = FastFloor(y); + int z1 = FastFloor(z); + + float xs = (float)(x - x1); + float ys = (float)(y - y1); + float zs = (float)(z - z1); + + x1 *= PrimeX; + y1 *= PrimeY; + z1 *= PrimeZ; + + int x0 = x1 - PrimeX; + int y0 = y1 - PrimeY; + int z0 = z1 - PrimeZ; + int x2 = x1 + PrimeX; + int y2 = y1 + PrimeY; + int z2 = z1 + PrimeZ; + int x3 = x1 + (int)((long)PrimeX << 1); + int y3 = y1 + (int)((long)PrimeY << 1); + int z3 = z1 + (int)((long)PrimeZ << 1); + + + return CubicLerp( + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), ValCoord(seed, x2, y0, z0), ValCoord(seed, x3, y0, z0), xs), + CubicLerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), ValCoord(seed, x2, y1, z0), ValCoord(seed, x3, y1, z0), xs), + CubicLerp(ValCoord(seed, x0, y2, z0), ValCoord(seed, x1, y2, z0), ValCoord(seed, x2, y2, z0), ValCoord(seed, x3, y2, z0), xs), + CubicLerp(ValCoord(seed, x0, y3, z0), ValCoord(seed, x1, y3, z0), ValCoord(seed, x2, y3, z0), ValCoord(seed, x3, y3, z0), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), ValCoord(seed, x2, y0, z1), ValCoord(seed, x3, y0, z1), xs), + CubicLerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), ValCoord(seed, x2, y1, z1), ValCoord(seed, x3, y1, z1), xs), + CubicLerp(ValCoord(seed, x0, y2, z1), ValCoord(seed, x1, y2, z1), ValCoord(seed, x2, y2, z1), ValCoord(seed, x3, y2, z1), xs), + CubicLerp(ValCoord(seed, x0, y3, z1), ValCoord(seed, x1, y3, z1), ValCoord(seed, x2, y3, z1), ValCoord(seed, x3, y3, z1), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z2), ValCoord(seed, x1, y0, z2), ValCoord(seed, x2, y0, z2), ValCoord(seed, x3, y0, z2), xs), + CubicLerp(ValCoord(seed, x0, y1, z2), ValCoord(seed, x1, y1, z2), ValCoord(seed, x2, y1, z2), ValCoord(seed, x3, y1, z2), xs), + CubicLerp(ValCoord(seed, x0, y2, z2), ValCoord(seed, x1, y2, z2), ValCoord(seed, x2, y2, z2), ValCoord(seed, x3, y2, z2), xs), + CubicLerp(ValCoord(seed, x0, y3, z2), ValCoord(seed, x1, y3, z2), ValCoord(seed, x2, y3, z2), ValCoord(seed, x3, y3, z2), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z3), ValCoord(seed, x1, y0, z3), ValCoord(seed, x2, y0, z3), ValCoord(seed, x3, y0, z3), xs), + CubicLerp(ValCoord(seed, x0, y1, z3), ValCoord(seed, x1, y1, z3), ValCoord(seed, x2, y1, z3), ValCoord(seed, x3, y1, z3), xs), + CubicLerp(ValCoord(seed, x0, y2, z3), ValCoord(seed, x1, y2, z3), ValCoord(seed, x2, y2, z3), ValCoord(seed, x3, y2, z3), xs), + CubicLerp(ValCoord(seed, x0, y3, z3), ValCoord(seed, x1, y3, z3), ValCoord(seed, x2, y3, z3), ValCoord(seed, x3, y3, z3), xs), + ys), + zs) * (1 / (1.5f * 1.5f * 1.5f)); + } + + + // Value Noise + + template + float SingleValue(int seed, FNfloat x, FNfloat y) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + + float xs = InterpHermite((float)(x - x0)); + float ys = InterpHermite((float)(y - y0)); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + float xf0 = Lerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), xs); + float xf1 = Lerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), xs); + + return Lerp(xf0, xf1, ys); + } + + template + float SingleValue(int seed, FNfloat x, FNfloat y, FNfloat z) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + int z0 = FastFloor(z); + + float xs = InterpHermite((float)(x - x0)); + float ys = InterpHermite((float)(y - y0)); + float zs = InterpHermite((float)(z - z0)); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + float xf00 = Lerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), xs); + float xf10 = Lerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), xs); + float xf01 = Lerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), xs); + float xf11 = Lerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), xs); + + float yf0 = Lerp(xf00, xf10, ys); + float yf1 = Lerp(xf01, xf11, ys); + + return Lerp(yf0, yf1, zs); + } + + + // Domain Warp + + template + void DoSingleDomainWarp(int seed, float amp, float freq, FNfloat x, FNfloat y, FNfloat& xr, FNfloat& yr) + { + switch (mDomainWarpType) + { + case DomainWarpType_OpenSimplex2: + SingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, xr, yr, false); + break; + case DomainWarpType_OpenSimplex2Reduced: + SingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, xr, yr, true); + break; + case DomainWarpType_BasicGrid: + SingleDomainWarpBasicGrid(seed, amp, freq, x, y, xr, yr); + break; + } + } + + template + void DoSingleDomainWarp(int seed, float amp, float freq, FNfloat x, FNfloat y, FNfloat z, FNfloat& xr, FNfloat& yr, FNfloat& zr) + { + switch (mDomainWarpType) + { + case DomainWarpType_OpenSimplex2: + SingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, xr, yr, zr, false); + break; + case DomainWarpType_OpenSimplex2Reduced: + SingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, xr, yr, zr, true); + break; + case DomainWarpType_BasicGrid: + SingleDomainWarpBasicGrid(seed, amp, freq, x, y, z, xr, yr, zr); + break; + } + } + + + // Domain Warp Single Wrapper + + template + void DomainWarpSingle(FNfloat& x, FNfloat& y) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + FNfloat xs = x; + FNfloat ys = y; + TransformDomainWarpCoordinate(xs, ys); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, x, y); + } + + template + void DomainWarpSingle(FNfloat& x, FNfloat& y, FNfloat& z) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + FNfloat xs = x; + FNfloat ys = y; + FNfloat zs = z; + TransformDomainWarpCoordinate(xs, ys, zs); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, x, y, z); + } + + + // Domain Warp Fractal Progressive + + template + void DomainWarpFractalProgressive(FNfloat& x, FNfloat& y) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + FNfloat xs = x; + FNfloat ys = y; + TransformDomainWarpCoordinate(xs, ys); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, x, y); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + template + void DomainWarpFractalProgressive(FNfloat& x, FNfloat& y, FNfloat& z) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + FNfloat xs = x; + FNfloat ys = y; + FNfloat zs = z; + TransformDomainWarpCoordinate(xs, ys, zs); + + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, x, y, z); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + + // Domain Warp Fractal Independant + + template + void DomainWarpFractalIndependent(FNfloat& x, FNfloat& y) + { + FNfloat xs = x; + FNfloat ys = y; + TransformDomainWarpCoordinate(xs, ys); + + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + DoSingleDomainWarp(seed, amp, freq, xs, ys, x, y); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + template + void DomainWarpFractalIndependent(FNfloat& x, FNfloat& y, FNfloat& z) + { + FNfloat xs = x; + FNfloat ys = y; + FNfloat zs = z; + TransformDomainWarpCoordinate(xs, ys, zs); + + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, x, y, z); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + + // Domain Warp Basic Grid + + template + void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat& xr, FNfloat& yr) + { + FNfloat xf = x * frequency; + FNfloat yf = y * frequency; + + int x0 = FastFloor(xf); + int y0 = FastFloor(yf); + + float xs = InterpHermite((float)(xf - x0)); + float ys = InterpHermite((float)(yf - y0)); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + int hash0 = Hash(seed, x0, y0) & (255 << 1); + int hash1 = Hash(seed, x1, y0) & (255 << 1); + + float lx0x = Lerp(Lookup::RandVecs2D[hash0], Lookup::RandVecs2D[hash1], xs); + float ly0x = Lerp(Lookup::RandVecs2D[hash0 | 1], Lookup::RandVecs2D[hash1 | 1], xs); + + hash0 = Hash(seed, x0, y1) & (255 << 1); + hash1 = Hash(seed, x1, y1) & (255 << 1); + + float lx1x = Lerp(Lookup::RandVecs2D[hash0], Lookup::RandVecs2D[hash1], xs); + float ly1x = Lerp(Lookup::RandVecs2D[hash0 | 1], Lookup::RandVecs2D[hash1 | 1], xs); + + xr += Lerp(lx0x, lx1x, ys) * warpAmp; + yr += Lerp(ly0x, ly1x, ys) * warpAmp; + } + + template + void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat z, FNfloat& xr, FNfloat& yr, FNfloat& zr) + { + FNfloat xf = x * frequency; + FNfloat yf = y * frequency; + FNfloat zf = z * frequency; + + int x0 = FastFloor(xf); + int y0 = FastFloor(yf); + int z0 = FastFloor(zf); + + float xs = InterpHermite((float)(xf - x0)); + float ys = InterpHermite((float)(yf - y0)); + float zs = InterpHermite((float)(zf - z0)); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + int hash0 = Hash(seed, x0, y0, z0) & (255 << 2); + int hash1 = Hash(seed, x1, y0, z0) & (255 << 2); + + float lx0x = Lerp(Lookup::RandVecs3D[hash0], Lookup::RandVecs3D[hash1], xs); + float ly0x = Lerp(Lookup::RandVecs3D[hash0 | 1], Lookup::RandVecs3D[hash1 | 1], xs); + float lz0x = Lerp(Lookup::RandVecs3D[hash0 | 2], Lookup::RandVecs3D[hash1 | 2], xs); + + hash0 = Hash(seed, x0, y1, z0) & (255 << 2); + hash1 = Hash(seed, x1, y1, z0) & (255 << 2); + + float lx1x = Lerp(Lookup::RandVecs3D[hash0], Lookup::RandVecs3D[hash1], xs); + float ly1x = Lerp(Lookup::RandVecs3D[hash0 | 1], Lookup::RandVecs3D[hash1 | 1], xs); + float lz1x = Lerp(Lookup::RandVecs3D[hash0 | 2], Lookup::RandVecs3D[hash1 | 2], xs); + + float lx0y = Lerp(lx0x, lx1x, ys); + float ly0y = Lerp(ly0x, ly1x, ys); + float lz0y = Lerp(lz0x, lz1x, ys); + + hash0 = Hash(seed, x0, y0, z1) & (255 << 2); + hash1 = Hash(seed, x1, y0, z1) & (255 << 2); + + lx0x = Lerp(Lookup::RandVecs3D[hash0], Lookup::RandVecs3D[hash1], xs); + ly0x = Lerp(Lookup::RandVecs3D[hash0 | 1], Lookup::RandVecs3D[hash1 | 1], xs); + lz0x = Lerp(Lookup::RandVecs3D[hash0 | 2], Lookup::RandVecs3D[hash1 | 2], xs); + + hash0 = Hash(seed, x0, y1, z1) & (255 << 2); + hash1 = Hash(seed, x1, y1, z1) & (255 << 2); + + lx1x = Lerp(Lookup::RandVecs3D[hash0], Lookup::RandVecs3D[hash1], xs); + ly1x = Lerp(Lookup::RandVecs3D[hash0 | 1], Lookup::RandVecs3D[hash1 | 1], xs); + lz1x = Lerp(Lookup::RandVecs3D[hash0 | 2], Lookup::RandVecs3D[hash1 | 2], xs); + + xr += Lerp(lx0y, Lerp(lx0x, lx1x, ys), zs) * warpAmp; + yr += Lerp(ly0y, Lerp(ly0x, ly1x, ys), zs) * warpAmp; + zr += Lerp(lz0y, Lerp(lz0x, lz1x, ys), zs) * warpAmp; + } + + + // Domain Warp Simplex/OpenSimplex2 + + template + void SingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat& xr, FNfloat& yr, bool outGradOnly) + { + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + x *= frequency; + y *= frequency; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNfloat F2 = 0.5f * (SQRT3 - 1); + * FNfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PrimeX; + j *= PrimeY; + + float vx, vy; + vx = vy = 0; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i, j, xo, yo); + else + GradCoordDual(seed, i, j, x0, y0, xo, yo); + vx += aaaa * xo; + vy += aaaa * yo; + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c > 0) + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + float cccc = (c * c) * (c * c); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i + PrimeX, j + PrimeY, xo, yo); + else + GradCoordDual(seed, i + PrimeX, j + PrimeY, x2, y2, xo, yo); + vx += cccc * xo; + vy += cccc * yo; + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i, j + PrimeY, xo, yo); + else + GradCoordDual(seed, i, j + PrimeY, x1, y1, xo, yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + GradCoordOut(seed, i + PrimeX, j, xo, yo); + else + GradCoordDual(seed, i + PrimeX, j, x1, y1, xo, yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + + xr += vx * warpAmp; + yr += vy * warpAmp; + } + + template + void SingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat z, FNfloat& xr, FNfloat& yr, FNfloat& zr, bool outGradOnly) + { + x *= frequency; + y *= frequency; + z *= frequency; + + /* + * --- Rotation moved to TransformDomainWarpCoordinate method --- + * const FNfloat R3 = (FNfloat)(2.0 / 3.0); + * FNfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastRound(x); + int j = FastRound(y); + int k = FastRound(z); + float x0 = (float)x - i; + float y0 = (float)y - j; + float z0 = (float)z - k; + + int xNSign = (int)(-x0 - 1.0f) | 1; + int yNSign = (int)(-y0 - 1.0f) | 1; + int zNSign = (int)(-z0 - 1.0f) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + + float vx, vy, vz; + vx = vy = vz = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; l < 2; l++) + { + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo, zo; + if (outGradOnly) + GradCoordOut(seed, i, j, k, xo, yo, zo); + else + GradCoordDual(seed, i, j, k, x0, y0, z0, xo, yo, zo); + vx += aaaa * xo; + vy += aaaa * yo; + vz += aaaa * zo; + } + + float b = a + 1; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b -= xNSign * 2 * x1; + i1 -= xNSign * PrimeX; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b -= yNSign * 2 * y1; + j1 -= yNSign * PrimeY; + } + else + { + z1 += zNSign; + b -= zNSign * 2 * z1; + k1 -= zNSign * PrimeZ; + } + + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo, zo; + if (outGradOnly) + GradCoordOut(seed, i1, j1, k1, xo, yo, zo); + else + GradCoordDual(seed, i1, j1, k1, x1, y1, z1, xo, yo, zo); + vx += bbbb * xo; + vy += bbbb * yo; + vz += bbbb * zo; + } + + if (l == 1) break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PrimeX; + j += (yNSign >> 1) & PrimeY; + k += (zNSign >> 1) & PrimeZ; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + xr += vx * warpAmp; + yr += vy * warpAmp; + zr += vz * warpAmp; + } +}; + +template <> +struct FastNoiseLite::Arguments_must_be_floating_point_values {}; +template <> +struct FastNoiseLite::Arguments_must_be_floating_point_values {}; +template <> +struct FastNoiseLite::Arguments_must_be_floating_point_values {}; + +template +const T FastNoiseLite::Lookup::Gradients2D[] = +{ + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f, + -0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f, +}; + +template +const T FastNoiseLite::Lookup::RandVecs2D[] = +{ + -0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f, + -0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, -0.892300288f, -0.4514423508f, -0.379844434f, -0.9250503802f, -0.9951650832f, 0.0982163789f, 0.7724397808f, -0.6350880136f, 0.7573283322f, -0.6530343002f, -0.9928004525f, -0.119780055f, + -0.0532665713f, 0.9985803285f, 0.9754253726f, -0.2203300762f, -0.7665018163f, 0.6422421394f, 0.991636706f, 0.1290606184f, -0.994696838f, 0.1028503788f, -0.5379205513f, -0.84299554f, 0.5022815471f, -0.8647041387f, 0.4559821461f, -0.8899889226f, + -0.8659131224f, -0.5001944266f, 0.0879458407f, -0.9961252577f, -0.5051684983f, 0.8630207346f, 0.7753185226f, -0.6315704146f, -0.6921944612f, 0.7217110418f, -0.5191659449f, -0.8546734591f, 0.8978622882f, -0.4402764035f, -0.1706774107f, 0.9853269617f, + -0.9353430106f, -0.3537420705f, -0.9992404798f, 0.03896746794f, -0.2882064021f, -0.9575683108f, -0.9663811329f, 0.2571137995f, -0.8759714238f, -0.4823630009f, -0.8303123018f, -0.5572983775f, 0.05110133755f, -0.9986934731f, -0.8558373281f, -0.5172450752f, + 0.09887025282f, 0.9951003332f, 0.9189016087f, 0.3944867976f, -0.2439375892f, -0.9697909324f, -0.8121409387f, -0.5834613061f, -0.9910431363f, 0.1335421355f, 0.8492423985f, -0.5280031709f, -0.9717838994f, -0.2358729591f, 0.9949457207f, 0.1004142068f, + 0.6241065508f, -0.7813392434f, 0.662910307f, 0.7486988212f, -0.7197418176f, 0.6942418282f, -0.8143370775f, -0.5803922158f, 0.104521054f, -0.9945226741f, -0.1065926113f, -0.9943027784f, 0.445799684f, -0.8951327509f, 0.105547406f, 0.9944142724f, + -0.992790267f, 0.1198644477f, -0.8334366408f, 0.552615025f, 0.9115561563f, -0.4111755999f, 0.8285544909f, -0.5599084351f, 0.7217097654f, -0.6921957921f, 0.4940492677f, -0.8694339084f, -0.3652321272f, -0.9309164803f, -0.9696606758f, 0.2444548501f, + 0.08925509731f, -0.996008799f, 0.5354071276f, -0.8445941083f, -0.1053576186f, 0.9944343981f, -0.9890284586f, 0.1477251101f, 0.004856104961f, 0.9999882091f, 0.9885598478f, 0.1508291331f, 0.9286129562f, -0.3710498316f, -0.5832393863f, -0.8123003252f, + 0.3015207509f, 0.9534596146f, -0.9575110528f, 0.2883965738f, 0.9715802154f, -0.2367105511f, 0.229981792f, 0.9731949318f, 0.955763816f, -0.2941352207f, 0.740956116f, 0.6715534485f, -0.9971513787f, -0.07542630764f, 0.6905710663f, -0.7232645452f, + -0.290713703f, -0.9568100872f, 0.5912777791f, -0.8064679708f, -0.9454592212f, -0.325740481f, 0.6664455681f, 0.74555369f, 0.6236134912f, 0.7817328275f, 0.9126993851f, -0.4086316587f, -0.8191762011f, 0.5735419353f, -0.8812745759f, -0.4726046147f, + 0.9953313627f, 0.09651672651f, 0.9855650846f, -0.1692969699f, -0.8495980887f, 0.5274306472f, 0.6174853946f, -0.7865823463f, 0.8508156371f, 0.52546432f, 0.9985032451f, -0.05469249926f, 0.1971371563f, -0.9803759185f, 0.6607855748f, -0.7505747292f, + -0.03097494063f, 0.9995201614f, -0.6731660801f, 0.739491331f, -0.7195018362f, -0.6944905383f, 0.9727511689f, 0.2318515979f, 0.9997059088f, -0.0242506907f, 0.4421787429f, -0.8969269532f, 0.9981350961f, -0.061043673f, -0.9173660799f, -0.3980445648f, + -0.8150056635f, -0.5794529907f, -0.8789331304f, 0.4769450202f, 0.0158605829f, 0.999874213f, -0.8095464474f, 0.5870558317f, -0.9165898907f, -0.3998286786f, -0.8023542565f, 0.5968480938f, -0.5176737917f, 0.8555780767f, -0.8154407307f, -0.5788405779f, + 0.4022010347f, -0.9155513791f, -0.9052556868f, -0.4248672045f, 0.7317445619f, 0.6815789728f, -0.5647632201f, -0.8252529947f, -0.8403276335f, -0.5420788397f, -0.9314281527f, 0.363925262f, 0.5238198472f, 0.8518290719f, 0.7432803869f, -0.6689800195f, + -0.985371561f, -0.1704197369f, 0.4601468731f, 0.88784281f, 0.825855404f, 0.5638819483f, 0.6182366099f, 0.7859920446f, 0.8331502863f, -0.553046653f, 0.1500307506f, 0.9886813308f, -0.662330369f, -0.7492119075f, -0.668598664f, 0.743623444f, + 0.7025606278f, 0.7116238924f, -0.5419389763f, -0.8404178401f, -0.3388616456f, 0.9408362159f, 0.8331530315f, 0.5530425174f, -0.2989720662f, -0.9542618632f, 0.2638522993f, 0.9645630949f, 0.124108739f, -0.9922686234f, -0.7282649308f, -0.6852956957f, + 0.6962500149f, 0.7177993569f, -0.9183535368f, 0.3957610156f, -0.6326102274f, -0.7744703352f, -0.9331891859f, -0.359385508f, -0.1153779357f, -0.9933216659f, 0.9514974788f, -0.3076565421f, -0.08987977445f, -0.9959526224f, 0.6678496916f, 0.7442961705f, + 0.7952400393f, -0.6062947138f, -0.6462007402f, -0.7631674805f, -0.2733598753f, 0.9619118351f, 0.9669590226f, -0.254931851f, -0.9792894595f, 0.2024651934f, -0.5369502995f, -0.8436138784f, -0.270036471f, -0.9628500944f, -0.6400277131f, 0.7683518247f, + -0.7854537493f, -0.6189203566f, 0.06005905383f, -0.9981948257f, -0.02455770378f, 0.9996984141f, -0.65983623f, 0.751409442f, -0.6253894466f, -0.7803127835f, -0.6210408851f, -0.7837781695f, 0.8348888491f, 0.5504185768f, -0.1592275245f, 0.9872419133f, + 0.8367622488f, 0.5475663786f, -0.8675753916f, -0.4973056806f, -0.2022662628f, -0.9793305667f, 0.9399189937f, 0.3413975472f, 0.9877404807f, -0.1561049093f, -0.9034455656f, 0.4287028224f, 0.1269804218f, -0.9919052235f, -0.3819600854f, 0.924178821f, + 0.9754625894f, 0.2201652486f, -0.3204015856f, -0.9472818081f, -0.9874760884f, 0.1577687387f, 0.02535348474f, -0.9996785487f, 0.4835130794f, -0.8753371362f, -0.2850799925f, -0.9585037287f, -0.06805516006f, -0.99768156f, -0.7885244045f, -0.6150034663f, + 0.3185392127f, -0.9479096845f, 0.8880043089f, 0.4598351306f, 0.6476921488f, -0.7619021462f, 0.9820241299f, 0.1887554194f, 0.9357275128f, -0.3527237187f, -0.8894895414f, 0.4569555293f, 0.7922791302f, 0.6101588153f, 0.7483818261f, 0.6632681526f, + -0.7288929755f, -0.6846276581f, 0.8729032783f, -0.4878932944f, 0.8288345784f, 0.5594937369f, 0.08074567077f, 0.9967347374f, 0.9799148216f, -0.1994165048f, -0.580730673f, -0.8140957471f, -0.4700049791f, -0.8826637636f, 0.2409492979f, 0.9705377045f, + 0.9437816757f, -0.3305694308f, -0.8927998638f, -0.4504535528f, -0.8069622304f, 0.5906030467f, 0.06258973166f, 0.9980393407f, -0.9312597469f, 0.3643559849f, 0.5777449785f, 0.8162173362f, -0.3360095855f, -0.941858566f, 0.697932075f, -0.7161639607f, + -0.002008157227f, -0.9999979837f, -0.1827294312f, -0.9831632392f, -0.6523911722f, 0.7578824173f, -0.4302626911f, -0.9027037258f, -0.9985126289f, -0.05452091251f, -0.01028102172f, -0.9999471489f, -0.4946071129f, 0.8691166802f, -0.2999350194f, 0.9539596344f, + 0.8165471961f, 0.5772786819f, 0.2697460475f, 0.962931498f, -0.7306287391f, -0.6827749597f, -0.7590952064f, -0.6509796216f, -0.907053853f, 0.4210146171f, -0.5104861064f, -0.8598860013f, 0.8613350597f, 0.5080373165f, 0.5007881595f, -0.8655698812f, + -0.654158152f, 0.7563577938f, -0.8382755311f, -0.545246856f, 0.6940070834f, 0.7199681717f, 0.06950936031f, 0.9975812994f, 0.1702942185f, -0.9853932612f, 0.2695973274f, 0.9629731466f, 0.5519612192f, -0.8338697815f, 0.225657487f, -0.9742067022f, + 0.4215262855f, -0.9068161835f, 0.4881873305f, -0.8727388672f, -0.3683854996f, -0.9296731273f, -0.9825390578f, 0.1860564427f, 0.81256471f, 0.5828709909f, 0.3196460933f, -0.9475370046f, 0.9570913859f, 0.2897862643f, -0.6876655497f, -0.7260276109f, + -0.9988770922f, -0.047376731f, -0.1250179027f, 0.992154486f, -0.8280133617f, 0.560708367f, 0.9324863769f, -0.3612051451f, 0.6394653183f, 0.7688199442f, -0.01623847064f, -0.9998681473f, -0.9955014666f, -0.09474613458f, -0.81453315f, 0.580117012f, + 0.4037327978f, -0.9148769469f, 0.9944263371f, 0.1054336766f, -0.1624711654f, 0.9867132919f, -0.9949487814f, -0.100383875f, -0.6995302564f, 0.7146029809f, 0.5263414922f, -0.85027327f, -0.5395221479f, 0.841971408f, 0.6579370318f, 0.7530729462f, + 0.01426758847f, -0.9998982128f, -0.6734383991f, 0.7392433447f, 0.639412098f, -0.7688642071f, 0.9211571421f, 0.3891908523f, -0.146637214f, -0.9891903394f, -0.782318098f, 0.6228791163f, -0.5039610839f, -0.8637263605f, -0.7743120191f, -0.6328039957f, +}; + +template +const T FastNoiseLite::Lookup::Gradients3D[] = +{ + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 1, 1, 0, 0, 0,-1, 1, 0, -1, 1, 0, 0, 0,-1,-1, 0 +}; + +template +const T FastNoiseLite::Lookup::RandVecs3D[] = +{ + -0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, -0.2739291014f, 0, 0.7217578935f, 0.6226212466f, -0.3023380997f, 0, 0.565683137f, -0.8208298145f, -0.0790000257f, 0, 0.760049034f, -0.5555979497f, -0.3370999617f, 0, 0.3713945616f, 0.5011264475f, 0.7816254623f, 0, 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0.06555605789f, -0.9774476623f, 0, -0.1148803697f, -0.8044887315f, 0.5827524187f, 0, + -0.7870349638f, 0.03447489231f, 0.6159443543f, 0, -0.2015596421f, 0.6859872284f, 0.6991389226f, 0, -0.08581082512f, -0.10920836f, -0.9903080513f, 0, 0.5532693395f, 0.7325250401f, -0.396610771f, 0, -0.1842489331f, -0.9777375055f, -0.1004076743f, 0, 0.0775473789f, -0.9111505856f, 0.4047110257f, 0, 0.1399838409f, 0.7601631212f, -0.6344734459f, 0, 0.4484419361f, -0.845289248f, 0.2904925424f, 0 +}; + +#endif diff --git a/FastNoise.cpp b/FastNoise.cpp deleted file mode 100644 index 3f88375..0000000 --- a/FastNoise.cpp +++ /dev/null @@ -1,2250 +0,0 @@ -// FastNoise.cpp -// -// MIT License -// -// Copyright(c) 2017 Jordan Peck -// -// Permission is hereby granted, free of charge, to any person obtaining a copy -// of this software and associated documentation files(the "Software"), to deal -// in the Software without restriction, including without limitation the rights -// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell -// copies of the Software, and to permit persons to whom the Software is -// furnished to do so, subject to the following conditions : -// -// The above copyright notice and this permission notice shall be included in all -// copies or substantial portions of the Software. -// -// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE -// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -// SOFTWARE. -// -// The developer's email is jorzixdan.me2@gzixmail.com (for great email, take -// off every 'zix'.) -// - -#include "FastNoise.h" - -#include -#include - -#include -#include - -const FN_DECIMAL GRAD_X[] = -{ - 1, -1, 1, -1, - 1, -1, 1, -1, - 0, 0, 0, 0 -}; -const FN_DECIMAL GRAD_Y[] = -{ - 1, 1, -1, -1, - 0, 0, 0, 0, - 1, -1, 1, -1 -}; -const FN_DECIMAL GRAD_Z[] = -{ - 0, 0, 0, 0, - 1, 1, -1, -1, - 1, 1, -1, -1 -}; - -const FN_DECIMAL GRAD_4D[] = -{ - 0,1,1,1,0,1,1,-1,0,1,-1,1,0,1,-1,-1, - 0,-1,1,1,0,-1,1,-1,0,-1,-1,1,0,-1,-1,-1, - 1,0,1,1,1,0,1,-1,1,0,-1,1,1,0,-1,-1, - -1,0,1,1,-1,0,1,-1,-1,0,-1,1,-1,0,-1,-1, - 1,1,0,1,1,1,0,-1,1,-1,0,1,1,-1,0,-1, - -1,1,0,1,-1,1,0,-1,-1,-1,0,1,-1,-1,0,-1, - 1,1,1,0,1,1,-1,0,1,-1,1,0,1,-1,-1,0, - -1,1,1,0,-1,1,-1,0,-1,-1,1,0,-1,-1,-1,0 -}; - -const FN_DECIMAL VAL_LUT[] = -{ - FN_DECIMAL(0.3490196078), FN_DECIMAL(0.4352941176), FN_DECIMAL(-0.4509803922), FN_DECIMAL(0.6392156863), FN_DECIMAL(0.5843137255), FN_DECIMAL(-0.1215686275), FN_DECIMAL(0.7176470588), FN_DECIMAL(-0.1058823529), FN_DECIMAL(0.3960784314), FN_DECIMAL(0.0431372549), FN_DECIMAL(-0.03529411765), FN_DECIMAL(0.3176470588), FN_DECIMAL(0.7254901961), FN_DECIMAL(0.137254902), FN_DECIMAL(0.8588235294), FN_DECIMAL(-0.8196078431), - FN_DECIMAL(-0.7960784314), FN_DECIMAL(-0.3333333333), FN_DECIMAL(-0.6705882353), FN_DECIMAL(-0.3882352941), FN_DECIMAL(0.262745098), FN_DECIMAL(0.3254901961), FN_DECIMAL(-0.6470588235), FN_DECIMAL(-0.9215686275), FN_DECIMAL(-0.5294117647), FN_DECIMAL(0.5294117647), FN_DECIMAL(-0.4666666667), FN_DECIMAL(0.8117647059), FN_DECIMAL(0.3803921569), FN_DECIMAL(0.662745098), FN_DECIMAL(0.03529411765), FN_DECIMAL(-0.6156862745), - FN_DECIMAL(-0.01960784314), FN_DECIMAL(-0.3568627451), FN_DECIMAL(-0.09019607843), FN_DECIMAL(0.7490196078), FN_DECIMAL(0.8352941176), FN_DECIMAL(-0.4039215686), FN_DECIMAL(-0.7490196078), FN_DECIMAL(0.9529411765), FN_DECIMAL(-0.0431372549), FN_DECIMAL(-0.9294117647), FN_DECIMAL(-0.6549019608), FN_DECIMAL(0.9215686275), FN_DECIMAL(-0.06666666667), FN_DECIMAL(-0.4431372549), FN_DECIMAL(0.4117647059), FN_DECIMAL(-0.4196078431), - FN_DECIMAL(-0.7176470588), FN_DECIMAL(-0.8117647059), FN_DECIMAL(-0.2549019608), FN_DECIMAL(0.4901960784), FN_DECIMAL(0.9137254902), FN_DECIMAL(0.7882352941), FN_DECIMAL(-1.0), FN_DECIMAL(-0.4745098039), FN_DECIMAL(0.7960784314), FN_DECIMAL(0.8509803922), FN_DECIMAL(-0.6784313725), FN_DECIMAL(0.4588235294), FN_DECIMAL(1.0), FN_DECIMAL(-0.1843137255), FN_DECIMAL(0.4509803922), FN_DECIMAL(0.1450980392), - FN_DECIMAL(-0.231372549), FN_DECIMAL(-0.968627451), FN_DECIMAL(-0.8588235294), FN_DECIMAL(0.4274509804), FN_DECIMAL(0.003921568627), FN_DECIMAL(-0.003921568627), FN_DECIMAL(0.2156862745), FN_DECIMAL(0.5058823529), FN_DECIMAL(0.7647058824), FN_DECIMAL(0.2078431373), FN_DECIMAL(-0.5921568627), FN_DECIMAL(0.5764705882), FN_DECIMAL(-0.1921568627), FN_DECIMAL(-0.937254902), FN_DECIMAL(0.08235294118), FN_DECIMAL(-0.08235294118), - FN_DECIMAL(0.9058823529), FN_DECIMAL(0.8274509804), FN_DECIMAL(0.02745098039), FN_DECIMAL(-0.168627451), FN_DECIMAL(-0.7803921569), FN_DECIMAL(0.1137254902), FN_DECIMAL(-0.9450980392), FN_DECIMAL(0.2), FN_DECIMAL(0.01960784314), FN_DECIMAL(0.5607843137), FN_DECIMAL(0.2705882353), FN_DECIMAL(0.4431372549), FN_DECIMAL(-0.9607843137), FN_DECIMAL(0.6156862745), FN_DECIMAL(0.9294117647), FN_DECIMAL(-0.07450980392), - FN_DECIMAL(0.3098039216), FN_DECIMAL(0.9921568627), FN_DECIMAL(-0.9137254902), FN_DECIMAL(-0.2941176471), FN_DECIMAL(-0.3411764706), FN_DECIMAL(-0.6235294118), FN_DECIMAL(-0.7647058824), FN_DECIMAL(-0.8901960784), FN_DECIMAL(0.05882352941), FN_DECIMAL(0.2392156863), FN_DECIMAL(0.7333333333), FN_DECIMAL(0.6549019608), FN_DECIMAL(0.2470588235), FN_DECIMAL(0.231372549), FN_DECIMAL(-0.3960784314), FN_DECIMAL(-0.05098039216), - FN_DECIMAL(-0.2235294118), FN_DECIMAL(-0.3725490196), FN_DECIMAL(0.6235294118), FN_DECIMAL(0.7019607843), FN_DECIMAL(-0.8274509804), FN_DECIMAL(0.4196078431), FN_DECIMAL(0.07450980392), FN_DECIMAL(0.8666666667), FN_DECIMAL(-0.537254902), FN_DECIMAL(-0.5058823529), FN_DECIMAL(-0.8039215686), FN_DECIMAL(0.09019607843), FN_DECIMAL(-0.4823529412), FN_DECIMAL(0.6705882353), FN_DECIMAL(-0.7882352941), FN_DECIMAL(0.09803921569), - FN_DECIMAL(-0.6078431373), FN_DECIMAL(0.8039215686), FN_DECIMAL(-0.6), FN_DECIMAL(-0.3254901961), FN_DECIMAL(-0.4117647059), FN_DECIMAL(-0.01176470588), FN_DECIMAL(0.4823529412), FN_DECIMAL(0.168627451), FN_DECIMAL(0.8745098039), FN_DECIMAL(-0.3647058824), FN_DECIMAL(-0.1607843137), FN_DECIMAL(0.568627451), FN_DECIMAL(-0.9921568627), FN_DECIMAL(0.9450980392), FN_DECIMAL(0.5137254902), FN_DECIMAL(0.01176470588), - FN_DECIMAL(-0.1450980392), FN_DECIMAL(-0.5529411765), FN_DECIMAL(-0.5764705882), FN_DECIMAL(-0.1137254902), FN_DECIMAL(0.5215686275), FN_DECIMAL(0.1607843137), FN_DECIMAL(0.3725490196), FN_DECIMAL(-0.2), FN_DECIMAL(-0.7254901961), FN_DECIMAL(0.631372549), FN_DECIMAL(0.7098039216), FN_DECIMAL(-0.568627451), FN_DECIMAL(0.1294117647), FN_DECIMAL(-0.3098039216), FN_DECIMAL(0.7411764706), FN_DECIMAL(-0.8509803922), - FN_DECIMAL(0.2549019608), FN_DECIMAL(-0.6392156863), FN_DECIMAL(-0.5607843137), FN_DECIMAL(-0.3176470588), FN_DECIMAL(0.937254902), FN_DECIMAL(0.9843137255), FN_DECIMAL(0.5921568627), FN_DECIMAL(0.6941176471), FN_DECIMAL(0.2862745098), FN_DECIMAL(-0.5215686275), FN_DECIMAL(0.1764705882), FN_DECIMAL(0.537254902), FN_DECIMAL(-0.4901960784), FN_DECIMAL(-0.4588235294), FN_DECIMAL(-0.2078431373), FN_DECIMAL(-0.2156862745), - FN_DECIMAL(0.7725490196), FN_DECIMAL(0.3647058824), FN_DECIMAL(-0.2392156863), FN_DECIMAL(0.2784313725), FN_DECIMAL(-0.8823529412), FN_DECIMAL(0.8980392157), FN_DECIMAL(0.1215686275), FN_DECIMAL(0.1058823529), FN_DECIMAL(-0.8745098039), FN_DECIMAL(-0.9843137255), FN_DECIMAL(-0.7019607843), FN_DECIMAL(0.9607843137), FN_DECIMAL(0.2941176471), FN_DECIMAL(0.3411764706), FN_DECIMAL(0.1529411765), FN_DECIMAL(0.06666666667), - FN_DECIMAL(-0.9764705882), FN_DECIMAL(0.3019607843), FN_DECIMAL(0.6470588235), FN_DECIMAL(-0.5843137255), FN_DECIMAL(0.05098039216), FN_DECIMAL(-0.5137254902), FN_DECIMAL(-0.137254902), FN_DECIMAL(0.3882352941), FN_DECIMAL(-0.262745098), FN_DECIMAL(-0.3019607843), FN_DECIMAL(-0.1764705882), FN_DECIMAL(-0.7568627451), FN_DECIMAL(0.1843137255), FN_DECIMAL(-0.5450980392), FN_DECIMAL(-0.4980392157), FN_DECIMAL(-0.2784313725), - FN_DECIMAL(-0.9529411765), FN_DECIMAL(-0.09803921569), FN_DECIMAL(0.8901960784), FN_DECIMAL(-0.2862745098), FN_DECIMAL(-0.3803921569), FN_DECIMAL(0.5529411765), FN_DECIMAL(0.7803921569), FN_DECIMAL(-0.8352941176), FN_DECIMAL(0.6862745098), FN_DECIMAL(0.7568627451), FN_DECIMAL(0.4980392157), FN_DECIMAL(-0.6862745098), FN_DECIMAL(-0.8980392157), FN_DECIMAL(-0.7725490196), FN_DECIMAL(-0.7098039216), FN_DECIMAL(-0.2470588235), - FN_DECIMAL(-0.9058823529), FN_DECIMAL(0.9764705882), FN_DECIMAL(0.1921568627), FN_DECIMAL(0.8431372549), FN_DECIMAL(-0.05882352941), FN_DECIMAL(0.3568627451), FN_DECIMAL(0.6078431373), FN_DECIMAL(0.5450980392), FN_DECIMAL(0.4039215686), FN_DECIMAL(-0.7333333333), FN_DECIMAL(-0.4274509804), FN_DECIMAL(0.6), FN_DECIMAL(0.6784313725), FN_DECIMAL(-0.631372549), FN_DECIMAL(-0.02745098039), FN_DECIMAL(-0.1294117647), - FN_DECIMAL(0.3333333333), FN_DECIMAL(-0.8431372549), FN_DECIMAL(0.2235294118), FN_DECIMAL(-0.3490196078), FN_DECIMAL(-0.6941176471), FN_DECIMAL(0.8823529412), FN_DECIMAL(0.4745098039), FN_DECIMAL(0.4666666667), FN_DECIMAL(-0.7411764706), FN_DECIMAL(-0.2705882353), FN_DECIMAL(0.968627451), FN_DECIMAL(0.8196078431), FN_DECIMAL(-0.662745098), FN_DECIMAL(-0.4352941176), FN_DECIMAL(-0.8666666667), FN_DECIMAL(-0.1529411765), -}; - -const FN_DECIMAL CELL_2D_X[] = -{ - FN_DECIMAL(-0.6440658039), FN_DECIMAL(-0.08028078721), FN_DECIMAL(0.9983546168), FN_DECIMAL(0.9869492062), FN_DECIMAL(0.9284746418), FN_DECIMAL(0.6051097552), FN_DECIMAL(-0.794167404), FN_DECIMAL(-0.3488667991), FN_DECIMAL(-0.943136526), FN_DECIMAL(-0.9968171318), FN_DECIMAL(0.8740961579), FN_DECIMAL(0.1421139764), FN_DECIMAL(0.4282553608), FN_DECIMAL(-0.9986665833), FN_DECIMAL(0.9996760121), FN_DECIMAL(-0.06248383632), - FN_DECIMAL(0.7120139305), FN_DECIMAL(0.8917660409), FN_DECIMAL(0.1094842955), FN_DECIMAL(-0.8730880804), FN_DECIMAL(0.2594811489), FN_DECIMAL(-0.6690063346), FN_DECIMAL(-0.9996834972), FN_DECIMAL(-0.8803608671), FN_DECIMAL(-0.8166554937), FN_DECIMAL(0.8955599676), FN_DECIMAL(-0.9398321388), FN_DECIMAL(0.07615451399), FN_DECIMAL(-0.7147270565), FN_DECIMAL(0.8707354457), FN_DECIMAL(-0.9580008579), FN_DECIMAL(0.4905965632), - FN_DECIMAL(0.786775944), FN_DECIMAL(0.1079711577), FN_DECIMAL(0.2686638979), FN_DECIMAL(0.6113487322), FN_DECIMAL(-0.530770584), FN_DECIMAL(-0.7837268286), FN_DECIMAL(-0.8558691039), FN_DECIMAL(-0.5726093896), FN_DECIMAL(-0.9830740914), FN_DECIMAL(0.7087766359), FN_DECIMAL(0.6807027153), FN_DECIMAL(-0.08864708788), FN_DECIMAL(0.6704485923), FN_DECIMAL(-0.1350735482), FN_DECIMAL(-0.9381333003), FN_DECIMAL(0.9756655376), - FN_DECIMAL(0.4231433671), FN_DECIMAL(-0.4959787385), FN_DECIMAL(0.1005554325), FN_DECIMAL(-0.7645857281), FN_DECIMAL(-0.5859053796), FN_DECIMAL(-0.9751154306), FN_DECIMAL(-0.6972258572), FN_DECIMAL(0.7907012002), FN_DECIMAL(-0.9109899213), FN_DECIMAL(-0.9584307894), FN_DECIMAL(-0.8269529333), FN_DECIMAL(0.2608264719), FN_DECIMAL(-0.7773760119), FN_DECIMAL(0.7606456974), FN_DECIMAL(-0.8961083758), FN_DECIMAL(-0.9838134719), - FN_DECIMAL(0.7338893576), FN_DECIMAL(0.2161226729), FN_DECIMAL(0.673509891), FN_DECIMAL(-0.5512056873), FN_DECIMAL(0.6899744332), FN_DECIMAL(0.868004831), FN_DECIMAL(0.5897430311), FN_DECIMAL(-0.8950444221), FN_DECIMAL(-0.3595752773), FN_DECIMAL(0.8209486981), FN_DECIMAL(-0.2912360132), FN_DECIMAL(-0.9965011374), FN_DECIMAL(0.9766994634), FN_DECIMAL(0.738790822), FN_DECIMAL(-0.4730947722), FN_DECIMAL(0.8946479441), - FN_DECIMAL(-0.6943628971), FN_DECIMAL(-0.6620468182), FN_DECIMAL(-0.0887255502), FN_DECIMAL(-0.7512250855), FN_DECIMAL(-0.5322986898), FN_DECIMAL(0.5226295385), FN_DECIMAL(0.2296318375), FN_DECIMAL(0.7915307344), FN_DECIMAL(-0.2756485999), FN_DECIMAL(-0.6900234522), FN_DECIMAL(0.07090588086), FN_DECIMAL(0.5981278485), FN_DECIMAL(0.3033429312), FN_DECIMAL(-0.7253142797), FN_DECIMAL(-0.9855874307), FN_DECIMAL(-0.1761843396), - FN_DECIMAL(-0.6438468325), FN_DECIMAL(-0.9956136595), FN_DECIMAL(0.8541580762), FN_DECIMAL(-0.9999807666), FN_DECIMAL(-0.02152416253), FN_DECIMAL(-0.8705983095), FN_DECIMAL(-0.1197138014), FN_DECIMAL(-0.992107781), FN_DECIMAL(-0.9091181546), FN_DECIMAL(0.788610536), FN_DECIMAL(-0.994636402), FN_DECIMAL(0.4211256853), FN_DECIMAL(0.3110430857), FN_DECIMAL(-0.4031127839), FN_DECIMAL(0.7610684239), FN_DECIMAL(0.7685674467), - FN_DECIMAL(0.152271555), FN_DECIMAL(-0.9364648723), FN_DECIMAL(0.1681333739), FN_DECIMAL(-0.3567427907), FN_DECIMAL(-0.418445483), FN_DECIMAL(-0.98774778), FN_DECIMAL(0.8705250765), FN_DECIMAL(-0.8911701067), FN_DECIMAL(-0.7315350966), FN_DECIMAL(0.6030885658), FN_DECIMAL(-0.4149130821), FN_DECIMAL(0.7585339481), FN_DECIMAL(0.6963196535), FN_DECIMAL(0.8332685012), FN_DECIMAL(-0.8086815232), FN_DECIMAL(0.7518116724), - FN_DECIMAL(-0.3490535894), FN_DECIMAL(0.6972110903), FN_DECIMAL(-0.8795676928), FN_DECIMAL(-0.6442331882), FN_DECIMAL(0.6610236811), FN_DECIMAL(-0.9853565782), FN_DECIMAL(-0.590338458), FN_DECIMAL(0.09843602117), FN_DECIMAL(0.5646534882), FN_DECIMAL(-0.6023259233), FN_DECIMAL(-0.3539248861), FN_DECIMAL(0.5132728656), FN_DECIMAL(0.9380385118), FN_DECIMAL(-0.7599270056), FN_DECIMAL(-0.7425936564), FN_DECIMAL(-0.6679610562), - FN_DECIMAL(-0.3018497816), FN_DECIMAL(0.814478266), FN_DECIMAL(0.03777430269), FN_DECIMAL(-0.7514235086), FN_DECIMAL(0.9662556939), FN_DECIMAL(-0.4720194901), FN_DECIMAL(-0.435054126), FN_DECIMAL(0.7091901235), FN_DECIMAL(0.929379209), FN_DECIMAL(0.9997434357), FN_DECIMAL(0.8306320299), FN_DECIMAL(-0.9434019629), FN_DECIMAL(-0.133133759), FN_DECIMAL(0.5048413216), FN_DECIMAL(0.3711995273), FN_DECIMAL(0.98552091), - FN_DECIMAL(0.7401857005), FN_DECIMAL(-0.9999981398), FN_DECIMAL(-0.2144033253), FN_DECIMAL(0.4808624681), FN_DECIMAL(-0.413835885), FN_DECIMAL(0.644229305), FN_DECIMAL(0.9626648696), FN_DECIMAL(0.1833665934), FN_DECIMAL(0.5794129), FN_DECIMAL(0.01404446873), FN_DECIMAL(0.4388494993), FN_DECIMAL(0.5213612322), FN_DECIMAL(-0.5281609948), FN_DECIMAL(-0.9745306846), FN_DECIMAL(-0.9904373013), FN_DECIMAL(0.9100232252), - FN_DECIMAL(-0.9914057719), FN_DECIMAL(0.7892627765), FN_DECIMAL(0.3364421659), FN_DECIMAL(-0.9416099764), FN_DECIMAL(0.7802732656), FN_DECIMAL(0.886302871), FN_DECIMAL(0.6524471291), FN_DECIMAL(0.5762186726), FN_DECIMAL(-0.08987644664), FN_DECIMAL(-0.2177026782), FN_DECIMAL(-0.9720345052), FN_DECIMAL(-0.05722538858), FN_DECIMAL(0.8105983127), FN_DECIMAL(0.3410261032), FN_DECIMAL(0.6452309645), FN_DECIMAL(-0.7810612152), - FN_DECIMAL(0.9989395718), FN_DECIMAL(-0.808247815), FN_DECIMAL(0.6370177929), FN_DECIMAL(0.5844658772), FN_DECIMAL(0.2054070861), FN_DECIMAL(0.055960522), FN_DECIMAL(-0.995827561), FN_DECIMAL(0.893409165), FN_DECIMAL(-0.931516824), FN_DECIMAL(0.328969469), FN_DECIMAL(-0.3193837488), FN_DECIMAL(0.7314755657), FN_DECIMAL(-0.7913517714), FN_DECIMAL(-0.2204109786), FN_DECIMAL(0.9955900414), FN_DECIMAL(-0.7112353139), - FN_DECIMAL(-0.7935008741), FN_DECIMAL(-0.9961918204), FN_DECIMAL(-0.9714163995), FN_DECIMAL(-0.9566188669), FN_DECIMAL(0.2748495632), FN_DECIMAL(-0.4681743221), FN_DECIMAL(-0.9614449642), FN_DECIMAL(0.585194072), FN_DECIMAL(0.4532946061), FN_DECIMAL(-0.9916113176), FN_DECIMAL(0.942479587), FN_DECIMAL(-0.9813704753), FN_DECIMAL(-0.6538429571), FN_DECIMAL(0.2923335053), FN_DECIMAL(-0.2246660704), FN_DECIMAL(-0.1800781949), - FN_DECIMAL(-0.9581216256), FN_DECIMAL(0.552215082), FN_DECIMAL(-0.9296791922), FN_DECIMAL(0.643183699), FN_DECIMAL(0.9997325981), FN_DECIMAL(-0.4606920354), FN_DECIMAL(-0.2148721265), FN_DECIMAL(0.3482070809), FN_DECIMAL(0.3075517813), FN_DECIMAL(0.6274756393), FN_DECIMAL(0.8910881765), FN_DECIMAL(-0.6397771309), FN_DECIMAL(-0.4479080125), FN_DECIMAL(-0.5247665011), FN_DECIMAL(-0.8386507094), FN_DECIMAL(0.3901291416), - FN_DECIMAL(0.1458336921), FN_DECIMAL(0.01624613149), FN_DECIMAL(-0.8273199879), FN_DECIMAL(0.5611100679), FN_DECIMAL(-0.8380219841), FN_DECIMAL(-0.9856122234), FN_DECIMAL(-0.861398618), FN_DECIMAL(0.6398413916), FN_DECIMAL(0.2694510795), FN_DECIMAL(0.4327334514), FN_DECIMAL(-0.9960265354), FN_DECIMAL(-0.939570655), FN_DECIMAL(-0.8846996446), FN_DECIMAL(0.7642113189), FN_DECIMAL(-0.7002080528), FN_DECIMAL(0.664508256), -}; -const FN_DECIMAL CELL_2D_Y[] = -{ - FN_DECIMAL(0.7649700911), FN_DECIMAL(0.9967722885), FN_DECIMAL(0.05734160033), FN_DECIMAL(-0.1610318741), FN_DECIMAL(0.371395799), FN_DECIMAL(-0.7961420628), FN_DECIMAL(0.6076990492), FN_DECIMAL(-0.9371723195), FN_DECIMAL(0.3324056156), FN_DECIMAL(0.07972205329), FN_DECIMAL(-0.4857529277), FN_DECIMAL(-0.9898503007), FN_DECIMAL(0.9036577593), FN_DECIMAL(0.05162417479), FN_DECIMAL(-0.02545330525), FN_DECIMAL(-0.998045976), - FN_DECIMAL(-0.7021653386), FN_DECIMAL(-0.4524967717), FN_DECIMAL(-0.9939885256), FN_DECIMAL(-0.4875625128), FN_DECIMAL(-0.9657481729), FN_DECIMAL(-0.7432567015), FN_DECIMAL(0.02515761212), FN_DECIMAL(0.4743044842), FN_DECIMAL(0.5771254669), FN_DECIMAL(0.4449408324), FN_DECIMAL(0.3416365773), FN_DECIMAL(0.9970960285), FN_DECIMAL(0.6994034849), FN_DECIMAL(0.4917517499), FN_DECIMAL(0.286765333), FN_DECIMAL(0.8713868327), - FN_DECIMAL(0.6172387009), FN_DECIMAL(0.9941540269), FN_DECIMAL(0.9632339851), FN_DECIMAL(-0.7913613129), FN_DECIMAL(0.847515538), FN_DECIMAL(0.6211056739), FN_DECIMAL(0.5171924952), FN_DECIMAL(-0.8198283277), FN_DECIMAL(-0.1832084353), FN_DECIMAL(0.7054329737), FN_DECIMAL(0.7325597678), FN_DECIMAL(0.9960630973), FN_DECIMAL(0.7419559859), FN_DECIMAL(0.9908355749), FN_DECIMAL(-0.346274329), FN_DECIMAL(0.2192641299), - FN_DECIMAL(-0.9060627411), FN_DECIMAL(-0.8683346653), FN_DECIMAL(0.9949314574), FN_DECIMAL(-0.6445220433), FN_DECIMAL(-0.8103794704), FN_DECIMAL(-0.2216977607), FN_DECIMAL(0.7168515217), FN_DECIMAL(0.612202264), FN_DECIMAL(-0.412428616), FN_DECIMAL(0.285325116), FN_DECIMAL(0.56227115), FN_DECIMAL(-0.9653857009), FN_DECIMAL(-0.6290361962), FN_DECIMAL(0.6491672535), FN_DECIMAL(0.443835306), FN_DECIMAL(-0.1791955706), - FN_DECIMAL(-0.6792690269), FN_DECIMAL(-0.9763662173), FN_DECIMAL(0.7391782104), FN_DECIMAL(0.8343693968), FN_DECIMAL(0.7238337389), FN_DECIMAL(0.4965557504), FN_DECIMAL(0.8075909592), FN_DECIMAL(-0.4459769977), FN_DECIMAL(-0.9331160806), FN_DECIMAL(-0.5710019572), FN_DECIMAL(0.9566512346), FN_DECIMAL(-0.08357920318), FN_DECIMAL(0.2146116448), FN_DECIMAL(-0.6739348049), FN_DECIMAL(0.8810115417), FN_DECIMAL(0.4467718167), - FN_DECIMAL(-0.7196250184), FN_DECIMAL(-0.749462481), FN_DECIMAL(0.9960561112), FN_DECIMAL(0.6600461127), FN_DECIMAL(-0.8465566164), FN_DECIMAL(-0.8525598897), FN_DECIMAL(-0.9732775654), FN_DECIMAL(0.6111293616), FN_DECIMAL(-0.9612584717), FN_DECIMAL(-0.7237870097), FN_DECIMAL(-0.9974830104), FN_DECIMAL(-0.8014006968), FN_DECIMAL(0.9528814544), FN_DECIMAL(-0.6884178931), FN_DECIMAL(-0.1691668301), FN_DECIMAL(0.9843571905), - FN_DECIMAL(0.7651544003), FN_DECIMAL(-0.09355982605), FN_DECIMAL(-0.5200134429), FN_DECIMAL(-0.006202125807), FN_DECIMAL(-0.9997683284), FN_DECIMAL(0.4919944954), FN_DECIMAL(-0.9928084436), FN_DECIMAL(-0.1253880012), FN_DECIMAL(-0.4165383308), FN_DECIMAL(-0.6148930171), FN_DECIMAL(-0.1034332049), FN_DECIMAL(-0.9070022917), FN_DECIMAL(-0.9503958117), FN_DECIMAL(0.9151503065), FN_DECIMAL(-0.6486716073), FN_DECIMAL(0.6397687707), - FN_DECIMAL(-0.9883386937), FN_DECIMAL(0.3507613761), FN_DECIMAL(0.9857642561), FN_DECIMAL(-0.9342026446), FN_DECIMAL(-0.9082419159), FN_DECIMAL(0.1560587169), FN_DECIMAL(0.4921240607), FN_DECIMAL(-0.453669308), FN_DECIMAL(0.6818037859), FN_DECIMAL(0.7976742329), FN_DECIMAL(0.9098610522), FN_DECIMAL(0.651633524), FN_DECIMAL(0.7177318024), FN_DECIMAL(-0.5528685241), FN_DECIMAL(0.5882467118), FN_DECIMAL(0.6593778956), - FN_DECIMAL(0.9371027648), FN_DECIMAL(-0.7168658839), FN_DECIMAL(-0.4757737632), FN_DECIMAL(0.7648291307), FN_DECIMAL(0.7503650398), FN_DECIMAL(0.1705063456), FN_DECIMAL(-0.8071558121), FN_DECIMAL(-0.9951433815), FN_DECIMAL(-0.8253280792), FN_DECIMAL(-0.7982502628), FN_DECIMAL(0.9352738503), FN_DECIMAL(0.8582254747), FN_DECIMAL(-0.3465310238), FN_DECIMAL(0.65000842), FN_DECIMAL(-0.6697422351), FN_DECIMAL(0.7441962291), - FN_DECIMAL(-0.9533555), FN_DECIMAL(0.5801940659), FN_DECIMAL(-0.9992862963), FN_DECIMAL(-0.659820211), FN_DECIMAL(0.2575848092), FN_DECIMAL(0.881588113), FN_DECIMAL(-0.9004043022), FN_DECIMAL(-0.7050172826), FN_DECIMAL(0.369126382), FN_DECIMAL(-0.02265088836), FN_DECIMAL(0.5568217228), FN_DECIMAL(-0.3316515286), FN_DECIMAL(0.991098079), FN_DECIMAL(-0.863212164), FN_DECIMAL(-0.9285531277), FN_DECIMAL(0.1695539323), - FN_DECIMAL(-0.672402505), FN_DECIMAL(-0.001928841934), FN_DECIMAL(0.9767452145), FN_DECIMAL(-0.8767960349), FN_DECIMAL(0.9103515037), FN_DECIMAL(-0.7648324016), FN_DECIMAL(0.2706960452), FN_DECIMAL(-0.9830446035), FN_DECIMAL(0.8150341657), FN_DECIMAL(-0.9999013716), FN_DECIMAL(-0.8985605806), FN_DECIMAL(0.8533360801), FN_DECIMAL(0.8491442537), FN_DECIMAL(-0.2242541966), FN_DECIMAL(-0.1379635899), FN_DECIMAL(-0.4145572694), - FN_DECIMAL(0.1308227633), FN_DECIMAL(0.6140555916), FN_DECIMAL(0.9417041303), FN_DECIMAL(-0.336705587), FN_DECIMAL(-0.6254387508), FN_DECIMAL(0.4631060578), FN_DECIMAL(-0.7578342456), FN_DECIMAL(-0.8172955655), FN_DECIMAL(-0.9959529228), FN_DECIMAL(-0.9760151351), FN_DECIMAL(0.2348380732), FN_DECIMAL(-0.9983612848), FN_DECIMAL(0.5856025746), FN_DECIMAL(-0.9400538266), FN_DECIMAL(-0.7639875669), FN_DECIMAL(0.6244544645), - FN_DECIMAL(0.04604054566), FN_DECIMAL(0.5888424828), FN_DECIMAL(0.7708490978), FN_DECIMAL(-0.8114182882), FN_DECIMAL(0.9786766212), FN_DECIMAL(-0.9984329822), FN_DECIMAL(0.09125496582), FN_DECIMAL(-0.4492438803), FN_DECIMAL(-0.3636982357), FN_DECIMAL(0.9443405575), FN_DECIMAL(-0.9476254645), FN_DECIMAL(-0.6818676535), FN_DECIMAL(-0.6113610831), FN_DECIMAL(0.9754070948), FN_DECIMAL(-0.0938108173), FN_DECIMAL(-0.7029540015), - FN_DECIMAL(-0.6085691109), FN_DECIMAL(-0.08718862881), FN_DECIMAL(-0.237381926), FN_DECIMAL(0.2913423132), FN_DECIMAL(0.9614872426), FN_DECIMAL(0.8836361266), FN_DECIMAL(-0.2749974196), FN_DECIMAL(-0.8108932717), FN_DECIMAL(-0.8913607575), FN_DECIMAL(0.129255541), FN_DECIMAL(-0.3342637104), FN_DECIMAL(-0.1921249337), FN_DECIMAL(-0.7566302845), FN_DECIMAL(-0.9563164339), FN_DECIMAL(-0.9744358146), FN_DECIMAL(0.9836522982), - FN_DECIMAL(-0.2863615732), FN_DECIMAL(0.8337016872), FN_DECIMAL(0.3683701937), FN_DECIMAL(0.7657119102), FN_DECIMAL(-0.02312427772), FN_DECIMAL(0.8875600535), FN_DECIMAL(0.976642191), FN_DECIMAL(0.9374176384), FN_DECIMAL(0.9515313457), FN_DECIMAL(-0.7786361937), FN_DECIMAL(-0.4538302125), FN_DECIMAL(-0.7685604874), FN_DECIMAL(-0.8940796454), FN_DECIMAL(-0.8512462154), FN_DECIMAL(0.5446696133), FN_DECIMAL(0.9207601495), - FN_DECIMAL(-0.9893091197), FN_DECIMAL(-0.9998680229), FN_DECIMAL(0.5617309299), FN_DECIMAL(-0.8277411985), FN_DECIMAL(0.545636467), FN_DECIMAL(0.1690223212), FN_DECIMAL(-0.5079295433), FN_DECIMAL(0.7685069899), FN_DECIMAL(-0.9630140787), FN_DECIMAL(0.9015219132), FN_DECIMAL(0.08905695279), FN_DECIMAL(-0.3423550559), FN_DECIMAL(-0.4661614943), FN_DECIMAL(-0.6449659371), FN_DECIMAL(0.7139388509), FN_DECIMAL(0.7472809229), -}; -const FN_DECIMAL CELL_3D_X[] = -{ - FN_DECIMAL(0.3752498686), FN_DECIMAL(0.687188096), FN_DECIMAL(0.2248135212), FN_DECIMAL(0.6692006647), FN_DECIMAL(-0.4376476931), FN_DECIMAL(0.6139972552), FN_DECIMAL(0.9494563929), FN_DECIMAL(0.8065108882), FN_DECIMAL(-0.2218812853), FN_DECIMAL(0.8484661167), FN_DECIMAL(0.5551817596), FN_DECIMAL(0.2133903499), FN_DECIMAL(0.5195126593), FN_DECIMAL(-0.6440141975), FN_DECIMAL(-0.5192897331), FN_DECIMAL(-0.3697654077), - FN_DECIMAL(-0.07927779647), FN_DECIMAL(0.4187757321), FN_DECIMAL(-0.750078731), FN_DECIMAL(0.6579554632), FN_DECIMAL(-0.6859803838), FN_DECIMAL(-0.6878407087), FN_DECIMAL(0.9490848347), FN_DECIMAL(0.5795829433), FN_DECIMAL(-0.5325976529), FN_DECIMAL(-0.1363699466), FN_DECIMAL(0.417665879), FN_DECIMAL(-0.9108236468), FN_DECIMAL(0.4438605427), FN_DECIMAL(0.819294887), FN_DECIMAL(-0.4033873915), FN_DECIMAL(-0.2817317705), - FN_DECIMAL(0.3969665622), FN_DECIMAL(0.5323450134), FN_DECIMAL(-0.6833017297), FN_DECIMAL(0.3881436661), FN_DECIMAL(-0.7119144767), FN_DECIMAL(-0.2306979838), FN_DECIMAL(-0.9398873022), FN_DECIMAL(0.1701906676), FN_DECIMAL(-0.4261839496), FN_DECIMAL(-0.003712295499), FN_DECIMAL(-0.734675004), FN_DECIMAL(-0.3195046015), FN_DECIMAL(0.7345307424), FN_DECIMAL(0.9766246496), FN_DECIMAL(-0.02003735175), FN_DECIMAL(-0.4824156342), - FN_DECIMAL(0.4245892007), FN_DECIMAL(0.9072427669), FN_DECIMAL(0.593346808), FN_DECIMAL(-0.8911762541), FN_DECIMAL(-0.7657571834), FN_DECIMAL(-0.5268198896), FN_DECIMAL(-0.8801903279), FN_DECIMAL(-0.6296409617), FN_DECIMAL(-0.09492481344), FN_DECIMAL(-0.4920470525), FN_DECIMAL(0.7307666154), FN_DECIMAL(-0.2514540636), FN_DECIMAL(-0.3356210347), FN_DECIMAL(-0.3522787894), FN_DECIMAL(0.87847885), FN_DECIMAL(-0.7424096346), - FN_DECIMAL(0.5757585274), FN_DECIMAL(0.4519299338), FN_DECIMAL(0.6420368628), FN_DECIMAL(-0.1128478447), FN_DECIMAL(0.499874883), FN_DECIMAL(0.5291681739), FN_DECIMAL(-0.5098837195), FN_DECIMAL(0.5639583502), FN_DECIMAL(-0.8456386526), FN_DECIMAL(-0.9657134875), FN_DECIMAL(-0.576437342), FN_DECIMAL(-0.5666013014), FN_DECIMAL(0.5667702405), FN_DECIMAL(-0.481316582), FN_DECIMAL(0.7313389916), FN_DECIMAL(-0.3805628566), - FN_DECIMAL(-0.6512675909), FN_DECIMAL(-0.2787156951), FN_DECIMAL(0.8648059114), FN_DECIMAL(-0.9730216276), FN_DECIMAL(-0.8335820906), FN_DECIMAL(0.2673159641), FN_DECIMAL(0.231150148), FN_DECIMAL(0.01286214638), FN_DECIMAL(0.6774953261), FN_DECIMAL(0.6542885718), FN_DECIMAL(-0.02545450161), FN_DECIMAL(0.2101238586), FN_DECIMAL(-0.5572105885), FN_DECIMAL(0.813705672), FN_DECIMAL(-0.7546026951), FN_DECIMAL(-0.2502500006), - FN_DECIMAL(-0.9979289381), FN_DECIMAL(0.7024037039), FN_DECIMAL(0.08990874624), FN_DECIMAL(0.8170812432), FN_DECIMAL(0.4226980265), FN_DECIMAL(-0.2442153475), FN_DECIMAL(-0.9183326731), FN_DECIMAL(0.6068222411), FN_DECIMAL(0.818676691), FN_DECIMAL(-0.7236735282), FN_DECIMAL(-0.5383903295), FN_DECIMAL(-0.6269337242), FN_DECIMAL(-0.0939331121), FN_DECIMAL(0.9203878539), FN_DECIMAL(-0.7256396824), FN_DECIMAL(0.6292431149), - FN_DECIMAL(0.4234156978), FN_DECIMAL(0.006685688024), FN_DECIMAL(-0.2598694113), FN_DECIMAL(0.6408036421), FN_DECIMAL(0.05899871622), FN_DECIMAL(0.7090281418), FN_DECIMAL(-0.5905222072), FN_DECIMAL(0.3128214264), FN_DECIMAL(-0.691925826), FN_DECIMAL(0.3634019349), FN_DECIMAL(-0.6772511147), FN_DECIMAL(-0.3204583896), FN_DECIMAL(-0.3906740409), FN_DECIMAL(-0.3342190395), FN_DECIMAL(-0.517779592), FN_DECIMAL(-0.6817711267), - FN_DECIMAL(0.6422383105), FN_DECIMAL(0.4388482478), FN_DECIMAL(0.2968562611), FN_DECIMAL(-0.2019778353), FN_DECIMAL(0.6014865048), FN_DECIMAL(0.9519280722), FN_DECIMAL(0.3398889569), FN_DECIMAL(0.8179709354), FN_DECIMAL(0.2365522154), FN_DECIMAL(0.3262175096), FN_DECIMAL(-0.8060715954), FN_DECIMAL(-0.2068642503), FN_DECIMAL(0.6208057279), FN_DECIMAL(-0.5274282502), FN_DECIMAL(-0.3722334928), FN_DECIMAL(-0.8923412971), - FN_DECIMAL(0.5341834201), FN_DECIMAL(-0.3663701513), FN_DECIMAL(-0.6114600319), FN_DECIMAL(0.5026307556), FN_DECIMAL(0.8396151729), FN_DECIMAL(0.9245042467), FN_DECIMAL(-0.7994843957), FN_DECIMAL(-0.5357200589), FN_DECIMAL(-0.6283359739), FN_DECIMAL(-0.61351886), FN_DECIMAL(-0.875632008), FN_DECIMAL(-0.5278879423), FN_DECIMAL(0.9087491985), FN_DECIMAL(-0.03500215466), FN_DECIMAL(-0.261365798), FN_DECIMAL(-0.579523541), - FN_DECIMAL(-0.3765052689), FN_DECIMAL(-0.74398252), FN_DECIMAL(0.4257318052), FN_DECIMAL(-0.1214508921), FN_DECIMAL(0.8561809753), FN_DECIMAL(0.6802835104), FN_DECIMAL(-0.5452131039), FN_DECIMAL(-0.1997156478), FN_DECIMAL(0.4562348357), FN_DECIMAL(-0.811704301), FN_DECIMAL(0.67793962), FN_DECIMAL(-0.9237819106), FN_DECIMAL(0.6973511259), FN_DECIMAL(-0.5189506), FN_DECIMAL(0.5517320032), FN_DECIMAL(-0.396710831), - FN_DECIMAL(0.5493762815), FN_DECIMAL(-0.2507853002), FN_DECIMAL(0.4788634005), FN_DECIMAL(0.387333516), FN_DECIMAL(-0.2176515694), FN_DECIMAL(0.6749832419), FN_DECIMAL(0.2148283022), FN_DECIMAL(-0.7521815872), FN_DECIMAL(0.4697000159), FN_DECIMAL(0.7890593699), FN_DECIMAL(-0.7606162952), FN_DECIMAL(0.01083397843), FN_DECIMAL(0.5254091908), FN_DECIMAL(-0.6748025877), FN_DECIMAL(0.751091524), FN_DECIMAL(0.05259056135), - FN_DECIMAL(0.01889481232), FN_DECIMAL(-0.6037423727), FN_DECIMAL(-0.6542965129), FN_DECIMAL(0.08873301081), FN_DECIMAL(-0.6191345671), FN_DECIMAL(0.4331858488), FN_DECIMAL(-0.3858351946), FN_DECIMAL(-0.1429059747), FN_DECIMAL(0.4118221036), FN_DECIMAL(-0.6247153214), FN_DECIMAL(-0.611423014), FN_DECIMAL(0.5542939606), FN_DECIMAL(-0.9432768808), FN_DECIMAL(-0.4567870451), FN_DECIMAL(-0.7349133547), FN_DECIMAL(0.399304489), - FN_DECIMAL(-0.7474927672), FN_DECIMAL(0.02589419753), FN_DECIMAL(0.783915821), FN_DECIMAL(0.6138668752), FN_DECIMAL(0.4276376047), FN_DECIMAL(-0.4347886353), FN_DECIMAL(0.02947841302), FN_DECIMAL(-0.833742746), FN_DECIMAL(0.3817221742), FN_DECIMAL(-0.8743368359), FN_DECIMAL(-0.3823443796), FN_DECIMAL(-0.6829243811), FN_DECIMAL(-0.3681903049), FN_DECIMAL(-0.367626833), FN_DECIMAL(-0.434583373), FN_DECIMAL(0.235891995), - FN_DECIMAL(-0.6874880269), FN_DECIMAL(-0.5115661773), FN_DECIMAL(-0.5534962601), FN_DECIMAL(0.5632777056), FN_DECIMAL(0.686191532), FN_DECIMAL(-0.05095871588), FN_DECIMAL(-0.06865785057), FN_DECIMAL(-0.5975288531), FN_DECIMAL(-0.6429790056), FN_DECIMAL(-0.3729361548), FN_DECIMAL(0.2237917666), FN_DECIMAL(0.6046773225), FN_DECIMAL(-0.5041542295), FN_DECIMAL(-0.03972191174), FN_DECIMAL(0.7028828406), FN_DECIMAL(-0.5560856498), - FN_DECIMAL(0.5898328456), FN_DECIMAL(-0.9308076766), FN_DECIMAL(0.4617069864), FN_DECIMAL(0.3190983137), FN_DECIMAL(0.9116567753), FN_DECIMAL(-0.45029554), FN_DECIMAL(0.3346334459), FN_DECIMAL(0.8525005645), FN_DECIMAL(0.2528483381), FN_DECIMAL(-0.8306630147), FN_DECIMAL(-0.6880390622), FN_DECIMAL(0.7448684026), FN_DECIMAL(-0.1963355843), FN_DECIMAL(-0.5900257974), FN_DECIMAL(0.9097057294), FN_DECIMAL(-0.2509196808), -}; -const FN_DECIMAL CELL_3D_Y[] = -{ - FN_DECIMAL(-0.6760585049), FN_DECIMAL(-0.09136176499), FN_DECIMAL(0.1681325679), FN_DECIMAL(-0.6688468686), FN_DECIMAL(-0.4822753902), FN_DECIMAL(-0.7891068824), FN_DECIMAL(-0.1877509944), FN_DECIMAL(0.548470914), FN_DECIMAL(-0.463339443), FN_DECIMAL(-0.4050542082), FN_DECIMAL(0.3218158513), FN_DECIMAL(0.2546493823), FN_DECIMAL(-0.3753271935), FN_DECIMAL(0.4745384887), FN_DECIMAL(0.481254652), FN_DECIMAL(-0.8934416489), - FN_DECIMAL(-0.6737085076), FN_DECIMAL(0.7469917228), FN_DECIMAL(0.3826230411), FN_DECIMAL(0.6751013678), FN_DECIMAL(-0.7248119515), FN_DECIMAL(-0.3224276742), FN_DECIMAL(-0.02076190936), FN_DECIMAL(-0.6404268166), FN_DECIMAL(-0.5292028444), FN_DECIMAL(0.7151414636), FN_DECIMAL(-0.6144655059), FN_DECIMAL(-0.369912124), FN_DECIMAL(0.6942067212), FN_DECIMAL(-0.4481558248), FN_DECIMAL(-0.6366894559), FN_DECIMAL(0.5956568471), - FN_DECIMAL(0.564274539), FN_DECIMAL(0.7145584688), FN_DECIMAL(0.6871918316), FN_DECIMAL(0.5657918509), FN_DECIMAL(-0.6275978114), FN_DECIMAL(0.4146983062), FN_DECIMAL(0.2638993789), FN_DECIMAL(-0.792633138), FN_DECIMAL(0.5706133514), FN_DECIMAL(0.8606546462), FN_DECIMAL(0.6490900316), FN_DECIMAL(-0.8242699196), FN_DECIMAL(0.6765819124), FN_DECIMAL(0.1959534069), FN_DECIMAL(-0.8426769757), FN_DECIMAL(-0.5917672797), - FN_DECIMAL(0.7517364266), FN_DECIMAL(0.03252559226), FN_DECIMAL(0.0883617105), FN_DECIMAL(0.4475064813), FN_DECIMAL(-0.1418643552), FN_DECIMAL(0.7343428473), FN_DECIMAL(0.3870192548), FN_DECIMAL(-0.7716703522), FN_DECIMAL(0.4839898327), FN_DECIMAL(0.7437439055), FN_DECIMAL(-0.5989573348), FN_DECIMAL(-0.8357068955), FN_DECIMAL(0.6086049038), FN_DECIMAL(0.9194627258), FN_DECIMAL(0.4718297238), FN_DECIMAL(-0.2650335884), - FN_DECIMAL(-0.6470352599), FN_DECIMAL(-0.5555181303), FN_DECIMAL(0.1222351235), FN_DECIMAL(0.7802044684), FN_DECIMAL(-0.8636947022), FN_DECIMAL(-0.2341352163), FN_DECIMAL(0.683030874), FN_DECIMAL(-0.5005858287), FN_DECIMAL(0.2334616211), FN_DECIMAL(0.2576877608), FN_DECIMAL(0.6666816727), FN_DECIMAL(-0.7663996863), FN_DECIMAL(0.794201982), FN_DECIMAL(0.6189308788), FN_DECIMAL(0.6071033261), FN_DECIMAL(-0.4206058253), - FN_DECIMAL(-0.3957336915), FN_DECIMAL(-0.8170257484), FN_DECIMAL(-0.1043240417), FN_DECIMAL(0.0002167596213), FN_DECIMAL(0.1816339018), FN_DECIMAL(-0.6838094939), FN_DECIMAL(-0.2495341969), FN_DECIMAL(-0.7116756954), FN_DECIMAL(-0.03361673621), FN_DECIMAL(-0.3350836431), FN_DECIMAL(0.2137186039), FN_DECIMAL(0.2557996786), FN_DECIMAL(0.7490117093), FN_DECIMAL(0.4942936549), FN_DECIMAL(-0.352686853), FN_DECIMAL(-0.3952445435), - FN_DECIMAL(-0.0459964767), FN_DECIMAL(-0.7115787471), FN_DECIMAL(0.08022899756), FN_DECIMAL(0.5362268157), FN_DECIMAL(-0.8258613686), FN_DECIMAL(0.1114171723), FN_DECIMAL(0.3882823051), FN_DECIMAL(-0.7915404457), FN_DECIMAL(0.3250957662), FN_DECIMAL(0.6401346464), FN_DECIMAL(-0.2662724517), FN_DECIMAL(-0.6727907114), FN_DECIMAL(-0.994730818), FN_DECIMAL(-0.3596358977), FN_DECIMAL(0.2344610069), FN_DECIMAL(-0.6645215546), - FN_DECIMAL(-0.7107590611), FN_DECIMAL(-0.4646617327), FN_DECIMAL(0.6717191355), FN_DECIMAL(0.5101893498), FN_DECIMAL(0.1185768238), FN_DECIMAL(0.236005093), FN_DECIMAL(-0.7811024061), FN_DECIMAL(0.5089325193), FN_DECIMAL(0.6073187658), FN_DECIMAL(-0.7930732557), FN_DECIMAL(-0.6822767155), FN_DECIMAL(0.3201532885), FN_DECIMAL(0.7545302807), FN_DECIMAL(0.1072664448), FN_DECIMAL(0.6784033173), FN_DECIMAL(-0.6595924967), - FN_DECIMAL(0.7276509498), FN_DECIMAL(0.5586689436), FN_DECIMAL(-0.6498636788), FN_DECIMAL(0.6789333174), FN_DECIMAL(0.7105966551), FN_DECIMAL(-0.2872214155), FN_DECIMAL(0.496746217), FN_DECIMAL(-0.3880337977), FN_DECIMAL(0.7324070604), FN_DECIMAL(-0.9326634749), FN_DECIMAL(-0.5867839255), FN_DECIMAL(0.8003043651), FN_DECIMAL(-0.1631882481), FN_DECIMAL(-0.6796374681), FN_DECIMAL(-0.8066678503), FN_DECIMAL(0.4238177418), - FN_DECIMAL(0.7715863549), FN_DECIMAL(0.5455367347), FN_DECIMAL(-0.03205115397), FN_DECIMAL(-0.6005545066), FN_DECIMAL(-0.5423640002), FN_DECIMAL(0.3569205906), FN_DECIMAL(-0.582071752), FN_DECIMAL(0.6407354361), FN_DECIMAL(0.7777142984), FN_DECIMAL(-0.09956428618), FN_DECIMAL(0.1100002681), FN_DECIMAL(0.8136349123), FN_DECIMAL(0.2923431904), FN_DECIMAL(0.9735794425), FN_DECIMAL(0.8324974864), FN_DECIMAL(-0.6179617717), - FN_DECIMAL(-0.9248386523), FN_DECIMAL(-0.6448780771), FN_DECIMAL(-0.5274402761), FN_DECIMAL(-0.7862170565), FN_DECIMAL(0.2682099744), FN_DECIMAL(-0.5848777694), FN_DECIMAL(-0.6364561467), FN_DECIMAL(-0.7167402514), FN_DECIMAL(-0.8677012494), FN_DECIMAL(0.4205286707), FN_DECIMAL(-0.7007832749), FN_DECIMAL(0.243272451), FN_DECIMAL(-0.1899846085), FN_DECIMAL(-0.6146124977), FN_DECIMAL(-0.8093357692), FN_DECIMAL(-0.03545096987), - FN_DECIMAL(-0.7191590868), FN_DECIMAL(0.7478645848), FN_DECIMAL(0.3623517328), FN_DECIMAL(0.8436992512), FN_DECIMAL(-0.2445711729), FN_DECIMAL(0.6897356637), FN_DECIMAL(-0.1708070787), FN_DECIMAL(0.4639272368), FN_DECIMAL(-0.7917186656), FN_DECIMAL(0.02980025428), FN_DECIMAL(0.6334156172), FN_DECIMAL(-0.9815544807), FN_DECIMAL(-0.2307217304), FN_DECIMAL(0.1080823318), FN_DECIMAL(0.5167601798), FN_DECIMAL(-0.845120016), - FN_DECIMAL(0.441572562), FN_DECIMAL(0.5876789172), FN_DECIMAL(-0.6365908737), FN_DECIMAL(0.68350166), FN_DECIMAL(0.5849723959), FN_DECIMAL(0.1164114357), FN_DECIMAL(-0.7379813884), FN_DECIMAL(-0.9613237178), FN_DECIMAL(-0.9071943084), FN_DECIMAL(-0.7682111105), FN_DECIMAL(0.639074459), FN_DECIMAL(-0.619358298), FN_DECIMAL(0.2807257131), FN_DECIMAL(-0.01800868791), FN_DECIMAL(0.3776607289), FN_DECIMAL(0.7207567823), - FN_DECIMAL(0.5536661486), FN_DECIMAL(-0.9974053117), FN_DECIMAL(-0.02047200006), FN_DECIMAL(-0.6739453804), FN_DECIMAL(-0.5607471297), FN_DECIMAL(0.8815553192), FN_DECIMAL(0.8275977415), FN_DECIMAL(0.3928902456), FN_DECIMAL(0.550991396), FN_DECIMAL(0.4247623676), FN_DECIMAL(-0.3436948871), FN_DECIMAL(-0.3653537677), FN_DECIMAL(0.3181702902), FN_DECIMAL(-0.6067173171), FN_DECIMAL(-0.8984128477), FN_DECIMAL(0.4220839766), - FN_DECIMAL(0.7238407199), FN_DECIMAL(-0.7766913695), FN_DECIMAL(0.6460037842), FN_DECIMAL(0.2544775664), FN_DECIMAL(0.6488840578), FN_DECIMAL(0.805016833), FN_DECIMAL(-0.9183807036), FN_DECIMAL(0.4144046357), FN_DECIMAL(0.270587208), FN_DECIMAL(-0.8813684494), FN_DECIMAL(0.6985971877), FN_DECIMAL(-0.7795603017), FN_DECIMAL(-0.8624480731), FN_DECIMAL(0.5532697017), FN_DECIMAL(0.711179521), FN_DECIMAL(-0.7798160574), - FN_DECIMAL(0.5225859041), FN_DECIMAL(0.1261859368), FN_DECIMAL(0.3398033582), FN_DECIMAL(-0.7472173667), FN_DECIMAL(-0.4032647119), FN_DECIMAL(-0.4246578154), FN_DECIMAL(0.8481212377), FN_DECIMAL(-0.2144838537), FN_DECIMAL(0.3431714491), FN_DECIMAL(0.5310188231), FN_DECIMAL(0.6682978632), FN_DECIMAL(0.3110433206), FN_DECIMAL(0.9263293599), FN_DECIMAL(-0.6155600569), FN_DECIMAL(0.07169784399), FN_DECIMAL(0.8985888773), -}; -const FN_DECIMAL CELL_3D_Z[] = -{ - FN_DECIMAL(-0.6341391283), FN_DECIMAL(-0.7207118346), FN_DECIMAL(0.9597866014), FN_DECIMAL(0.3237504235), FN_DECIMAL(-0.7588642466), FN_DECIMAL(-0.01782410481), FN_DECIMAL(0.2515593809), FN_DECIMAL(0.2207257205), FN_DECIMAL(-0.8579541106), FN_DECIMAL(0.3406410681), FN_DECIMAL(0.7669470462), FN_DECIMAL(-0.9431957648), FN_DECIMAL(0.7676171537), FN_DECIMAL(-0.6000491115), FN_DECIMAL(-0.7062096948), FN_DECIMAL(0.2550207115), - FN_DECIMAL(0.7347325213), FN_DECIMAL(0.5163625202), FN_DECIMAL(-0.5394270162), FN_DECIMAL(0.3336656285), FN_DECIMAL(-0.0638635111), FN_DECIMAL(-0.6503195787), FN_DECIMAL(0.3143356798), FN_DECIMAL(-0.5039217245), FN_DECIMAL(0.6605180464), FN_DECIMAL(-0.6855479011), FN_DECIMAL(-0.6693185756), FN_DECIMAL(0.1832083647), FN_DECIMAL(-0.5666258437), FN_DECIMAL(0.3576482138), FN_DECIMAL(-0.6571949095), FN_DECIMAL(-0.7522101635), - FN_DECIMAL(-0.7238865886), FN_DECIMAL(0.4538887323), FN_DECIMAL(0.2467106257), FN_DECIMAL(0.7274778869), FN_DECIMAL(0.3151170655), FN_DECIMAL(-0.8802293764), FN_DECIMAL(-0.2167232729), FN_DECIMAL(0.5854637865), FN_DECIMAL(0.7019741052), FN_DECIMAL(0.5091756071), FN_DECIMAL(0.1973189533), FN_DECIMAL(0.46743546), FN_DECIMAL(0.05197599597), FN_DECIMAL(0.088354718), FN_DECIMAL(0.5380464843), FN_DECIMAL(-0.6458224544), - FN_DECIMAL(-0.5045952393), FN_DECIMAL(0.419347884), FN_DECIMAL(0.8000823542), FN_DECIMAL(-0.07445020656), FN_DECIMAL(-0.6272881641), FN_DECIMAL(-0.428020311), FN_DECIMAL(-0.2747382083), FN_DECIMAL(-0.08987283726), FN_DECIMAL(0.8699098354), FN_DECIMAL(0.4524761885), FN_DECIMAL(-0.3274603257), FN_DECIMAL(0.4882262167), FN_DECIMAL(-0.7189983256), FN_DECIMAL(0.1746079907), FN_DECIMAL(0.0751772698), FN_DECIMAL(-0.6152927202), - FN_DECIMAL(0.4998474673), FN_DECIMAL(-0.6979677227), FN_DECIMAL(0.7568667263), FN_DECIMAL(-0.6152612058), FN_DECIMAL(0.06447140991), FN_DECIMAL(-0.8155744872), FN_DECIMAL(-0.5229602449), FN_DECIMAL(0.6567836838), FN_DECIMAL(-0.4799905631), FN_DECIMAL(0.03153534591), FN_DECIMAL(0.4724992466), FN_DECIMAL(-0.3026458097), FN_DECIMAL(-0.2191225827), FN_DECIMAL(-0.620692287), FN_DECIMAL(0.3107552588), FN_DECIMAL(0.8235670294), - FN_DECIMAL(0.6474915988), FN_DECIMAL(-0.5047637941), FN_DECIMAL(0.4911488878), FN_DECIMAL(-0.2307138167), FN_DECIMAL(-0.5216800015), FN_DECIMAL(0.6789305939), FN_DECIMAL(0.9403734863), FN_DECIMAL(0.702390397), FN_DECIMAL(0.7347584625), FN_DECIMAL(0.6779567958), FN_DECIMAL(0.9765635805), FN_DECIMAL(-0.9436177661), FN_DECIMAL(-0.358465925), FN_DECIMAL(-0.3058706624), FN_DECIMAL(0.5533414464), FN_DECIMAL(-0.8838306897), - FN_DECIMAL(0.04496841812), FN_DECIMAL(0.01687374963), FN_DECIMAL(-0.9927133148), FN_DECIMAL(-0.211752318), FN_DECIMAL(0.3732015249), FN_DECIMAL(0.9632990593), FN_DECIMAL(-0.07682417004), FN_DECIMAL(-0.07232213047), FN_DECIMAL(0.4733721775), FN_DECIMAL(0.2579229713), FN_DECIMAL(0.7995216286), FN_DECIMAL(0.3928189967), FN_DECIMAL(0.04107517667), FN_DECIMAL(0.1534542912), FN_DECIMAL(0.6468965045), FN_DECIMAL(0.4030684878), - FN_DECIMAL(-0.5617300988), FN_DECIMAL(-0.885463029), FN_DECIMAL(0.693729985), FN_DECIMAL(-0.5736527866), FN_DECIMAL(-0.9911905409), FN_DECIMAL(-0.66451538), FN_DECIMAL(0.2028855685), FN_DECIMAL(0.8019541421), FN_DECIMAL(-0.3903877149), FN_DECIMAL(-0.4888495114), FN_DECIMAL(-0.2753714057), FN_DECIMAL(-0.8915202143), FN_DECIMAL(0.5273119089), FN_DECIMAL(0.9363714773), FN_DECIMAL(-0.5212228249), FN_DECIMAL(-0.31642672), - FN_DECIMAL(0.2409440761), FN_DECIMAL(-0.703776404), FN_DECIMAL(-0.6996810411), FN_DECIMAL(-0.7058714505), FN_DECIMAL(-0.3650566783), FN_DECIMAL(0.1064744278), FN_DECIMAL(0.7985729102), FN_DECIMAL(0.424680257), FN_DECIMAL(-0.6384535592), FN_DECIMAL(0.1540161646), FN_DECIMAL(-0.07702731943), FN_DECIMAL(-0.5627789132), FN_DECIMAL(-0.7667919169), FN_DECIMAL(-0.509815999), FN_DECIMAL(0.4590525092), FN_DECIMAL(0.1552595611), - FN_DECIMAL(0.345402042), FN_DECIMAL(0.7537656024), FN_DECIMAL(0.7906259247), FN_DECIMAL(-0.6218493452), FN_DECIMAL(0.02979350071), FN_DECIMAL(-0.1337893489), FN_DECIMAL(-0.1483818606), FN_DECIMAL(0.549965562), FN_DECIMAL(0.01882482408), FN_DECIMAL(-0.7833783002), FN_DECIMAL(0.4702855809), FN_DECIMAL(0.2435827372), FN_DECIMAL(0.2978428332), FN_DECIMAL(0.2256499906), FN_DECIMAL(0.4885036897), FN_DECIMAL(0.5312962584), - FN_DECIMAL(0.05401156992), FN_DECIMAL(0.1749922158), FN_DECIMAL(-0.7352273018), FN_DECIMAL(0.6058980284), FN_DECIMAL(0.4416079111), FN_DECIMAL(0.4417378638), FN_DECIMAL(0.5455879807), FN_DECIMAL(-0.6681295324), FN_DECIMAL(0.1973431441), FN_DECIMAL(0.4053292055), FN_DECIMAL(0.2220375492), FN_DECIMAL(0.2957118467), FN_DECIMAL(0.6910913512), FN_DECIMAL(0.5940890106), FN_DECIMAL(-0.2014135283), FN_DECIMAL(-0.9172588213), - FN_DECIMAL(-0.4254361401), FN_DECIMAL(-0.6146586825), FN_DECIMAL(-0.7996193253), FN_DECIMAL(-0.3716777111), FN_DECIMAL(-0.9448876842), FN_DECIMAL(-0.2620349924), FN_DECIMAL(0.9615995749), FN_DECIMAL(-0.4679683524), FN_DECIMAL(0.3905937144), FN_DECIMAL(0.613593722), FN_DECIMAL(0.1422937358), FN_DECIMAL(0.1908754211), FN_DECIMAL(0.8189704912), FN_DECIMAL(-0.7300408736), FN_DECIMAL(-0.4108776451), FN_DECIMAL(-0.5319834504), - FN_DECIMAL(-0.8970265651), FN_DECIMAL(-0.5386359045), FN_DECIMAL(0.4082255906), FN_DECIMAL(0.7245356676), FN_DECIMAL(0.5239080873), FN_DECIMAL(-0.8937552226), FN_DECIMAL(-0.553637673), FN_DECIMAL(0.2354455182), FN_DECIMAL(-0.0860293075), FN_DECIMAL(-0.1399373318), FN_DECIMAL(-0.4666323327), FN_DECIMAL(0.5560157407), FN_DECIMAL(0.1772619533), FN_DECIMAL(-0.8893937725), FN_DECIMAL(-0.5632714576), FN_DECIMAL(-0.5666264959), - FN_DECIMAL(-0.3670263736), FN_DECIMAL(-0.06717242579), FN_DECIMAL(0.6205295181), FN_DECIMAL(-0.4110536264), FN_DECIMAL(0.7090054553), FN_DECIMAL(0.183899597), FN_DECIMAL(-0.5605470555), FN_DECIMAL(0.3879565548), FN_DECIMAL(0.7420893903), FN_DECIMAL(-0.2347595118), FN_DECIMAL(-0.8577217497), FN_DECIMAL(0.6325590203), FN_DECIMAL(-0.8736152276), FN_DECIMAL(0.7048011129), FN_DECIMAL(-0.06317948268), FN_DECIMAL(0.8753285574), - FN_DECIMAL(-0.05843650473), FN_DECIMAL(-0.3674922622), FN_DECIMAL(-0.5256624401), FN_DECIMAL(0.7861039337), FN_DECIMAL(0.3287714416), FN_DECIMAL(0.5910593099), FN_DECIMAL(-0.3896960134), FN_DECIMAL(0.6864605361), FN_DECIMAL(0.7164918431), FN_DECIMAL(-0.290014277), FN_DECIMAL(-0.6796169617), FN_DECIMAL(0.1632515592), FN_DECIMAL(0.04485347486), FN_DECIMAL(0.8320545697), FN_DECIMAL(0.01339408056), FN_DECIMAL(-0.2874989857), - FN_DECIMAL(0.615630723), FN_DECIMAL(0.3430367014), FN_DECIMAL(0.8193658136), FN_DECIMAL(-0.5829600957), FN_DECIMAL(0.07911697781), FN_DECIMAL(0.7854296063), FN_DECIMAL(-0.4107442306), FN_DECIMAL(0.4766964066), FN_DECIMAL(-0.9045999527), FN_DECIMAL(-0.1673856787), FN_DECIMAL(0.2828077348), FN_DECIMAL(-0.5902737632), FN_DECIMAL(-0.321506229), FN_DECIMAL(-0.5224513133), FN_DECIMAL(-0.4090169985), FN_DECIMAL(-0.3599685311), -}; - -static int FastFloor(FN_DECIMAL f) { return (f >= 0 ? (int)f : (int)f - 1); } -static int FastRound(FN_DECIMAL f) { return (f >= 0) ? (int)(f + FN_DECIMAL(0.5)) : (int)(f - FN_DECIMAL(0.5)); } -static int FastAbs(int i) { return abs(i); } -static FN_DECIMAL FastAbs(FN_DECIMAL f) { return fabs(f); } -static FN_DECIMAL Lerp(FN_DECIMAL a, FN_DECIMAL b, FN_DECIMAL t) { return a + t * (b - a); } -static FN_DECIMAL InterpHermiteFunc(FN_DECIMAL t) { return t*t*(3 - 2 * t); } -static FN_DECIMAL InterpQuinticFunc(FN_DECIMAL t) { return t*t*t*(t*(t * 6 - 15) + 10); } -static FN_DECIMAL CubicLerp(FN_DECIMAL a, FN_DECIMAL b, FN_DECIMAL c, FN_DECIMAL d, FN_DECIMAL t) -{ - FN_DECIMAL p = (d - c) - (a - b); - return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b; -} - -void FastNoise::SetSeed(int seed) -{ - m_seed = seed; - - std::mt19937_64 gen(seed); - - for (int i = 0; i < 256; i++) - m_perm[i] = i; - - for (int j = 0; j < 256; j++) - { - int rng = (int)(gen() % (256 - j)); - int k = rng + j; - int l = m_perm[j]; - m_perm[j] = m_perm[j + 256] = m_perm[k]; - m_perm[k] = l; - m_perm12[j] = m_perm12[j + 256] = m_perm[j] % 12; - } -} - -void FastNoise::CalculateFractalBounding() -{ - FN_DECIMAL amp = m_gain; - FN_DECIMAL ampFractal = 1.0f; - for (int i = 1; i < m_octaves; i++) - { - ampFractal += amp; - amp *= m_gain; - } - m_fractalBounding = 1.0f / ampFractal; -} - -void FastNoise::SetCellularDistance2Indices(int cellularDistanceIndex0, int cellularDistanceIndex1) -{ - m_cellularDistanceIndex0 = std::min(cellularDistanceIndex0, cellularDistanceIndex1); - m_cellularDistanceIndex1 = std::max(cellularDistanceIndex0, cellularDistanceIndex1); - - m_cellularDistanceIndex0 = std::min(std::max(m_cellularDistanceIndex0, 0), FN_CELLULAR_INDEX_MAX); - m_cellularDistanceIndex1 = std::min(std::max(m_cellularDistanceIndex1, 0), FN_CELLULAR_INDEX_MAX); -} - -void FastNoise::GetCellularDistance2Indices(int& cellularDistanceIndex0, int& cellularDistanceIndex1) const -{ - cellularDistanceIndex0 = m_cellularDistanceIndex0; - cellularDistanceIndex1 = m_cellularDistanceIndex1; -} - -unsigned char FastNoise::Index2D_12(unsigned char offset, int x, int y) const -{ - return m_perm12[(x & 0xff) + m_perm[(y & 0xff) + offset]]; -} -unsigned char FastNoise::Index3D_12(unsigned char offset, int x, int y, int z) const -{ - return m_perm12[(x & 0xff) + m_perm[(y & 0xff) + m_perm[(z & 0xff) + offset]]]; -} -unsigned char FastNoise::Index4D_32(unsigned char offset, int x, int y, int z, int w) const -{ - return m_perm[(x & 0xff) + m_perm[(y & 0xff) + m_perm[(z & 0xff) + m_perm[(w & 0xff) + offset]]]] & 31; -} -unsigned char FastNoise::Index2D_256(unsigned char offset, int x, int y) const -{ - return m_perm[(x & 0xff) + m_perm[(y & 0xff) + offset]]; -} -unsigned char FastNoise::Index3D_256(unsigned char offset, int x, int y, int z) const -{ - return m_perm[(x & 0xff) + m_perm[(y & 0xff) + m_perm[(z & 0xff) + offset]]]; -} -unsigned char FastNoise::Index4D_256(unsigned char offset, int x, int y, int z, int w) const -{ - return m_perm[(x & 0xff) + m_perm[(y & 0xff) + m_perm[(z & 0xff) + m_perm[(w & 0xff) + offset]]]]; -} - -// Hashing -#define X_PRIME 1619 -#define Y_PRIME 31337 -#define Z_PRIME 6971 -#define W_PRIME 1013 - -static FN_DECIMAL ValCoord2D(int seed, int x, int y) -{ - int n = seed; - n ^= X_PRIME * x; - n ^= Y_PRIME * y; - - return (n * n * n * 60493) / FN_DECIMAL(2147483648); -} -static FN_DECIMAL ValCoord3D(int seed, int x, int y, int z) -{ - int n = seed; - n ^= X_PRIME * x; - n ^= Y_PRIME * y; - n ^= Z_PRIME * z; - - return (n * n * n * 60493) / FN_DECIMAL(2147483648); -} -static FN_DECIMAL ValCoord4D(int seed, int x, int y, int z, int w) -{ - int n = seed; - n ^= X_PRIME * x; - n ^= Y_PRIME * y; - n ^= Z_PRIME * z; - n ^= W_PRIME * w; - - return (n * n * n * 60493) / FN_DECIMAL(2147483648); -} - -FN_DECIMAL FastNoise::ValCoord2DFast(unsigned char offset, int x, int y) const -{ - return VAL_LUT[Index2D_256(offset, x, y)]; -} -FN_DECIMAL FastNoise::ValCoord3DFast(unsigned char offset, int x, int y, int z) const -{ - return VAL_LUT[Index3D_256(offset, x, y, z)]; -} - -FN_DECIMAL FastNoise::GradCoord2D(unsigned char offset, int x, int y, FN_DECIMAL xd, FN_DECIMAL yd) const -{ - unsigned char lutPos = Index2D_12(offset, x, y); - - return xd*GRAD_X[lutPos] + yd*GRAD_Y[lutPos]; -} -FN_DECIMAL FastNoise::GradCoord3D(unsigned char offset, int x, int y, int z, FN_DECIMAL xd, FN_DECIMAL yd, FN_DECIMAL zd) const -{ - unsigned char lutPos = Index3D_12(offset, x, y, z); - - return xd*GRAD_X[lutPos] + yd*GRAD_Y[lutPos] + zd*GRAD_Z[lutPos]; -} -FN_DECIMAL FastNoise::GradCoord4D(unsigned char offset, int x, int y, int z, int w, FN_DECIMAL xd, FN_DECIMAL yd, FN_DECIMAL zd, FN_DECIMAL wd) const -{ - unsigned char lutPos = Index4D_32(offset, x, y, z, w) << 2; - - return xd*GRAD_4D[lutPos] + yd*GRAD_4D[lutPos + 1] + zd*GRAD_4D[lutPos + 2] + wd*GRAD_4D[lutPos + 3]; -} - -FN_DECIMAL FastNoise::GetNoise(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - x *= m_frequency; - y *= m_frequency; - z *= m_frequency; - - switch (m_noiseType) - { - case Value: - return SingleValue(0, x, y, z); - case ValueFractal: - switch (m_fractalType) - { - case FBM: - return SingleValueFractalFBM(x, y, z); - case Billow: - return SingleValueFractalBillow(x, y, z); - case RigidMulti: - return SingleValueFractalRigidMulti(x, y, z); - default: - return 0; - } - case Perlin: - return SinglePerlin(0, x, y, z); - case PerlinFractal: - switch (m_fractalType) - { - case FBM: - return SinglePerlinFractalFBM(x, y, z); - case Billow: - return SinglePerlinFractalBillow(x, y, z); - case RigidMulti: - return SinglePerlinFractalRigidMulti(x, y, z); - default: - return 0; - } - case Simplex: - return SingleSimplex(0, x, y, z); - case SimplexFractal: - switch (m_fractalType) - { - case FBM: - return SingleSimplexFractalFBM(x, y, z); - case Billow: - return SingleSimplexFractalBillow(x, y, z); - case RigidMulti: - return SingleSimplexFractalRigidMulti(x, y, z); - default: - return 0; - } - case Cellular: - switch (m_cellularReturnType) - { - case CellValue: - case NoiseLookup: - case Distance: - return SingleCellular(x, y, z); - default: - return SingleCellular2Edge(x, y, z); - } - case WhiteNoise: - return GetWhiteNoise(x, y, z); - case Cubic: - return SingleCubic(0, x, y, z); - case CubicFractal: - switch (m_fractalType) - { - case FBM: - return SingleCubicFractalFBM(x, y, z); - case Billow: - return SingleCubicFractalBillow(x, y, z); - case RigidMulti: - return SingleCubicFractalRigidMulti(x, y, z); - } - default: - return 0; - } -} - -FN_DECIMAL FastNoise::GetNoise(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - switch (m_noiseType) - { - case Value: - return SingleValue(0, x, y); - case ValueFractal: - switch (m_fractalType) - { - case FBM: - return SingleValueFractalFBM(x, y); - case Billow: - return SingleValueFractalBillow(x, y); - case RigidMulti: - return SingleValueFractalRigidMulti(x, y); - } - case Perlin: - return SinglePerlin(0, x, y); - case PerlinFractal: - switch (m_fractalType) - { - case FBM: - return SinglePerlinFractalFBM(x, y); - case Billow: - return SinglePerlinFractalBillow(x, y); - case RigidMulti: - return SinglePerlinFractalRigidMulti(x, y); - } - case Simplex: - return SingleSimplex(0, x, y); - case SimplexFractal: - switch (m_fractalType) - { - case FBM: - return SingleSimplexFractalFBM(x, y); - case Billow: - return SingleSimplexFractalBillow(x, y); - case RigidMulti: - return SingleSimplexFractalRigidMulti(x, y); - } - case Cellular: - switch (m_cellularReturnType) - { - case CellValue: - case NoiseLookup: - case Distance: - return SingleCellular(x, y); - default: - return SingleCellular2Edge(x, y); - } - case WhiteNoise: - return GetWhiteNoise(x, y); - case Cubic: - return SingleCubic(0, x, y); - case CubicFractal: - switch (m_fractalType) - { - case FBM: - return SingleCubicFractalFBM(x, y); - case Billow: - return SingleCubicFractalBillow(x, y); - case RigidMulti: - return SingleCubicFractalRigidMulti(x, y); - } - } - return 0; -} - -// White Noise -FN_DECIMAL FastNoise::GetWhiteNoise(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z, FN_DECIMAL w) const -{ - return ValCoord4D(m_seed, - *reinterpret_cast(&x) ^ (*reinterpret_cast(&x) >> 16), - *reinterpret_cast(&y) ^ (*reinterpret_cast(&y) >> 16), - *reinterpret_cast(&z) ^ (*reinterpret_cast(&z) >> 16), - *reinterpret_cast(&w) ^ (*reinterpret_cast(&w) >> 16)); -} - -FN_DECIMAL FastNoise::GetWhiteNoise(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - return ValCoord3D(m_seed, - *reinterpret_cast(&x) ^ (*reinterpret_cast(&x) >> 16), - *reinterpret_cast(&y) ^ (*reinterpret_cast(&y) >> 16), - *reinterpret_cast(&z) ^ (*reinterpret_cast(&z) >> 16)); -} - -FN_DECIMAL FastNoise::GetWhiteNoise(FN_DECIMAL x, FN_DECIMAL y) const -{ - return ValCoord2D(m_seed, - *reinterpret_cast(&x) ^ (*reinterpret_cast(&x) >> 16), - *reinterpret_cast(&y) ^ (*reinterpret_cast(&y) >> 16)); -} - -FN_DECIMAL FastNoise::GetWhiteNoiseInt(int x, int y, int z, int w) const -{ - return ValCoord4D(m_seed, x, y, z, w); -} - -FN_DECIMAL FastNoise::GetWhiteNoiseInt(int x, int y, int z) const -{ - return ValCoord3D(m_seed, x, y, z); -} - -FN_DECIMAL FastNoise::GetWhiteNoiseInt(int x, int y) const -{ - return ValCoord2D(m_seed, x, y); -} - -// Value Noise -FN_DECIMAL FastNoise::GetValueFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - x *= m_frequency; - y *= m_frequency; - z *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SingleValueFractalFBM(x, y, z); - case Billow: - return SingleValueFractalBillow(x, y, z); - case RigidMulti: - return SingleValueFractalRigidMulti(x, y, z); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleValueFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = SingleValue(m_perm[0], x, y, z); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += SingleValue(m_perm[i], x, y, z) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleValueFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = FastAbs(SingleValue(m_perm[0], x, y, z)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SingleValue(m_perm[i], x, y, z)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleValueFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = 1 - FastAbs(SingleValue(m_perm[0], x, y, z)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SingleValue(m_perm[i], x, y, z))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetValue(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - return SingleValue(0, x * m_frequency, y * m_frequency, z * m_frequency); -} - -FN_DECIMAL FastNoise::SingleValue(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - int x0 = FastFloor(x); - int y0 = FastFloor(y); - int z0 = FastFloor(z); - int x1 = x0 + 1; - int y1 = y0 + 1; - int z1 = z0 + 1; - - FN_DECIMAL xs, ys, zs; - switch (m_interp) - { - case Linear: - xs = x - (FN_DECIMAL)x0; - ys = y - (FN_DECIMAL)y0; - zs = z - (FN_DECIMAL)z0; - break; - case Hermite: - xs = InterpHermiteFunc(x - (FN_DECIMAL)x0); - ys = InterpHermiteFunc(y - (FN_DECIMAL)y0); - zs = InterpHermiteFunc(z - (FN_DECIMAL)z0); - break; - case Quintic: - xs = InterpQuinticFunc(x - (FN_DECIMAL)x0); - ys = InterpQuinticFunc(y - (FN_DECIMAL)y0); - zs = InterpQuinticFunc(z - (FN_DECIMAL)z0); - break; - } - - FN_DECIMAL xf00 = Lerp(ValCoord3DFast(offset, x0, y0, z0), ValCoord3DFast(offset, x1, y0, z0), xs); - FN_DECIMAL xf10 = Lerp(ValCoord3DFast(offset, x0, y1, z0), ValCoord3DFast(offset, x1, y1, z0), xs); - FN_DECIMAL xf01 = Lerp(ValCoord3DFast(offset, x0, y0, z1), ValCoord3DFast(offset, x1, y0, z1), xs); - FN_DECIMAL xf11 = Lerp(ValCoord3DFast(offset, x0, y1, z1), ValCoord3DFast(offset, x1, y1, z1), xs); - - FN_DECIMAL yf0 = Lerp(xf00, xf10, ys); - FN_DECIMAL yf1 = Lerp(xf01, xf11, ys); - - return Lerp(yf0, yf1, zs); -} - -FN_DECIMAL FastNoise::GetValueFractal(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SingleValueFractalFBM(x, y); - case Billow: - return SingleValueFractalBillow(x, y); - case RigidMulti: - return SingleValueFractalRigidMulti(x, y); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleValueFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = SingleValue(m_perm[0], x, y); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += SingleValue(m_perm[i], x, y) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleValueFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = FastAbs(SingleValue(m_perm[0], x, y)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - amp *= m_gain; - sum += (FastAbs(SingleValue(m_perm[i], x, y)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleValueFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = 1 - FastAbs(SingleValue(m_perm[0], x, y)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SingleValue(m_perm[i], x, y))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetValue(FN_DECIMAL x, FN_DECIMAL y) const -{ - return SingleValue(0, x * m_frequency, y * m_frequency); -} - -FN_DECIMAL FastNoise::SingleValue(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const -{ - int x0 = FastFloor(x); - int y0 = FastFloor(y); - int x1 = x0 + 1; - int y1 = y0 + 1; - - FN_DECIMAL xs, ys; - switch (m_interp) - { - case Linear: - xs = x - (FN_DECIMAL)x0; - ys = y - (FN_DECIMAL)y0; - break; - case Hermite: - xs = InterpHermiteFunc(x - (FN_DECIMAL)x0); - ys = InterpHermiteFunc(y - (FN_DECIMAL)y0); - break; - case Quintic: - xs = InterpQuinticFunc(x - (FN_DECIMAL)x0); - ys = InterpQuinticFunc(y - (FN_DECIMAL)y0); - break; - } - - FN_DECIMAL xf0 = Lerp(ValCoord2DFast(offset, x0, y0), ValCoord2DFast(offset, x1, y0), xs); - FN_DECIMAL xf1 = Lerp(ValCoord2DFast(offset, x0, y1), ValCoord2DFast(offset, x1, y1), xs); - - return Lerp(xf0, xf1, ys); -} - -// Perlin Noise -FN_DECIMAL FastNoise::GetPerlinFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - x *= m_frequency; - y *= m_frequency; - z *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SinglePerlinFractalFBM(x, y, z); - case Billow: - return SinglePerlinFractalBillow(x, y, z); - case RigidMulti: - return SinglePerlinFractalRigidMulti(x, y, z); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SinglePerlinFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = SinglePerlin(m_perm[0], x, y, z); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += SinglePerlin(m_perm[i], x, y, z) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SinglePerlinFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = FastAbs(SinglePerlin(m_perm[0], x, y, z)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SinglePerlin(m_perm[i], x, y, z)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SinglePerlinFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = 1 - FastAbs(SinglePerlin(m_perm[0], x, y, z)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SinglePerlin(m_perm[i], x, y, z))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetPerlin(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - return SinglePerlin(0, x * m_frequency, y * m_frequency, z * m_frequency); -} - -FN_DECIMAL FastNoise::SinglePerlin(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - int x0 = FastFloor(x); - int y0 = FastFloor(y); - int z0 = FastFloor(z); - int x1 = x0 + 1; - int y1 = y0 + 1; - int z1 = z0 + 1; - - FN_DECIMAL xs, ys, zs; - switch (m_interp) - { - case Linear: - xs = x - (FN_DECIMAL)x0; - ys = y - (FN_DECIMAL)y0; - zs = z - (FN_DECIMAL)z0; - break; - case Hermite: - xs = InterpHermiteFunc(x - (FN_DECIMAL)x0); - ys = InterpHermiteFunc(y - (FN_DECIMAL)y0); - zs = InterpHermiteFunc(z - (FN_DECIMAL)z0); - break; - case Quintic: - xs = InterpQuinticFunc(x - (FN_DECIMAL)x0); - ys = InterpQuinticFunc(y - (FN_DECIMAL)y0); - zs = InterpQuinticFunc(z - (FN_DECIMAL)z0); - break; - } - - FN_DECIMAL xd0 = x - (FN_DECIMAL)x0; - FN_DECIMAL yd0 = y - (FN_DECIMAL)y0; - FN_DECIMAL zd0 = z - (FN_DECIMAL)z0; - FN_DECIMAL xd1 = xd0 - 1; - FN_DECIMAL yd1 = yd0 - 1; - FN_DECIMAL zd1 = zd0 - 1; - - FN_DECIMAL xf00 = Lerp(GradCoord3D(offset, x0, y0, z0, xd0, yd0, zd0), GradCoord3D(offset, x1, y0, z0, xd1, yd0, zd0), xs); - FN_DECIMAL xf10 = Lerp(GradCoord3D(offset, x0, y1, z0, xd0, yd1, zd0), GradCoord3D(offset, x1, y1, z0, xd1, yd1, zd0), xs); - FN_DECIMAL xf01 = Lerp(GradCoord3D(offset, x0, y0, z1, xd0, yd0, zd1), GradCoord3D(offset, x1, y0, z1, xd1, yd0, zd1), xs); - FN_DECIMAL xf11 = Lerp(GradCoord3D(offset, x0, y1, z1, xd0, yd1, zd1), GradCoord3D(offset, x1, y1, z1, xd1, yd1, zd1), xs); - - FN_DECIMAL yf0 = Lerp(xf00, xf10, ys); - FN_DECIMAL yf1 = Lerp(xf01, xf11, ys); - - return Lerp(yf0, yf1, zs); -} - -FN_DECIMAL FastNoise::GetPerlinFractal(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SinglePerlinFractalFBM(x, y); - case Billow: - return SinglePerlinFractalBillow(x, y); - case RigidMulti: - return SinglePerlinFractalRigidMulti(x, y); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SinglePerlinFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = SinglePerlin(m_perm[0], x, y); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += SinglePerlin(m_perm[i], x, y) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SinglePerlinFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = FastAbs(SinglePerlin(m_perm[0], x, y)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SinglePerlin(m_perm[i], x, y)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SinglePerlinFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = 1 - FastAbs(SinglePerlin(m_perm[0], x, y)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SinglePerlin(m_perm[i], x, y))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetPerlin(FN_DECIMAL x, FN_DECIMAL y) const -{ - return SinglePerlin(0, x * m_frequency, y * m_frequency); -} - -FN_DECIMAL FastNoise::SinglePerlin(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const -{ - int x0 = FastFloor(x); - int y0 = FastFloor(y); - int x1 = x0 + 1; - int y1 = y0 + 1; - - FN_DECIMAL xs, ys; - switch (m_interp) - { - case Linear: - xs = x - (FN_DECIMAL)x0; - ys = y - (FN_DECIMAL)y0; - break; - case Hermite: - xs = InterpHermiteFunc(x - (FN_DECIMAL)x0); - ys = InterpHermiteFunc(y - (FN_DECIMAL)y0); - break; - case Quintic: - xs = InterpQuinticFunc(x - (FN_DECIMAL)x0); - ys = InterpQuinticFunc(y - (FN_DECIMAL)y0); - break; - } - - FN_DECIMAL xd0 = x - (FN_DECIMAL)x0; - FN_DECIMAL yd0 = y - (FN_DECIMAL)y0; - FN_DECIMAL xd1 = xd0 - 1; - FN_DECIMAL yd1 = yd0 - 1; - - FN_DECIMAL xf0 = Lerp(GradCoord2D(offset, x0, y0, xd0, yd0), GradCoord2D(offset, x1, y0, xd1, yd0), xs); - FN_DECIMAL xf1 = Lerp(GradCoord2D(offset, x0, y1, xd0, yd1), GradCoord2D(offset, x1, y1, xd1, yd1), xs); - - return Lerp(xf0, xf1, ys); -} - -// Simplex Noise - -FN_DECIMAL FastNoise::GetSimplexFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - x *= m_frequency; - y *= m_frequency; - z *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SingleSimplexFractalFBM(x, y, z); - case Billow: - return SingleSimplexFractalBillow(x, y, z); - case RigidMulti: - return SingleSimplexFractalRigidMulti(x, y, z); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleSimplexFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = SingleSimplex(m_perm[0], x, y, z); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += SingleSimplex(m_perm[i], x, y, z) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleSimplexFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = FastAbs(SingleSimplex(m_perm[0], x, y, z)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SingleSimplex(m_perm[i], x, y, z)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleSimplexFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = 1 - FastAbs(SingleSimplex(m_perm[0], x, y, z)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SingleSimplex(m_perm[i], x, y, z))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetSimplex(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - return SingleSimplex(0, x * m_frequency, y * m_frequency, z * m_frequency); -} - -static const FN_DECIMAL F3 = 1 / FN_DECIMAL(3); -static const FN_DECIMAL G3 = 1 / FN_DECIMAL(6); - -FN_DECIMAL FastNoise::SingleSimplex(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL t = (x + y + z) * F3; - int i = FastFloor(x + t); - int j = FastFloor(y + t); - int k = FastFloor(z + t); - - t = (i + j + k) * G3; - FN_DECIMAL X0 = i - t; - FN_DECIMAL Y0 = j - t; - FN_DECIMAL Z0 = k - t; - - FN_DECIMAL x0 = x - X0; - FN_DECIMAL y0 = y - Y0; - FN_DECIMAL z0 = z - Z0; - - int i1, j1, k1; - int i2, j2, k2; - - if (x0 >= y0) - { - if (y0 >= z0) - { - i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0; - } - else if (x0 >= z0) - { - i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1; - } - else // x0 < z0 - { - i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1; - } - } - else // x0 < y0 - { - if (y0 < z0) - { - i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1; - } - else if (x0 < z0) - { - i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1; - } - else // x0 >= z0 - { - i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0; - } - } - - FN_DECIMAL x1 = x0 - i1 + G3; - FN_DECIMAL y1 = y0 - j1 + G3; - FN_DECIMAL z1 = z0 - k1 + G3; - FN_DECIMAL x2 = x0 - i2 + 2*G3; - FN_DECIMAL y2 = y0 - j2 + 2*G3; - FN_DECIMAL z2 = z0 - k2 + 2*G3; - FN_DECIMAL x3 = x0 - 1 + 3*G3; - FN_DECIMAL y3 = y0 - 1 + 3*G3; - FN_DECIMAL z3 = z0 - 1 + 3*G3; - - FN_DECIMAL n0, n1, n2, n3; - - t = FN_DECIMAL(0.6) - x0*x0 - y0*y0 - z0*z0; - if (t < 0) n0 = 0; - else - { - t *= t; - n0 = t*t*GradCoord3D(offset, i, j, k, x0, y0, z0); - } - - t = FN_DECIMAL(0.6) - x1*x1 - y1*y1 - z1*z1; - if (t < 0) n1 = 0; - else - { - t *= t; - n1 = t*t*GradCoord3D(offset, i + i1, j + j1, k + k1, x1, y1, z1); - } - - t = FN_DECIMAL(0.6) - x2*x2 - y2*y2 - z2*z2; - if (t < 0) n2 = 0; - else - { - t *= t; - n2 = t*t*GradCoord3D(offset, i + i2, j + j2, k + k2, x2, y2, z2); - } - - t = FN_DECIMAL(0.6) - x3*x3 - y3*y3 - z3*z3; - if (t < 0) n3 = 0; - else - { - t *= t; - n3 = t*t*GradCoord3D(offset, i + 1, j + 1, k + 1, x3, y3, z3); - } - - return 32 * (n0 + n1 + n2 + n3); -} - -FN_DECIMAL FastNoise::GetSimplexFractal(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SingleSimplexFractalFBM(x, y); - case Billow: - return SingleSimplexFractalBillow(x, y); - case RigidMulti: - return SingleSimplexFractalRigidMulti(x, y); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleSimplexFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = SingleSimplex(m_perm[0], x, y); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += SingleSimplex(m_perm[i], x, y) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleSimplexFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = FastAbs(SingleSimplex(m_perm[0], x, y)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SingleSimplex(m_perm[i], x, y)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleSimplexFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = 1 - FastAbs(SingleSimplex(m_perm[0], x, y)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SingleSimplex(m_perm[i], x, y))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::SingleSimplexFractalBlend(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = SingleSimplex(m_perm[0], x, y); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum *= SingleSimplex(m_perm[i], x, y) * amp + 1; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::GetSimplex(FN_DECIMAL x, FN_DECIMAL y) const -{ - return SingleSimplex(0, x * m_frequency, y * m_frequency); -} - -//static const FN_DECIMAL F2 = 1 / FN_DECIMAL(2); -//static const FN_DECIMAL G2 = 1 / FN_DECIMAL(4); - -static const FN_DECIMAL SQRT3 = FN_DECIMAL(1.7320508075688772935274463415059); -static const FN_DECIMAL F2 = FN_DECIMAL(0.5) * (SQRT3 - FN_DECIMAL(1.0)); -static const FN_DECIMAL G2 = (FN_DECIMAL(3.0) - SQRT3) / FN_DECIMAL(6.0); - -FN_DECIMAL FastNoise::SingleSimplex(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL t = (x + y) * F2; - int i = FastFloor(x + t); - int j = FastFloor(y + t); - - t = (i + j) * G2; - FN_DECIMAL X0 = i - t; - FN_DECIMAL Y0 = j - t; - - FN_DECIMAL x0 = x - X0; - FN_DECIMAL y0 = y - Y0; - - int i1, j1; - if (x0 > y0) - { - i1 = 1; j1 = 0; - } - else - { - i1 = 0; j1 = 1; - } - - FN_DECIMAL x1 = x0 - (FN_DECIMAL)i1 + G2; - FN_DECIMAL y1 = y0 - (FN_DECIMAL)j1 + G2; - FN_DECIMAL x2 = x0 - 1 + 2*G2; - FN_DECIMAL y2 = y0 - 1 + 2*G2; - - FN_DECIMAL n0, n1, n2; - - t = FN_DECIMAL(0.5) - x0*x0 - y0*y0; - if (t < 0) n0 = 0; - else - { - t *= t; - n0 = t * t * GradCoord2D(offset, i, j, x0, y0); - } - - t = FN_DECIMAL(0.5) - x1*x1 - y1*y1; - if (t < 0) n1 = 0; - else - { - t *= t; - n1 = t*t*GradCoord2D(offset, i + i1, j + j1, x1, y1); - } - - t = FN_DECIMAL(0.5) - x2*x2 - y2*y2; - if (t < 0) n2 = 0; - else - { - t *= t; - n2 = t*t*GradCoord2D(offset, i + 1, j + 1, x2, y2); - } - - return 70 * (n0 + n1 + n2); -} - -FN_DECIMAL FastNoise::GetSimplex(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z, FN_DECIMAL w) const -{ - return SingleSimplex(0, x * m_frequency, y * m_frequency, z * m_frequency, w * m_frequency); -} - -static const FN_DECIMAL F4 = (sqrt(FN_DECIMAL(5)) - 1) / 4; -static const FN_DECIMAL G4 = (5 - sqrt(FN_DECIMAL(5))) / 20; - -FN_DECIMAL FastNoise::SingleSimplex(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z, FN_DECIMAL w) const -{ - FN_DECIMAL n0, n1, n2, n3, n4; - FN_DECIMAL t = (x + y + z + w) * F4; - int i = FastFloor(x + t); - int j = FastFloor(y + t); - int k = FastFloor(z + t); - int l = FastFloor(w + t); - t = (i + j + k + l) * G4; - FN_DECIMAL X0 = i - t; - FN_DECIMAL Y0 = j - t; - FN_DECIMAL Z0 = k - t; - FN_DECIMAL W0 = l - t; - FN_DECIMAL x0 = x - X0; - FN_DECIMAL y0 = y - Y0; - FN_DECIMAL z0 = z - Z0; - FN_DECIMAL w0 = w - W0; - - int rankx = 0; - int ranky = 0; - int rankz = 0; - int rankw = 0; - - if (x0 > y0) rankx++; else ranky++; - if (x0 > z0) rankx++; else rankz++; - if (x0 > w0) rankx++; else rankw++; - if (y0 > z0) ranky++; else rankz++; - if (y0 > w0) ranky++; else rankw++; - if (z0 > w0) rankz++; else rankw++; - - int i1 = rankx >= 3 ? 1 : 0; - int j1 = ranky >= 3 ? 1 : 0; - int k1 = rankz >= 3 ? 1 : 0; - int l1 = rankw >= 3 ? 1 : 0; - - int i2 = rankx >= 2 ? 1 : 0; - int j2 = ranky >= 2 ? 1 : 0; - int k2 = rankz >= 2 ? 1 : 0; - int l2 = rankw >= 2 ? 1 : 0; - - int i3 = rankx >= 1 ? 1 : 0; - int j3 = ranky >= 1 ? 1 : 0; - int k3 = rankz >= 1 ? 1 : 0; - int l3 = rankw >= 1 ? 1 : 0; - - FN_DECIMAL x1 = x0 - i1 + G4; - FN_DECIMAL y1 = y0 - j1 + G4; - FN_DECIMAL z1 = z0 - k1 + G4; - FN_DECIMAL w1 = w0 - l1 + G4; - FN_DECIMAL x2 = x0 - i2 + 2*G4; - FN_DECIMAL y2 = y0 - j2 + 2*G4; - FN_DECIMAL z2 = z0 - k2 + 2*G4; - FN_DECIMAL w2 = w0 - l2 + 2*G4; - FN_DECIMAL x3 = x0 - i3 + 3*G4; - FN_DECIMAL y3 = y0 - j3 + 3*G4; - FN_DECIMAL z3 = z0 - k3 + 3*G4; - FN_DECIMAL w3 = w0 - l3 + 3*G4; - FN_DECIMAL x4 = x0 - 1 + 4*G4; - FN_DECIMAL y4 = y0 - 1 + 4*G4; - FN_DECIMAL z4 = z0 - 1 + 4*G4; - FN_DECIMAL w4 = w0 - 1 + 4*G4; - - t = FN_DECIMAL(0.6) - x0*x0 - y0*y0 - z0*z0 - w0*w0; - if (t < 0) n0 = 0; - else { - t *= t; - n0 = t * t * GradCoord4D(offset, i, j, k, l, x0, y0, z0, w0); - } - t = FN_DECIMAL(0.6) - x1*x1 - y1*y1 - z1*z1 - w1*w1; - if (t < 0) n1 = 0; - else { - t *= t; - n1 = t * t * GradCoord4D(offset, i + i1, j + j1, k + k1, l + l1, x1, y1, z1, w1); - } - t = FN_DECIMAL(0.6) - x2*x2 - y2*y2 - z2*z2 - w2*w2; - if (t < 0) n2 = 0; - else { - t *= t; - n2 = t * t * GradCoord4D(offset, i + i2, j + j2, k + k2, l + l2, x2, y2, z2, w2); - } - t = FN_DECIMAL(0.6) - x3*x3 - y3*y3 - z3*z3 - w3*w3; - if (t < 0) n3 = 0; - else { - t *= t; - n3 = t * t * GradCoord4D(offset, i + i3, j + j3, k + k3, l + l3, x3, y3, z3, w3); - } - t = FN_DECIMAL(0.6) - x4*x4 - y4*y4 - z4*z4 - w4*w4; - if (t < 0) n4 = 0; - else { - t *= t; - n4 = t * t * GradCoord4D(offset, i + 1, j + 1, k + 1, l + 1, x4, y4, z4, w4); - } - - return 27 * (n0 + n1 + n2 + n3 + n4); -} - -// Cubic Noise -FN_DECIMAL FastNoise::GetCubicFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - x *= m_frequency; - y *= m_frequency; - z *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SingleCubicFractalFBM(x, y, z); - case Billow: - return SingleCubicFractalBillow(x, y, z); - case RigidMulti: - return SingleCubicFractalRigidMulti(x, y, z); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleCubicFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = SingleCubic(m_perm[0], x, y, z); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += SingleCubic(m_perm[i], x, y, z) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleCubicFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = FastAbs(SingleCubic(m_perm[0], x, y, z)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SingleCubic(m_perm[i], x, y, z)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleCubicFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - FN_DECIMAL sum = 1 - FastAbs(SingleCubic(m_perm[0], x, y, z)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - z *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SingleCubic(m_perm[i], x, y, z))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetCubic(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - return SingleCubic(0, x * m_frequency, y * m_frequency, z * m_frequency); -} - -const FN_DECIMAL CUBIC_3D_BOUNDING = 1 / (FN_DECIMAL(1.5) * FN_DECIMAL(1.5) * FN_DECIMAL(1.5)); - -FN_DECIMAL FastNoise::SingleCubic(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - int x1 = FastFloor(x); - int y1 = FastFloor(y); - int z1 = FastFloor(z); - - int x0 = x1 - 1; - int y0 = y1 - 1; - int z0 = z1 - 1; - int x2 = x1 + 1; - int y2 = y1 + 1; - int z2 = z1 + 1; - int x3 = x1 + 2; - int y3 = y1 + 2; - int z3 = z1 + 2; - - FN_DECIMAL xs = x - (FN_DECIMAL)x1; - FN_DECIMAL ys = y - (FN_DECIMAL)y1; - FN_DECIMAL zs = z - (FN_DECIMAL)z1; - - return CubicLerp( - CubicLerp( - CubicLerp(ValCoord3DFast(offset, x0, y0, z0), ValCoord3DFast(offset, x1, y0, z0), ValCoord3DFast(offset, x2, y0, z0), ValCoord3DFast(offset, x3, y0, z0), xs), - CubicLerp(ValCoord3DFast(offset, x0, y1, z0), ValCoord3DFast(offset, x1, y1, z0), ValCoord3DFast(offset, x2, y1, z0), ValCoord3DFast(offset, x3, y1, z0), xs), - CubicLerp(ValCoord3DFast(offset, x0, y2, z0), ValCoord3DFast(offset, x1, y2, z0), ValCoord3DFast(offset, x2, y2, z0), ValCoord3DFast(offset, x3, y2, z0), xs), - CubicLerp(ValCoord3DFast(offset, x0, y3, z0), ValCoord3DFast(offset, x1, y3, z0), ValCoord3DFast(offset, x2, y3, z0), ValCoord3DFast(offset, x3, y3, z0), xs), - ys), - CubicLerp( - CubicLerp(ValCoord3DFast(offset, x0, y0, z1), ValCoord3DFast(offset, x1, y0, z1), ValCoord3DFast(offset, x2, y0, z1), ValCoord3DFast(offset, x3, y0, z1), xs), - CubicLerp(ValCoord3DFast(offset, x0, y1, z1), ValCoord3DFast(offset, x1, y1, z1), ValCoord3DFast(offset, x2, y1, z1), ValCoord3DFast(offset, x3, y1, z1), xs), - CubicLerp(ValCoord3DFast(offset, x0, y2, z1), ValCoord3DFast(offset, x1, y2, z1), ValCoord3DFast(offset, x2, y2, z1), ValCoord3DFast(offset, x3, y2, z1), xs), - CubicLerp(ValCoord3DFast(offset, x0, y3, z1), ValCoord3DFast(offset, x1, y3, z1), ValCoord3DFast(offset, x2, y3, z1), ValCoord3DFast(offset, x3, y3, z1), xs), - ys), - CubicLerp( - CubicLerp(ValCoord3DFast(offset, x0, y0, z2), ValCoord3DFast(offset, x1, y0, z2), ValCoord3DFast(offset, x2, y0, z2), ValCoord3DFast(offset, x3, y0, z2), xs), - CubicLerp(ValCoord3DFast(offset, x0, y1, z2), ValCoord3DFast(offset, x1, y1, z2), ValCoord3DFast(offset, x2, y1, z2), ValCoord3DFast(offset, x3, y1, z2), xs), - CubicLerp(ValCoord3DFast(offset, x0, y2, z2), ValCoord3DFast(offset, x1, y2, z2), ValCoord3DFast(offset, x2, y2, z2), ValCoord3DFast(offset, x3, y2, z2), xs), - CubicLerp(ValCoord3DFast(offset, x0, y3, z2), ValCoord3DFast(offset, x1, y3, z2), ValCoord3DFast(offset, x2, y3, z2), ValCoord3DFast(offset, x3, y3, z2), xs), - ys), - CubicLerp( - CubicLerp(ValCoord3DFast(offset, x0, y0, z3), ValCoord3DFast(offset, x1, y0, z3), ValCoord3DFast(offset, x2, y0, z3), ValCoord3DFast(offset, x3, y0, z3), xs), - CubicLerp(ValCoord3DFast(offset, x0, y1, z3), ValCoord3DFast(offset, x1, y1, z3), ValCoord3DFast(offset, x2, y1, z3), ValCoord3DFast(offset, x3, y1, z3), xs), - CubicLerp(ValCoord3DFast(offset, x0, y2, z3), ValCoord3DFast(offset, x1, y2, z3), ValCoord3DFast(offset, x2, y2, z3), ValCoord3DFast(offset, x3, y2, z3), xs), - CubicLerp(ValCoord3DFast(offset, x0, y3, z3), ValCoord3DFast(offset, x1, y3, z3), ValCoord3DFast(offset, x2, y3, z3), ValCoord3DFast(offset, x3, y3, z3), xs), - ys), - zs) * CUBIC_3D_BOUNDING; -} - - -FN_DECIMAL FastNoise::GetCubicFractal(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - switch (m_fractalType) - { - case FBM: - return SingleCubicFractalFBM(x, y); - case Billow: - return SingleCubicFractalBillow(x, y); - case RigidMulti: - return SingleCubicFractalRigidMulti(x, y); - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleCubicFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = SingleCubic(m_perm[0], x, y); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += SingleCubic(m_perm[i], x, y) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleCubicFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = FastAbs(SingleCubic(m_perm[0], x, y)) * 2 - 1; - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum += (FastAbs(SingleCubic(m_perm[i], x, y)) * 2 - 1) * amp; - } - - return sum * m_fractalBounding; -} - -FN_DECIMAL FastNoise::SingleCubicFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const -{ - FN_DECIMAL sum = 1 - FastAbs(SingleCubic(m_perm[0], x, y)); - FN_DECIMAL amp = 1; - int i = 0; - - while (++i < m_octaves) - { - x *= m_lacunarity; - y *= m_lacunarity; - - amp *= m_gain; - sum -= (1 - FastAbs(SingleCubic(m_perm[i], x, y))) * amp; - } - - return sum; -} - -FN_DECIMAL FastNoise::GetCubic(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - return SingleCubic(0, x, y); -} - -const FN_DECIMAL CUBIC_2D_BOUNDING = 1 / (FN_DECIMAL(1.5) * FN_DECIMAL(1.5)); - -FN_DECIMAL FastNoise::SingleCubic(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const -{ - int x1 = FastFloor(x); - int y1 = FastFloor(y); - - int x0 = x1 - 1; - int y0 = y1 - 1; - int x2 = x1 + 1; - int y2 = y1 + 1; - int x3 = x1 + 2; - int y3 = y1 + 2; - - FN_DECIMAL xs = x - (FN_DECIMAL)x1; - FN_DECIMAL ys = y - (FN_DECIMAL)y1; - - return CubicLerp( - CubicLerp(ValCoord2DFast(offset, x0, y0), ValCoord2DFast(offset, x1, y0), ValCoord2DFast(offset, x2, y0), ValCoord2DFast(offset, x3, y0), xs), - CubicLerp(ValCoord2DFast(offset, x0, y1), ValCoord2DFast(offset, x1, y1), ValCoord2DFast(offset, x2, y1), ValCoord2DFast(offset, x3, y1), xs), - CubicLerp(ValCoord2DFast(offset, x0, y2), ValCoord2DFast(offset, x1, y2), ValCoord2DFast(offset, x2, y2), ValCoord2DFast(offset, x3, y2), xs), - CubicLerp(ValCoord2DFast(offset, x0, y3), ValCoord2DFast(offset, x1, y3), ValCoord2DFast(offset, x2, y3), ValCoord2DFast(offset, x3, y3), xs), - ys) * CUBIC_2D_BOUNDING; -} - -// Cellular Noise -FN_DECIMAL FastNoise::GetCellular(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - x *= m_frequency; - y *= m_frequency; - z *= m_frequency; - - switch (m_cellularReturnType) - { - case CellValue: - case NoiseLookup: - case Distance: - return SingleCellular(x, y, z); - default: - return SingleCellular2Edge(x, y, z); - } -} - -FN_DECIMAL FastNoise::SingleCellular(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - int xr = FastRound(x); - int yr = FastRound(y); - int zr = FastRound(z); - - FN_DECIMAL distance = 999999; - int xc, yc, zc; - - switch (m_cellularDistanceFunction) - { - case Euclidean: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - for (int zi = zr - 1; zi <= zr + 1; zi++) - { - unsigned char lutPos = Index3D_256(0, xi, yi, zi); - - FN_DECIMAL vecX = xi - x + CELL_3D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_3D_Y[lutPos] * m_cellularJitter; - FN_DECIMAL vecZ = zi - z + CELL_3D_Z[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; - - if (newDistance < distance) - { - distance = newDistance; - xc = xi; - yc = yi; - zc = zi; - } - } - } - } - break; - case Manhattan: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - for (int zi = zr - 1; zi <= zr + 1; zi++) - { - unsigned char lutPos = Index3D_256(0, xi, yi, zi); - - FN_DECIMAL vecX = xi - x + CELL_3D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_3D_Y[lutPos] * m_cellularJitter; - FN_DECIMAL vecZ = zi - z + CELL_3D_Z[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ); - - if (newDistance < distance) - { - distance = newDistance; - xc = xi; - yc = yi; - zc = zi; - } - } - } - } - break; - case Natural: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - for (int zi = zr - 1; zi <= zr + 1; zi++) - { - unsigned char lutPos = Index3D_256(0, xi, yi, zi); - - FN_DECIMAL vecX = xi - x + CELL_3D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_3D_Y[lutPos] * m_cellularJitter; - FN_DECIMAL vecZ = zi - z + CELL_3D_Z[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = (FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); - - if (newDistance < distance) - { - distance = newDistance; - xc = xi; - yc = yi; - zc = zi; - } - } - } - } - break; - default: - break; - } - - unsigned char lutPos; - switch (m_cellularReturnType) - { - case CellValue: - return ValCoord3D(m_seed, xc, yc, zc); - - case NoiseLookup: - assert(m_cellularNoiseLookup); - - lutPos = Index3D_256(0, xc, yc, zc); - return m_cellularNoiseLookup->GetNoise(xc + CELL_3D_X[lutPos] * m_cellularJitter, yc + CELL_3D_Y[lutPos] * m_cellularJitter, zc + CELL_3D_Z[lutPos] * m_cellularJitter); - - case Distance: - return distance; - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleCellular2Edge(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const -{ - int xr = FastRound(x); - int yr = FastRound(y); - int zr = FastRound(z); - - FN_DECIMAL distance[FN_CELLULAR_INDEX_MAX+1] = { 999999,999999,999999,999999 }; - - switch (m_cellularDistanceFunction) - { - case Euclidean: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - for (int zi = zr - 1; zi <= zr + 1; zi++) - { - unsigned char lutPos = Index3D_256(0, xi, yi, zi); - - FN_DECIMAL vecX = xi - x + CELL_3D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_3D_Y[lutPos] * m_cellularJitter; - FN_DECIMAL vecZ = zi - z + CELL_3D_Z[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; - - for (int i = m_cellularDistanceIndex1; i > 0; i--) - distance[i] = fmax(fmin(distance[i], newDistance), distance[i - 1]); - distance[0] = fmin(distance[0], newDistance); - } - } - } - break; - case Manhattan: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - for (int zi = zr - 1; zi <= zr + 1; zi++) - { - unsigned char lutPos = Index3D_256(0, xi, yi, zi); - - FN_DECIMAL vecX = xi - x + CELL_3D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_3D_Y[lutPos] * m_cellularJitter; - FN_DECIMAL vecZ = zi - z + CELL_3D_Z[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ); - - for (int i = m_cellularDistanceIndex1; i > 0; i--) - distance[i] = fmax(fmin(distance[i], newDistance), distance[i - 1]); - distance[0] = fmin(distance[0], newDistance); - } - } - } - break; - case Natural: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - for (int zi = zr - 1; zi <= zr + 1; zi++) - { - unsigned char lutPos = Index3D_256(0, xi, yi, zi); - - FN_DECIMAL vecX = xi - x + CELL_3D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_3D_Y[lutPos] * m_cellularJitter; - FN_DECIMAL vecZ = zi - z + CELL_3D_Z[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = (FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); - - for (int i = m_cellularDistanceIndex1; i > 0; i--) - distance[i] = fmax(fmin(distance[i], newDistance), distance[i - 1]); - distance[0] = fmin(distance[0], newDistance); - } - } - } - break; - default: - break; - } - - switch (m_cellularReturnType) - { - case Distance2: - return distance[m_cellularDistanceIndex1]; - case Distance2Add: - return distance[m_cellularDistanceIndex1] + distance[m_cellularDistanceIndex0]; - case Distance2Sub: - return distance[m_cellularDistanceIndex1] - distance[m_cellularDistanceIndex0]; - case Distance2Mul: - return distance[m_cellularDistanceIndex1] * distance[m_cellularDistanceIndex0]; - case Distance2Div: - return distance[m_cellularDistanceIndex0] / distance[m_cellularDistanceIndex1]; - default: - return 0; - } -} - -FN_DECIMAL FastNoise::GetCellular(FN_DECIMAL x, FN_DECIMAL y) const -{ - x *= m_frequency; - y *= m_frequency; - - switch (m_cellularReturnType) - { - case CellValue: - case NoiseLookup: - case Distance: - return SingleCellular(x, y); - default: - return SingleCellular2Edge(x, y); - } -} - -FN_DECIMAL FastNoise::SingleCellular(FN_DECIMAL x, FN_DECIMAL y) const -{ - int xr = FastRound(x); - int yr = FastRound(y); - - FN_DECIMAL distance = 999999; - int xc, yc; - - switch (m_cellularDistanceFunction) - { - default: - case Euclidean: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - unsigned char lutPos = Index2D_256(0, xi, yi); - - FN_DECIMAL vecX = xi - x + CELL_2D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_2D_Y[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = vecX * vecX + vecY * vecY; - - if (newDistance < distance) - { - distance = newDistance; - xc = xi; - yc = yi; - } - } - } - break; - case Manhattan: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - unsigned char lutPos = Index2D_256(0, xi, yi); - - FN_DECIMAL vecX = xi - x + CELL_2D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_2D_Y[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = (FastAbs(vecX) + FastAbs(vecY)); - - if (newDistance < distance) - { - distance = newDistance; - xc = xi; - yc = yi; - } - } - } - break; - case Natural: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - unsigned char lutPos = Index2D_256(0, xi, yi); - - FN_DECIMAL vecX = xi - x + CELL_2D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_2D_Y[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = (FastAbs(vecX) + FastAbs(vecY)) + (vecX * vecX + vecY * vecY); - - if (newDistance < distance) - { - distance = newDistance; - xc = xi; - yc = yi; - } - } - } - break; - } - - unsigned char lutPos; - switch (m_cellularReturnType) - { - case CellValue: - return ValCoord2D(m_seed, xc, yc); - - case NoiseLookup: - assert(m_cellularNoiseLookup); - - lutPos = Index2D_256(0, xc, yc); - return m_cellularNoiseLookup->GetNoise(xc + CELL_2D_X[lutPos] * m_cellularJitter, yc + CELL_2D_Y[lutPos] * m_cellularJitter); - - case Distance: - return distance; - default: - return 0; - } -} - -FN_DECIMAL FastNoise::SingleCellular2Edge(FN_DECIMAL x, FN_DECIMAL y) const -{ - int xr = FastRound(x); - int yr = FastRound(y); - - FN_DECIMAL distance[FN_CELLULAR_INDEX_MAX + 1] = { 999999,999999,999999,999999 }; - - switch (m_cellularDistanceFunction) - { - default: - case Euclidean: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - unsigned char lutPos = Index2D_256(0, xi, yi); - - FN_DECIMAL vecX = xi - x + CELL_2D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_2D_Y[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = vecX * vecX + vecY * vecY; - - for (int i = m_cellularDistanceIndex1; i > 0; i--) - distance[i] = fmax(fmin(distance[i], newDistance), distance[i - 1]); - distance[0] = fmin(distance[0], newDistance); - } - } - break; - case Manhattan: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - unsigned char lutPos = Index2D_256(0, xi, yi); - - FN_DECIMAL vecX = xi - x + CELL_2D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_2D_Y[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = FastAbs(vecX) + FastAbs(vecY); - - for (int i = m_cellularDistanceIndex1; i > 0; i--) - distance[i] = fmax(fmin(distance[i], newDistance), distance[i - 1]); - distance[0] = fmin(distance[0], newDistance); - } - } - break; - case Natural: - for (int xi = xr - 1; xi <= xr + 1; xi++) - { - for (int yi = yr - 1; yi <= yr + 1; yi++) - { - unsigned char lutPos = Index2D_256(0, xi, yi); - - FN_DECIMAL vecX = xi - x + CELL_2D_X[lutPos] * m_cellularJitter; - FN_DECIMAL vecY = yi - y + CELL_2D_Y[lutPos] * m_cellularJitter; - - FN_DECIMAL newDistance = (FastAbs(vecX) + FastAbs(vecY)) + (vecX * vecX + vecY * vecY); - - for (int i = m_cellularDistanceIndex1; i > 0; i--) - distance[i] = fmax(fmin(distance[i], newDistance), distance[i - 1]); - distance[0] = fmin(distance[0], newDistance); - } - } - break; - } - - switch (m_cellularReturnType) - { - case Distance2: - return distance[m_cellularDistanceIndex1]; - case Distance2Add: - return distance[m_cellularDistanceIndex1] + distance[m_cellularDistanceIndex0]; - case Distance2Sub: - return distance[m_cellularDistanceIndex1] - distance[m_cellularDistanceIndex0]; - case Distance2Mul: - return distance[m_cellularDistanceIndex1] * distance[m_cellularDistanceIndex0]; - case Distance2Div: - return distance[m_cellularDistanceIndex0] / distance[m_cellularDistanceIndex1]; - default: - return 0; - } -} - -void FastNoise::GradientPerturb(FN_DECIMAL& x, FN_DECIMAL& y, FN_DECIMAL& z) const -{ - SingleGradientPerturb(0, m_gradientPerturbAmp, m_frequency, x, y, z); -} - -void FastNoise::GradientPerturbFractal(FN_DECIMAL& x, FN_DECIMAL& y, FN_DECIMAL& z) const -{ - FN_DECIMAL amp = m_gradientPerturbAmp * m_fractalBounding; - FN_DECIMAL freq = m_frequency; - int i = 0; - - SingleGradientPerturb(m_perm[0], amp, m_frequency, x, y, z); - - while (++i < m_octaves) - { - freq *= m_lacunarity; - amp *= m_gain; - SingleGradientPerturb(m_perm[i], amp, freq, x, y, z); - } -} - -void FastNoise::SingleGradientPerturb(unsigned char offset, FN_DECIMAL warpAmp, FN_DECIMAL frequency, FN_DECIMAL& x, FN_DECIMAL& y, FN_DECIMAL& z) const -{ - FN_DECIMAL xf = x * frequency; - FN_DECIMAL yf = y * frequency; - FN_DECIMAL zf = z * frequency; - - int x0 = FastFloor(xf); - int y0 = FastFloor(yf); - int z0 = FastFloor(zf); - int x1 = x0 + 1; - int y1 = y0 + 1; - int z1 = z0 + 1; - - FN_DECIMAL xs, ys, zs; - switch (m_interp) - { - default: - case Linear: - xs = xf - (FN_DECIMAL)x0; - ys = yf - (FN_DECIMAL)y0; - zs = zf - (FN_DECIMAL)z0; - break; - case Hermite: - xs = InterpHermiteFunc(xf - (FN_DECIMAL)x0); - ys = InterpHermiteFunc(yf - (FN_DECIMAL)y0); - zs = InterpHermiteFunc(zf - (FN_DECIMAL)z0); - break; - case Quintic: - xs = InterpQuinticFunc(xf - (FN_DECIMAL)x0); - ys = InterpQuinticFunc(yf - (FN_DECIMAL)y0); - zs = InterpQuinticFunc(zf - (FN_DECIMAL)z0); - break; - } - - int lutPos0 = Index3D_256(offset, x0, y0, z0); - int lutPos1 = Index3D_256(offset, x1, y0, z0); - - FN_DECIMAL lx0x = Lerp(CELL_3D_X[lutPos0], CELL_3D_X[lutPos1], xs); - FN_DECIMAL ly0x = Lerp(CELL_3D_Y[lutPos0], CELL_3D_Y[lutPos1], xs); - FN_DECIMAL lz0x = Lerp(CELL_3D_Z[lutPos0], CELL_3D_Z[lutPos1], xs); - - lutPos0 = Index3D_256(offset, x0, y1, z0); - lutPos1 = Index3D_256(offset, x1, y1, z0); - - FN_DECIMAL lx1x = Lerp(CELL_3D_X[lutPos0], CELL_3D_X[lutPos1], xs); - FN_DECIMAL ly1x = Lerp(CELL_3D_Y[lutPos0], CELL_3D_Y[lutPos1], xs); - FN_DECIMAL lz1x = Lerp(CELL_3D_Z[lutPos0], CELL_3D_Z[lutPos1], xs); - - FN_DECIMAL lx0y = Lerp(lx0x, lx1x, ys); - FN_DECIMAL ly0y = Lerp(ly0x, ly1x, ys); - FN_DECIMAL lz0y = Lerp(lz0x, lz1x, ys); - - lutPos0 = Index3D_256(offset, x0, y0, z1); - lutPos1 = Index3D_256(offset, x1, y0, z1); - - lx0x = Lerp(CELL_3D_X[lutPos0], CELL_3D_X[lutPos1], xs); - ly0x = Lerp(CELL_3D_Y[lutPos0], CELL_3D_Y[lutPos1], xs); - lz0x = Lerp(CELL_3D_Z[lutPos0], CELL_3D_Z[lutPos1], xs); - - lutPos0 = Index3D_256(offset, x0, y1, z1); - lutPos1 = Index3D_256(offset, x1, y1, z1); - - lx1x = Lerp(CELL_3D_X[lutPos0], CELL_3D_X[lutPos1], xs); - ly1x = Lerp(CELL_3D_Y[lutPos0], CELL_3D_Y[lutPos1], xs); - lz1x = Lerp(CELL_3D_Z[lutPos0], CELL_3D_Z[lutPos1], xs); - - x += Lerp(lx0y, Lerp(lx0x, lx1x, ys), zs) * warpAmp; - y += Lerp(ly0y, Lerp(ly0x, ly1x, ys), zs) * warpAmp; - z += Lerp(lz0y, Lerp(lz0x, lz1x, ys), zs) * warpAmp; -} - -void FastNoise::GradientPerturb(FN_DECIMAL& x, FN_DECIMAL& y) const -{ - SingleGradientPerturb(0, m_gradientPerturbAmp, m_frequency, x, y); -} - -void FastNoise::GradientPerturbFractal(FN_DECIMAL& x, FN_DECIMAL& y) const -{ - FN_DECIMAL amp = m_gradientPerturbAmp * m_fractalBounding; - FN_DECIMAL freq = m_frequency; - int i = 0; - - SingleGradientPerturb(m_perm[0], amp, m_frequency, x, y); - - while (++i < m_octaves) - { - freq *= m_lacunarity; - amp *= m_gain; - SingleGradientPerturb(m_perm[i], amp, freq, x, y); - } -} - -void FastNoise::SingleGradientPerturb(unsigned char offset, FN_DECIMAL warpAmp, FN_DECIMAL frequency, FN_DECIMAL& x, FN_DECIMAL& y) const -{ - FN_DECIMAL xf = x * frequency; - FN_DECIMAL yf = y * frequency; - - int x0 = FastFloor(xf); - int y0 = FastFloor(yf); - int x1 = x0 + 1; - int y1 = y0 + 1; - - FN_DECIMAL xs, ys; - switch (m_interp) - { - default: - case Linear: - xs = xf - (FN_DECIMAL)x0; - ys = yf - (FN_DECIMAL)y0; - break; - case Hermite: - xs = InterpHermiteFunc(xf - (FN_DECIMAL)x0); - ys = InterpHermiteFunc(yf - (FN_DECIMAL)y0); - break; - case Quintic: - xs = InterpQuinticFunc(xf - (FN_DECIMAL)x0); - ys = InterpQuinticFunc(yf - (FN_DECIMAL)y0); - break; - } - - int lutPos0 = Index2D_256(offset, x0, y0); - int lutPos1 = Index2D_256(offset, x1, y0); - - FN_DECIMAL lx0x = Lerp(CELL_2D_X[lutPos0], CELL_2D_X[lutPos1], xs); - FN_DECIMAL ly0x = Lerp(CELL_2D_Y[lutPos0], CELL_2D_Y[lutPos1], xs); - - lutPos0 = Index2D_256(offset, x0, y1); - lutPos1 = Index2D_256(offset, x1, y1); - - FN_DECIMAL lx1x = Lerp(CELL_2D_X[lutPos0], CELL_2D_X[lutPos1], xs); - FN_DECIMAL ly1x = Lerp(CELL_2D_Y[lutPos0], CELL_2D_Y[lutPos1], xs); - - x += Lerp(lx0x, lx1x, ys) * warpAmp; - y += Lerp(ly0x, ly1x, ys) * warpAmp; -} diff --git a/FastNoise.h b/FastNoise.h deleted file mode 100644 index 902f95f..0000000 --- a/FastNoise.h +++ /dev/null @@ -1,311 +0,0 @@ -// FastNoise.h -// -// MIT License -// -// Copyright(c) 2017 Jordan Peck -// -// Permission is hereby granted, free of charge, to any person obtaining a copy -// of this software and associated documentation files(the "Software"), to deal -// in the Software without restriction, including without limitation the rights -// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell -// copies of the Software, and to permit persons to whom the Software is -// furnished to do so, subject to the following conditions : -// -// The above copyright notice and this permission notice shall be included in all -// copies or substantial portions of the Software. -// -// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE -// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -// SOFTWARE. -// -// The developer's email is jorzixdan.me2@gzixmail.com (for great email, take -// off every 'zix'.) -// - -// VERSION: 0.4.1 - -#ifndef FASTNOISE_H -#define FASTNOISE_H - -// Uncomment the line below to use doubles throughout FastNoise instead of floats -//#define FN_USE_DOUBLES - -#define FN_CELLULAR_INDEX_MAX 3 - -#ifdef FN_USE_DOUBLES -typedef double FN_DECIMAL; -#else -typedef float FN_DECIMAL; -#endif - -class FastNoise -{ -public: - explicit FastNoise(int seed = 1337) { SetSeed(seed); CalculateFractalBounding(); } - - enum NoiseType { Value, ValueFractal, Perlin, PerlinFractal, Simplex, SimplexFractal, Cellular, WhiteNoise, Cubic, CubicFractal }; - enum Interp { Linear, Hermite, Quintic }; - enum FractalType { FBM, Billow, RigidMulti }; - enum CellularDistanceFunction { Euclidean, Manhattan, Natural }; - enum CellularReturnType { CellValue, NoiseLookup, Distance, Distance2, Distance2Add, Distance2Sub, Distance2Mul, Distance2Div }; - - // Sets seed used for all noise types - // Default: 1337 - void SetSeed(int seed); - - // Returns seed used for all noise types - int GetSeed() const { return m_seed; } - - // Sets frequency for all noise types - // Default: 0.01 - void SetFrequency(FN_DECIMAL frequency) { m_frequency = frequency; } - - // Returns frequency used for all noise types - FN_DECIMAL GetFrequency() const { return m_frequency; } - - // Changes the interpolation method used to smooth between noise values - // Possible interpolation methods (lowest to highest quality) : - // - Linear - // - Hermite - // - Quintic - // Used in Value, Perlin Noise and Position Warping - // Default: Quintic - void SetInterp(Interp interp) { m_interp = interp; } - - // Returns interpolation method used for supported noise types - Interp GetInterp() const { return m_interp; } - - // Sets noise return type of GetNoise(...) - // Default: Simplex - void SetNoiseType(NoiseType noiseType) { m_noiseType = noiseType; } - - // Returns the noise type used by GetNoise - NoiseType GetNoiseType() const { return m_noiseType; } - - // Sets octave count for all fractal noise types - // Default: 3 - void SetFractalOctaves(int octaves) { m_octaves = octaves; CalculateFractalBounding(); } - - // Returns octave count for all fractal noise types - int GetFractalOctaves() const { return m_octaves; } - - // Sets octave lacunarity for all fractal noise types - // Default: 2.0 - void SetFractalLacunarity(FN_DECIMAL lacunarity) { m_lacunarity = lacunarity; } - - // Returns octave lacunarity for all fractal noise types - FN_DECIMAL GetFractalLacunarity() const { return m_lacunarity; } - - // Sets octave gain for all fractal noise types - // Default: 0.5 - void SetFractalGain(FN_DECIMAL gain) { m_gain = gain; CalculateFractalBounding(); } - - // Returns octave gain for all fractal noise types - FN_DECIMAL GetFractalGain() const { return m_gain; } - - // Sets method for combining octaves in all fractal noise types - // Default: FBM - void SetFractalType(FractalType fractalType) { m_fractalType = fractalType; } - - // Returns method for combining octaves in all fractal noise types - FractalType GetFractalType() const { return m_fractalType; } - - - // Sets distance function used in cellular noise calculations - // Default: Euclidean - void SetCellularDistanceFunction(CellularDistanceFunction cellularDistanceFunction) { m_cellularDistanceFunction = cellularDistanceFunction; } - - // Returns the distance function used in cellular noise calculations - CellularDistanceFunction GetCellularDistanceFunction() const { return m_cellularDistanceFunction; } - - // Sets return type from cellular noise calculations - // Note: NoiseLookup requires another FastNoise object be set with SetCellularNoiseLookup() to function - // Default: CellValue - void SetCellularReturnType(CellularReturnType cellularReturnType) { m_cellularReturnType = cellularReturnType; } - - // Returns the return type from cellular noise calculations - CellularReturnType GetCellularReturnType() const { return m_cellularReturnType; } - - // Noise used to calculate a cell value if cellular return type is NoiseLookup - // The lookup value is acquired through GetNoise() so ensure you SetNoiseType() on the noise lookup, value, Perlin or simplex is recommended - void SetCellularNoiseLookup(FastNoise* noise) { m_cellularNoiseLookup = noise; } - - // Returns the noise used to calculate a cell value if the cellular return type is NoiseLookup - FastNoise* GetCellularNoiseLookup() const { return m_cellularNoiseLookup; } - - // Sets the 2 distance indices used for distance2 return types - // Default: 0, 1 - // Note: index0 should be lower than index1 - // Both indices must be >= 0, index1 must be < 4 - void SetCellularDistance2Indices(int cellularDistanceIndex0, int cellularDistanceIndex1); - - // Returns the 2 distance indices used for distance2 return types - void GetCellularDistance2Indices(int& cellularDistanceIndex0, int& cellularDistanceIndex1) const; - - // Sets the maximum distance a cellular point can move from its grid position - // Setting this high will make artifacts more common - // Default: 0.45 - void SetCellularJitter(FN_DECIMAL cellularJitter) { m_cellularJitter = cellularJitter; } - - // Returns the maximum distance a cellular point can move from its grid position - FN_DECIMAL GetCellularJitter() const { return m_cellularJitter; } - - // Sets the maximum warp distance from original location when using GradientPerturb{Fractal}(...) - // Default: 1.0 - void SetGradientPerturbAmp(FN_DECIMAL gradientPerturbAmp) { m_gradientPerturbAmp = gradientPerturbAmp; } - - // Returns the maximum warp distance from original location when using GradientPerturb{Fractal}(...) - FN_DECIMAL GetGradientPerturbAmp() const { return m_gradientPerturbAmp; } - - //2D - FN_DECIMAL GetValue(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL GetValueFractal(FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL GetPerlin(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL GetPerlinFractal(FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL GetSimplex(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL GetSimplexFractal(FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL GetCellular(FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL GetWhiteNoise(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL GetWhiteNoiseInt(int x, int y) const; - - FN_DECIMAL GetCubic(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL GetCubicFractal(FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL GetNoise(FN_DECIMAL x, FN_DECIMAL y) const; - - void GradientPerturb(FN_DECIMAL& x, FN_DECIMAL& y) const; - void GradientPerturbFractal(FN_DECIMAL& x, FN_DECIMAL& y) const; - - //3D - FN_DECIMAL GetValue(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL GetValueFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL GetPerlin(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL GetPerlinFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL GetSimplex(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL GetSimplexFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL GetCellular(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL GetWhiteNoise(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL GetWhiteNoiseInt(int x, int y, int z) const; - - FN_DECIMAL GetCubic(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL GetCubicFractal(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL GetNoise(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - void GradientPerturb(FN_DECIMAL& x, FN_DECIMAL& y, FN_DECIMAL& z) const; - void GradientPerturbFractal(FN_DECIMAL& x, FN_DECIMAL& y, FN_DECIMAL& z) const; - - //4D - FN_DECIMAL GetSimplex(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z, FN_DECIMAL w) const; - - FN_DECIMAL GetWhiteNoise(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z, FN_DECIMAL w) const; - FN_DECIMAL GetWhiteNoiseInt(int x, int y, int z, int w) const; - -private: - unsigned char m_perm[512]; - unsigned char m_perm12[512]; - - int m_seed = 1337; - FN_DECIMAL m_frequency = FN_DECIMAL(0.01); - Interp m_interp = Quintic; - NoiseType m_noiseType = Simplex; - - int m_octaves = 3; - FN_DECIMAL m_lacunarity = FN_DECIMAL(2); - FN_DECIMAL m_gain = FN_DECIMAL(0.5); - FractalType m_fractalType = FBM; - FN_DECIMAL m_fractalBounding; - - CellularDistanceFunction m_cellularDistanceFunction = Euclidean; - CellularReturnType m_cellularReturnType = CellValue; - FastNoise* m_cellularNoiseLookup = nullptr; - int m_cellularDistanceIndex0 = 0; - int m_cellularDistanceIndex1 = 1; - FN_DECIMAL m_cellularJitter = FN_DECIMAL(0.45); - - FN_DECIMAL m_gradientPerturbAmp = FN_DECIMAL(1); - - void CalculateFractalBounding(); - - //2D - FN_DECIMAL SingleValueFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleValueFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleValueFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleValue(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL SinglePerlinFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SinglePerlinFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SinglePerlinFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SinglePerlin(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL SingleSimplexFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleSimplexFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleSimplexFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleSimplexFractalBlend(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleSimplex(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL SingleCubicFractalFBM(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleCubicFractalBillow(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleCubicFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleCubic(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y) const; - - FN_DECIMAL SingleCellular(FN_DECIMAL x, FN_DECIMAL y) const; - FN_DECIMAL SingleCellular2Edge(FN_DECIMAL x, FN_DECIMAL y) const; - - void SingleGradientPerturb(unsigned char offset, FN_DECIMAL warpAmp, FN_DECIMAL frequency, FN_DECIMAL& x, FN_DECIMAL& y) const; - - //3D - FN_DECIMAL SingleValueFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleValueFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleValueFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleValue(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL SinglePerlinFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SinglePerlinFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SinglePerlinFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SinglePerlin(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL SingleSimplexFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleSimplexFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleSimplexFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleSimplex(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL SingleCubicFractalFBM(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleCubicFractalBillow(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleCubicFractalRigidMulti(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleCubic(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - FN_DECIMAL SingleCellular(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - FN_DECIMAL SingleCellular2Edge(FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z) const; - - void SingleGradientPerturb(unsigned char offset, FN_DECIMAL warpAmp, FN_DECIMAL frequency, FN_DECIMAL& x, FN_DECIMAL& y, FN_DECIMAL& z) const; - - //4D - FN_DECIMAL SingleSimplex(unsigned char offset, FN_DECIMAL x, FN_DECIMAL y, FN_DECIMAL z, FN_DECIMAL w) const; - - inline unsigned char Index2D_12(unsigned char offset, int x, int y) const; - inline unsigned char Index3D_12(unsigned char offset, int x, int y, int z) const; - inline unsigned char Index4D_32(unsigned char offset, int x, int y, int z, int w) const; - inline unsigned char Index2D_256(unsigned char offset, int x, int y) const; - inline unsigned char Index3D_256(unsigned char offset, int x, int y, int z) const; - inline unsigned char Index4D_256(unsigned char offset, int x, int y, int z, int w) const; - - inline FN_DECIMAL ValCoord2DFast(unsigned char offset, int x, int y) const; - inline FN_DECIMAL ValCoord3DFast(unsigned char offset, int x, int y, int z) const; - inline FN_DECIMAL GradCoord2D(unsigned char offset, int x, int y, FN_DECIMAL xd, FN_DECIMAL yd) const; - inline FN_DECIMAL GradCoord3D(unsigned char offset, int x, int y, int z, FN_DECIMAL xd, FN_DECIMAL yd, FN_DECIMAL zd) const; - inline FN_DECIMAL GradCoord4D(unsigned char offset, int x, int y, int z, int w, FN_DECIMAL xd, FN_DECIMAL yd, FN_DECIMAL zd, FN_DECIMAL wd) const; -}; -#endif diff --git a/HLSL/FastNoiseLite.hlsl b/HLSL/FastNoiseLite.hlsl new file mode 100644 index 0000000..69361be --- /dev/null +++ b/HLSL/FastNoiseLite.hlsl @@ -0,0 +1,2315 @@ +// MIT License +// +// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com) +// Copyright(c) 2020 Contributors +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files(the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions : +// +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +// +// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll +// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo +// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd +// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx +// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx +// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd +// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo +// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo +// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo +// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo +// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo +// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo +// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl +// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c +// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c +// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc +// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll +// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo +// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd +// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk +// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000 +// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX +// +// VERSION: 1.0 +// https://github.com/Auburn/FastNoise + +// Switch between using floats or doubles for input position +typedef float FNLfloat; +//typedef double FNLfloat; + +// Noise Type +#define FNL_NOISE_OPENSIMPLEX2 0 +#define FNL_NOISE_OPENSIMPLEX2S 1 +#define FNL_NOISE_CELLULAR 2 +#define FNL_NOISE_PERLIN 3 +#define FNL_NOISE_VALUE_CUBIC 4 +#define FNL_NOISE_VALUE 5 +typedef int fnl_noise_type; + +// Rotation types +#define FNL_ROTATION_NONE 0 +#define FNL_ROTATION_IMPROVE_XY_PLANES 1 +#define FNL_ROTATION_IMPROVE_XZ_PLANES 2 +typedef int fnl_rotation_type_3d; + +// Fractal types +#define FNL_FRACTAL_NONE 0 +#define FNL_FRACTAL_FBM 1 +#define FNL_FRACTAL_RIDGED 2 +#define FNL_FRACTAL_PINGPONG 3 +#define FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE 4 +#define FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT 5 +typedef int fnl_fractal_type; + +#define FNL_CELLULAR_DISTANCE_EUCLIDEAN 0 +#define FNL_CELLULAR_DISTANCE_EUCLIDEANSQ 1 +#define FNL_CELLULAR_DISTANCE_MANHATTAN 2 +#define FNL_CELLULAR_DISTANCE_HYBRID 3 +typedef int fnl_cellular_distance_func; + +#define FNL_CELLULAR_RETURN_TYPE_CELLVALUE 0 +#define FNL_CELLULAR_RETURN_TYPE_DISTANCE 1 +#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2 2 +#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD 3 +#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB 4 +#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL 5 +#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV 6 +typedef int fnl_cellular_return_type; + +#define FNL_DOMAIN_WARP_OPENSIMPLEX2 0 +#define FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED 1 +#define FNL_DOMAIN_WARP_BASICGRID 2 +typedef int fnl_domain_warp_type; + +/** + * Structure containing entire noise system state. + * @note Must only be created using fnlCreateState(optional: seed). To ensure defaults are set. + */ +struct fnl_state +{ + /** + * Seed used for all noise types. + * @remark Default: 1337 + */ + int seed; + + /** + * The frequency for all noise types. + * @remark Default: 0.01 + */ + float frequency; + + /** + * The noise algorithm to be used by GetNoise(...). + * @remark Default: FNL_NOISE_OPENSIMPLEX2 + */ + fnl_noise_type noise_type; + + /** + * Sets noise rotation type for 3D. + * @remark Default: FNL_ROTATION_NONE + */ + fnl_rotation_type_3d rotation_type_3d; + + /** + * The method used for combining octaves for all fractal noise types. + * @remark Default: None + * @remark FNL_FRACTAL_DOMAIN_WARP_... only effects fnlDomainWarp... + */ + fnl_fractal_type fractal_type; + + /** + * The octave count for all fractal noise types. + * @remark Default: 3 + */ + int octaves; + + /** + * The octave lacunarity for all fractal noise types. + * @remark Default: 2.0 + */ + float lacunarity; + + /** + * The octave gain for all fractal noise types. + * @remark Default: 0.5 + */ + float gain; + + /** + * The octave weighting for all none Domaain Warp fractal types. + * @remark Default: 0.0 + * @remark + */ + float weighted_strength; + + /** + * The strength of the fractal ping pong effect. + * @remark Default: 2.0 + */ + float ping_pong_strength; + + /** + * The distance function used in cellular noise calculations. + * @remark Default: FNL_CELLULAR_FUNC_DISTANCE + */ + fnl_cellular_distance_func cellular_distance_func; + + /** + * The cellular return type from cellular noise calculations. + * @remark Default: FNL_CELLULAR_RETURN_TYPE_EUCLIEANSQ + */ + fnl_cellular_return_type cellular_return_type; + + /** + * The maximum distance a cellular point can move from it's grid position. + * @remark Default: 1.0 + * @note Setting this higher than 1 will cause artifacts. + */ + float cellular_jitter_mod; + + /** + * The warp algorithm when using fnlDomainWarp... + * @remark Default: OpenSimplex2 + */ + fnl_domain_warp_type domain_warp_type; + + /** + * The maximum warp distance from original position when using fnlDomainWarp... + * @remark Default: 1.0 + */ + float domain_warp_amp; +}; + +/** + * Creates a noise state with default values. + * @param seed Optionally set the state seed. + */ +fnl_state fnlCreateState(int seed = 1337); + +/** + * 2D noise at given position using the state settings + * @returns Noise output bounded between -1 and 1. + */ +float fnlGetNoise2D(fnl_state state, FNLfloat x, FNLfloat y); + +/** + * 3D noise at given position using the state settings + * @returns Noise output bounded between -1 and 1. + */ +float fnlGetNoise3D(fnl_state state, FNLfloat x, FNLfloat y, FNLfloat z); + +/** + * 2D warps the input position using current domain warp settings. + * + * Example usage with fnlGetNoise2D: + * ``` + * fnlDomainWarp2D(state, x, y); + * noise = fnlGetNoise2D(state, x, y); + * ``` + */ +void fnlDomainWarp2D(fnl_state state, inout FNLfloat x, inout FNLfloat y); + +/** + * 3D warps the input position using current domain warp settings. + * + * Example usage with fnlGetNoise3D: + * ``` + * fnlDomainWarp3D(state, x, y, z); + * noise = fnlGetNoise3D(state, x, y, z); + * ``` + */ +void fnlDomainWarp3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z); + +// From here on, this is private implementation + +// Constants + +static const float GRADIENTS_2D[] = +{ + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f, + -0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f, +}; + +static const float RAND_VECS_2D[] = +{ + -0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f, + -0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, 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0.7976208196f, -0.3160000073f, 0, + -0.3794024848f, 0.9245608561f, -0.03522751494f, 0, 0.8229248658f, 0.2745365933f, -0.4974176556f, 0, -0.5404114394f, 0.6091141441f, 0.5804613989f, 0, 0.8036581901f, -0.2703029469f, 0.5301601931f, 0, 0.6044318879f, 0.6832968393f, 0.4095943388f, 0, 0.06389988817f, 0.9658208605f, -0.2512108074f, 0, 0.1087113286f, 0.7402471173f, -0.6634877936f, 0, -0.713427712f, -0.6926784018f, 0.1059128479f, 0, + 0.6458897819f, -0.5724548511f, -0.5050958653f, 0, -0.6553931414f, 0.7381471625f, 0.159995615f, 0, 0.3910961323f, 0.9188871375f, -0.05186755998f, 0, -0.4879022471f, -0.5904376907f, 0.6429111375f, 0, 0.6014790094f, 0.7707441366f, -0.2101820095f, 0, -0.5677173047f, 0.7511360995f, 0.3368851762f, 0, 0.7858573506f, 0.226674665f, 0.5753666838f, 0, -0.4520345543f, -0.604222686f, -0.6561857263f, 0, + 0.002272116345f, 0.4132844051f, -0.9105991643f, 0, -0.5815751419f, -0.5162925989f, 0.6286591339f, 0, -0.03703704785f, 0.8273785755f, 0.5604221175f, 0, -0.5119692504f, 0.7953543429f, -0.3244980058f, 0, -0.2682417366f, -0.9572290247f, -0.1084387619f, 0, -0.2322482736f, -0.9679131102f, -0.09594243324f, 0, 0.3554328906f, -0.8881505545f, 0.2913006227f, 0, 0.7346520519f, -0.4371373164f, 0.5188422971f, 0, + 0.9985120116f, 0.04659011161f, -0.02833944577f, 0, -0.3727687496f, -0.9082481361f, 0.1900757285f, 0, 0.91737377f, -0.3483642108f, 0.1925298489f, 0, 0.2714911074f, 0.4147529736f, -0.8684886582f, 0, 0.5131763485f, -0.7116334161f, 0.4798207128f, 0, -0.8737353606f, 0.18886992f, -0.4482350644f, 0, 0.8460043821f, -0.3725217914f, 0.3814499973f, 0, 0.8978727456f, -0.1780209141f, -0.4026575304f, 0, + 0.2178065647f, -0.9698322841f, -0.1094789531f, 0, -0.1518031304f, -0.7788918132f, -0.6085091231f, 0, -0.2600384876f, -0.4755398075f, -0.8403819825f, 0, 0.572313509f, -0.7474340931f, -0.3373418503f, 0, -0.7174141009f, 0.1699017182f, -0.6756111411f, 0, -0.684180784f, 0.02145707593f, -0.7289967412f, 0, -0.2007447902f, 0.06555605789f, -0.9774476623f, 0, -0.1148803697f, -0.8044887315f, 0.5827524187f, 0, + -0.7870349638f, 0.03447489231f, 0.6159443543f, 0, -0.2015596421f, 0.6859872284f, 0.6991389226f, 0, -0.08581082512f, -0.10920836f, -0.9903080513f, 0, 0.5532693395f, 0.7325250401f, -0.396610771f, 0, -0.1842489331f, -0.9777375055f, -0.1004076743f, 0, 0.0775473789f, -0.9111505856f, 0.4047110257f, 0, 0.1399838409f, 0.7601631212f, -0.6344734459f, 0, 0.4484419361f, -0.845289248f, 0.2904925424f, 0 +}; + +// Utilities + +static inline float _fnlFastMin(float x, float y) { return x < y ? x : y; } + +static inline float _fnlFastMax(float x, float y) { return x > y ? x : y; } + +static inline float _fnlFastAbs(float f) { return f < 0 ? -f : f; } + +static inline float _fnlFastSqrt(float a) { return sqrt(a); } + +static inline int _fnlFastFloor(FNLfloat f) { return (f >= 0 ? (int)f : (int)f - 1); } + +static inline int _fnlFastRound(FNLfloat f) { return (f >= 0) ? (int)(f + 0.5f) : (int)(f - 0.5f); } + +static inline float _fnlLerp(float a, float b, float t) { return a + t * (b - a); } + +static inline float _fnlInterpHermite(float t) { return t * t * (3 - 2 * t); } + +static inline float _fnlInterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); } + +static inline float _fnlCubicLerp(float a, float b, float c, float d, float t) +{ + float p = (d - c) - (a - b); + return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b; +} + +static inline float _fnlPingPong(float t) +{ + t -= (int)(t * 0.5f) * 2; + return t < 1 ? t : 2 - t; +} + +static float _fnlCalculateFractalBounding(fnl_state state) +{ + float gain = _fnlFastAbs(state.gain); + float amp = gain; + float ampFractal = 1.0f; + for (int i = 1; i < state.octaves; i++) + { + ampFractal += amp; + amp *= gain; + } + return 1.0f / ampFractal; +} + +// Hashing + +static const int PRIME_X = 501125321; +static const int PRIME_Y = 1136930381; +static const int PRIME_Z = 1720413743; + +static inline int _fnlHash2D(int seed, int xPrimed, int yPrimed) +{ + int hash = seed ^ xPrimed ^ yPrimed; + + hash *= 0x27d4eb2d; + return hash; +} + +static inline int _fnlHash3D(int seed, int xPrimed, int yPrimed, int zPrimed) +{ + int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed; + + hash *= 0x27d4eb2d; + return hash; +} + +static inline float _fnlValCoord2D(int seed, int xPrimed, int yPrimed) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); +} + +static inline float _fnlValCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); +} + +static inline float _fnlGradCoord2D(int seed, int xPrimed, int yPrimed, float xd, float yd) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + hash ^= hash >> 15; + hash &= 127 << 1; + return xd * GRADIENTS_2D[hash] + yd * GRADIENTS_2D[hash | 1]; +} + +static inline float _fnlGradCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + hash ^= hash >> 15; + hash &= 63 << 2; + return xd * GRADIENTS_3D[hash] + yd * GRADIENTS_3D[hash | 1] + zd * GRADIENTS_3D[hash | 2]; +} + +static inline void _fnlGradCoordOut2D(int seed, int xPrimed, int yPrimed, out float xo, out float yo) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed) & (255 << 1); + + xo = RAND_VECS_2D[hash]; + yo = RAND_VECS_2D[hash | 1]; +} + +static inline void _fnlGradCoordOut3D(int seed, int xPrimed, int yPrimed, int zPrimed, out float xo, out float yo, out float zo) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed) & (255 << 2); + + xo = RAND_VECS_3D[hash]; + yo = RAND_VECS_3D[hash | 1]; + zo = RAND_VECS_3D[hash | 2]; +} + +static inline void _fnlGradCoordDual2D(int seed, int xPrimed, int yPrimed, float xd, float yd, out float xo, out float yo) +{ + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + + float xg = GRADIENTS_2D[index1]; + float yg = GRADIENTS_2D[index1 | 1]; + float value = xd * xg + yd * yg; + + float xgo = RAND_VECS_2D[index2]; + float ygo = RAND_VECS_2D[index2 | 1]; + + xo = value * xgo; + yo = value * ygo; +} + +static inline void _fnlGradCoordDual3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, out float xo, out float yo, out float zo) +{ + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int index1 = hash & (63 << 2); + int index2 = (hash >> 6) & (255 << 2); + + float xg = GRADIENTS_3D[index1]; + float yg = GRADIENTS_3D[index1 | 1]; + float zg = GRADIENTS_3D[index1 | 2]; + float value = xd * xg + yd * yg + zd * zg; + + float xgo = RAND_VECS_3D[index2]; + float ygo = RAND_VECS_3D[index2 | 1]; + float zgo = RAND_VECS_3D[index2 | 2]; + + xo = value * xgo; + yo = value * ygo; + zo = value * zgo; +} + +// Generic Noise Gen + +static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleCellular2D(fnl_state state, int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleCellular3D(fnl_state state, int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); +static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y); +static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z); + +static float _fnlGenNoiseSingle2D(fnl_state state, int seed, FNLfloat x, FNLfloat y) +{ + switch (state.noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + return _fnlSingleSimplex2D(seed, x, y); + case FNL_NOISE_OPENSIMPLEX2S: + return _fnlSingleOpenSimplex2S2D(seed, x, y); + case FNL_NOISE_CELLULAR: + return _fnlSingleCellular2D(state, seed, x, y); + case FNL_NOISE_PERLIN: + return _fnlSinglePerlin2D(seed, x, y); + case FNL_NOISE_VALUE_CUBIC: + return _fnlSingleValueCubic2D(seed, x, y); + case FNL_NOISE_VALUE: + return _fnlSingleValue2D(seed, x, y); + default: + return 0; + } +} + +static float _fnlGenNoiseSingle3D(fnl_state state, int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + switch (state.noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + return _fnlSingleOpenSimplex23D(seed, x, y, z); + case FNL_NOISE_OPENSIMPLEX2S: + return _fnlSingleOpenSimplex2S3D(seed, x, y, z); + case FNL_NOISE_CELLULAR: + return _fnlSingleCellular3D(state, seed, x, y, z); + case FNL_NOISE_PERLIN: + return _fnlSinglePerlin3D(seed, x, y, z); + case FNL_NOISE_VALUE_CUBIC: + return _fnlSingleValueCubic3D(seed, x, y, z); + case FNL_NOISE_VALUE: + return _fnlSingleValue3D(seed, x, y, z); + default: + return 0; + } +} + +// Noise Coordinate Transforms (frequency, and possible skew or rotation) + +static void _fnlTransformNoiseCoordinate2D(fnl_state state, inout FNLfloat x, inout FNLfloat y) +{ + x *= state.frequency; + y *= state.frequency; + + switch (state.noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + case FNL_NOISE_OPENSIMPLEX2S: + { + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat F2 = 0.5f * (SQRT3 - 1); + FNLfloat t = (x + y) * F2; + x += t; + y += t; + } + break; + default: + break; + } +} + +static void _fnlTransformNoiseCoordinate3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z) +{ + x *= state.frequency; + y *= state.frequency; + z *= state.frequency; + + switch (state.rotation_type_3d) + { + case FNL_ROTATION_IMPROVE_XY_PLANES: + { + FNLfloat xy = x + y; + FNLfloat s2 = xy * -(FNLfloat)0.211324865405187; + z *= (FNLfloat)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (FNLfloat)0.577350269189626; + } + break; + case FNL_ROTATION_IMPROVE_XZ_PLANES: + { + FNLfloat xz = x + z; + FNLfloat s2 = xz * -(FNLfloat)0.211324865405187; + y *= (FNLfloat)0.577350269189626; + x += s2 - y; + z += s2 - y; + y += xz * (FNLfloat)0.577350269189626; + } + break; + default: + switch (state.noise_type) + { + case FNL_NOISE_OPENSIMPLEX2: + case FNL_NOISE_OPENSIMPLEX2S: + { + const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + FNLfloat r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + break; + } +} + +// Domain Warp Coordinate Transforms + +static void _fnlTransformDomainWarpCoordinate2D(fnl_state state, inout FNLfloat x, inout FNLfloat y) +{ + switch (state.domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + { + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat F2 = 0.5f * (SQRT3 - 1); + FNLfloat t = (x + y) * F2; + x += t; + y += t; + } + break; + default: + break; + } +} + +static void _fnlTransformDomainWarpCoordinate3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z) +{ + switch (state.rotation_type_3d) + { + case FNL_ROTATION_IMPROVE_XY_PLANES: + { + FNLfloat xy = x + y; + FNLfloat s2 = xy * -(FNLfloat)0.211324865405187; + z *= (FNLfloat)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (FNLfloat)0.577350269189626; + } + break; + case FNL_ROTATION_IMPROVE_XZ_PLANES: + { + FNLfloat xz = x + z; + FNLfloat s2 = xz * -(FNLfloat)0.211324865405187; + y *= (FNLfloat)0.577350269189626; + x += s2 - y; + z += s2 - y; + y += xz * (FNLfloat)0.577350269189626; + } + break; + default: + switch (state.domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + { + const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + FNLfloat r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + } +} + +// Fractal FBm + +static float _fnlGenFractalFBM2D(fnl_state state, FNLfloat x, FNLfloat y) +{ + int seed = state.seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state.octaves; i++) + { + float noise = _fnlGenNoiseSingle2D(state, seed++, x, y); + sum += noise * amp; + amp *= _fnlLerp(1.0f, _fnlFastMin(noise + 1, 2) * 0.5f, state.weighted_strength); + + x *= state.lacunarity; + y *= state.lacunarity; + amp *= state.gain; + } + + return sum; +} + +static float _fnlGenFractalFBM3D(fnl_state state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int seed = state.seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state.octaves; i++) + { + float noise = _fnlGenNoiseSingle3D(state, seed++, x, y, z); + sum += noise * amp; + amp *= _fnlLerp(1.0f, (noise + 1) * 0.5f, state.weighted_strength); + + x *= state.lacunarity; + y *= state.lacunarity; + z *= state.lacunarity; + amp *= state.gain; + } + + return sum; +} + +// Fractal Ridged + +static float _fnlGenFractalRidged2D(fnl_state state, FNLfloat x, FNLfloat y) +{ + int seed = state.seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state.octaves; i++) + { + float noise = _fnlFastAbs(_fnlGenNoiseSingle2D(state, seed++, x, y)); + sum += (noise * -2 + 1) * amp; + amp *= _fnlLerp(1.0f, 1 - noise, state.weighted_strength); + + x *= state.lacunarity; + y *= state.lacunarity; + amp *= state.gain; + } + + return sum; +} + +static float _fnlGenFractalRidged3D(fnl_state state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int seed = state.seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state.octaves; i++) + { + float noise = _fnlFastAbs(_fnlGenNoiseSingle3D(state, seed++, x, y, z)); + sum += (noise * -2 + 1) * amp; + amp *= _fnlLerp(1.0f, 1 - noise, state.weighted_strength); + + x *= state.lacunarity; + y *= state.lacunarity; + z *= state.lacunarity; + amp *= state.gain; + } + + return sum; +} + +// Fractal PingPong + +static float _fnlGenFractalPingPong2D(fnl_state state, FNLfloat x, FNLfloat y) +{ + int seed = state.seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state.octaves; i++) + { + float noise = _fnlPingPong((_fnlGenNoiseSingle2D(state, seed++, x, y) + 1) * state.ping_pong_strength); + sum += (noise - 0.5f) * 2 * amp; + amp *= _fnlLerp(1.0f, noise, state.weighted_strength); + + x *= state.lacunarity; + y *= state.lacunarity; + amp *= state.gain; + } + + return sum; +} + +static float _fnlGenFractalPingPong3D(fnl_state state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int seed = state.seed; + float sum = 0; + float amp = _fnlCalculateFractalBounding(state); + + for (int i = 0; i < state.octaves; i++) + { + float noise = _fnlPingPong((_fnlGenNoiseSingle3D(state, seed++, x, y, z) + 1) * state.ping_pong_strength); + sum += (noise - 0.5f) * 2 * amp; + amp *= _fnlLerp(1.0f, noise, state.weighted_strength); + + x *= state.lacunarity; + y *= state.lacunarity; + z *= state.lacunarity; + amp *= state.gain; + } + + return sum; +} + +// Simplex/OpenSimplex2 Noise + +static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y) +{ + // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex. + + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PRIME_X; + j *= PRIME_Y; + + float n0, n1, n2; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a <= 0) + n0 = 0; + else + { + n0 = (a * a) * (a * a) * _fnlGradCoord2D(seed, i, j, x0, y0); + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c <= 0) + n2 = 0; + else + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + n2 = (c * c) * (c * c) * _fnlGradCoord2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2); + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) + n1 = 0; + else + { + n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x1, y1); + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) + n1 = 0; + else + { + n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i + PRIME_X, j, x1, y1); + } + } + + return (n0 + n1 + n2) * 99.83685446303647f; +} + +static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + // 3D OpenSimplex2 case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = _fnlFastRound(x); + int j = _fnlFastRound(y); + int k = _fnlFastRound(z); + float x0 = (float)(x - i); + float y0 = (float)(y - j); + float z0 = (float)(z - k); + + int xNSign = (int)(-1.0f - x0) | 1; + int yNSign = (int)(-1.0f - y0) | 1; + int zNSign = (int)(-1.0f - z0) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PRIME_X; + j *= PRIME_Y; + k *= PRIME_Z; + + float value = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; l < 2; l++) + { + if (a > 0) + { + value += (a * a) * (a * a) * _fnlGradCoord3D(seed, i, j, k, x0, y0, z0); + } + + float b = a + 1; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b -= xNSign * 2 * x1; + i1 -= xNSign * PRIME_X; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b -= yNSign * 2 * y1; + j1 -= yNSign * PRIME_Y; + } + else + { + z1 += zNSign; + b -= zNSign * 2 * z1; + k1 -= zNSign * PRIME_Z; + } + + if (b > 0) + { + value += (b * b) * (b * b) * _fnlGradCoord3D(seed, i1, j1, k1, x1, y1, z1); + } + + if (l == 1) + break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PRIME_X; + j += (yNSign >> 1) & PRIME_Y; + k += (zNSign >> 1) & PRIME_Z; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + return value * 32.69428253173828125f; +} + +// OpenSimplex2S Noise + +static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y) +{ + // 2D OpenSimplex2S case is a modified 2D simplex noise. + + const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059; + const FNLfloat G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + i *= PRIME_X; + j *= PRIME_Y; + int i1 = i + PRIME_X; + int j1 = j + PRIME_Y; + + float t = (xi + yi) * (float)G2; + float x0 = xi - t; + float y0 = yi - t; + + int aMask = (int)((xi + yi + 1) * -0.5f); + int bMask = (int)((xi - (aMask + 2)) * 0.5f - yi); + int cMask = (int)((yi - (aMask + 2)) * 0.5f - xi); + + float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0; + float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord2D(seed, i, j, x0, y0); + + float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0); + float x1 = x0 - (float)(1 - 2 * G2); + float y1 = y0 - (float)(1 - 2 * G2); + value += (a1 * a1) * (a1 * a1) * _fnlGradCoord2D(seed, i1, j1, x1, y1); + + int di2 = ~(aMask | cMask) | 1; + int ndj2 = (aMask & bMask) << 1; + float t2 = (di2 - ndj2) * (float)G2; + float x2 = x0 - di2 + t2; + float y2 = y0 + ndj2 + t2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i1 + (di2 & (-PRIME_X << 1)), j + (ndj2 & (PRIME_Y << 1)), x2, y2); + } + + int ndi3 = (aMask & cMask) << 1; + int dj3 = ~(aMask | bMask) | 1; + float t3 = (dj3 - ndi3) * (float)G2; + float x3 = x0 + ndi3 + t3; + float y3 = y0 - dj3 + t3; + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * _fnlGradCoord2D(seed, i + (ndi3 & (PRIME_X << 1)), j1 + (dj3 & (-PRIME_Y << 1)), x3, y3); + } + + return value * 18.24196194486065f; +} + +static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + // 3D OpenSimplex2S case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + int k = _fnlFastFloor(z); + float xi = (float)(x - i); + float yi = (float)(y - j); + float zi = (float)(z - k); + + i *= PRIME_X; + j *= PRIME_Y; + k *= PRIME_Z; + int seed2 = seed + 1293373; + + int xNMask = (int)(-0.5f - xi); + int yNMask = (int)(-0.5f - yi); + int zNMask = (int)(-0.5f - zi); + + float x0 = xi + xNMask; + float y0 = yi + yNMask; + float z0 = zi + zNMask; + float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0; + float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x0, y0, z0); + + float x1 = xi - 0.5f; + float y1 = yi - 0.5f; + float z1 = zi - 0.5f; + float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1; + value += (a1 * a1) * (a1 * a1) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + PRIME_Y, k + PRIME_Z, x1, y1, z1); + + float xAFlipMask0 = ((xNMask | 1) << 1) * x1; + float yAFlipMask0 = ((yNMask | 1) << 1) * y1; + float zAFlipMask0 = ((zNMask | 1) << 1) * z1; + float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f; + float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f; + float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f; + + bool skip5 = false; + float a2 = xAFlipMask0 + a0; + if (a2 > 0) + { + float x2 = x0 - (xNMask | 1); + float y2 = y0; + float z2 = z0; + value += (a2 * a2) * (a2 * a2) * _fnlGradCoord3D(seed, + i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x2, y2, z2); + } + else + { + float a3 = yAFlipMask0 + zAFlipMask0 + a0; + if (a3 > 0) + { + float x3 = x0; + float y3 = y0 - (yNMask | 1); + float z3 = z0 - (zNMask | 1); + value += (a3 * a3) * (a3 * a3) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x3, y3, z3); + } + + float a4 = xAFlipMask1 + a1; + if (a4 > 0) + { + float x4 = (xNMask | 1) + x1; + float y4 = y1; + float z4 = z1; + value += (a4 * a4) * (a4 * a4) * _fnlGradCoord3D(seed2, + i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + PRIME_Z, x4, y4, z4); + skip5 = true; + } + } + + bool skip9 = false; + float a6 = yAFlipMask0 + a0; + if (a6 > 0) + { + float x6 = x0; + float y6 = y0 - (yNMask | 1); + float z6 = z0; + value += (a6 * a6) * (a6 * a6) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x6, y6, z6); + } + else + { + float a7 = xAFlipMask0 + zAFlipMask0 + a0; + if (a7 > 0) + { + float x7 = x0 - (xNMask | 1); + float y7 = y0; + float z7 = z0 - (zNMask | 1); + value += (a7 * a7) * (a7 * a7) * _fnlGradCoord3D(seed, + i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x7, y7, z7); + } + + float a8 = yAFlipMask1 + a1; + if (a8 > 0) + { + float x8 = x1; + float y8 = (yNMask | 1) + y1; + float z8 = z1; + value += (a8 * a8) * (a8 * a8) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, x8, y8, z8); + skip9 = true; + } + } + + bool skipD = false; + float aA = zAFlipMask0 + a0; + if (aA > 0) + { + float xA = x0; + float yA = y0; + float zA = z0 - (zNMask | 1); + value += (aA * aA) * (aA * aA) * _fnlGradCoord3D(seed, + i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), xA, yA, zA); + } + else + { + float aB = xAFlipMask0 + yAFlipMask0 + a0; + if (aB > 0) + { + float xB = x0 - (xNMask | 1); + float yB = y0 - (yNMask | 1); + float zB = z0; + value += (aB * aB) * (aB * aB) * _fnlGradCoord3D(seed, + i + (~xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), xB, yB, zB); + } + + float aC = zAFlipMask1 + a1; + if (aC > 0) + { + float xC = x1; + float yC = y1; + float zC = (zNMask | 1) + z1; + value += (aC * aC) * (aC * aC) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), xC, yC, zC); + skipD = true; + } + } + + if (!skip5) + { + float a5 = yAFlipMask1 + zAFlipMask1 + a1; + if (a5 > 0) + { + float x5 = x1; + float y5 = (yNMask | 1) + y1; + float z5 = (zNMask | 1) + z1; + value += (a5 * a5) * (a5 * a5) * _fnlGradCoord3D(seed2, + i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + (zNMask & (PRIME_Z << 1)), x5, y5, z5); + } + } + + if (!skip9) + { + float a9 = xAFlipMask1 + zAFlipMask1 + a1; + if (a9 > 0) + { + float x9 = (xNMask | 1) + x1; + float y9 = y1; + float z9 = (zNMask | 1) + z1; + value += (a9 * a9) * (a9 * a9) * _fnlGradCoord3D(seed2, + i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), x9, y9, z9); + } + } + + if (!skipD) + { + float aD = xAFlipMask1 + yAFlipMask1 + a1; + if (aD > 0) + { + float xD = (xNMask | 1) + x1; + float yD = (yNMask | 1) + y1; + float zD = z1; + value += (aD * aD) * (aD * aD) * _fnlGradCoord3D(seed2, + i + (xNMask & (PRIME_X << 1)), j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, xD, yD, zD); + } + } + + return value * 9.046026385208288f; +} + +// Cellular Noise + +static float _fnlSingleCellular2D(fnl_state state, int seed, FNLfloat x, FNLfloat y) +{ + int xr = _fnlFastRound(x); + int yr = _fnlFastRound(y); + + float distance0 = 1e10f; + float distance1 = 1e10f; + int closestHash = 0; + + float cellularJitter = 0.5f * state.cellular_jitter_mod; + + int xPrimed = (xr - 1) * PRIME_X; + int yPrimedBase = (yr - 1) * PRIME_Y; + + switch (state.cellular_distance_func) + { + default: + case FNL_CELLULAR_DISTANCE_EUCLIDEAN: + case FNL_CELLULAR_DISTANCE_EUCLIDEANSQ: + { + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY; + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + case FNL_CELLULAR_DISTANCE_MANHATTAN: + { + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter; + + float newDistance = _fnlFastAbs(vecX) + _fnlFastAbs(vecY); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + case FNL_CELLULAR_DISTANCE_HYBRID: + { + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = _fnlHash2D(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter; + + float newDistance = (_fnlFastAbs(vecX) + _fnlFastAbs(vecY)) + (vecX * vecX + vecY * vecY); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + } + + if (state.cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN && state.cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE) + { + distance0 = _fnlFastSqrt(distance0); + if (state.cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE2) + distance1 = _fnlFastSqrt(distance1); + } + + switch (state.cellular_return_type) + { + case FNL_CELLULAR_RETURN_TYPE_CELLVALUE: + return closestHash * (1 / 2147483648.0f); + case FNL_CELLULAR_RETURN_TYPE_DISTANCE: + return distance0 - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2: + return distance1 - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD: + return (distance1 + distance0) * 0.5f - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB: + return distance1 - distance0 - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL: + return distance1 * distance0 * 0.5f - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV: + return distance0 / distance1 - 1; + default: + return 0; + } +} + +static float _fnlSingleCellular3D(fnl_state state, int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int xr = _fnlFastRound(x); + int yr = _fnlFastRound(y); + int zr = _fnlFastRound(z); + + float distance0 = 1e10f; + float distance1 = 1e10f; + int closestHash = 0; + + float cellularJitter = 0.39614353f * state.cellular_jitter_mod; + + int xPrimed = (xr - 1) * PRIME_X; + int yPrimedBase = (yr - 1) * PRIME_Y; + int zPrimedBase = (zr - 1) * PRIME_Z; + + switch (state.cellular_distance_func) + { + default: + case FNL_CELLULAR_DISTANCE_EUCLIDEAN: + case FNL_CELLULAR_DISTANCE_EUCLIDEANSQ: + { + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PRIME_Z; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + case FNL_CELLULAR_DISTANCE_MANHATTAN: + { + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter; + + float newDistance = _fnlFastAbs(vecX) + _fnlFastAbs(vecY) + _fnlFastAbs(vecZ); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PRIME_Z; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + case FNL_CELLULAR_DISTANCE_HYBRID: + { + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter; + + float newDistance = (_fnlFastAbs(vecX) + _fnlFastAbs(vecY) + _fnlFastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); + + distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PRIME_Z; + } + yPrimed += PRIME_Y; + } + xPrimed += PRIME_X; + } + break; + } + } + + if (state.cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN && state.cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE) + { + distance0 = _fnlFastSqrt(distance0); + if (state.cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE2) + distance1 = _fnlFastSqrt(distance1); + } + + switch (state.cellular_return_type) + { + case FNL_CELLULAR_RETURN_TYPE_CELLVALUE: + return closestHash * (1 / 2147483648.0f); + case FNL_CELLULAR_RETURN_TYPE_DISTANCE: + return distance0 - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2: + return distance1 - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD: + return (distance1 + distance0) * 0.5f - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB: + return distance1 - distance0 - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL: + return distance1 * distance0 * 0.5f - 1; + case FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV: + return distance0 / distance1 - 1; + default: + return 0; + } +} + +// Perlin Noise + +static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + + float xs = _fnlInterpQuintic(xd0); + float ys = _fnlInterpQuintic(yd0); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + + float xf0 = _fnlLerp(_fnlGradCoord2D(seed, x0, y0, xd0, yd0), _fnlGradCoord2D(seed, x1, y0, xd1, yd0), xs); + float xf1 = _fnlLerp(_fnlGradCoord2D(seed, x0, y1, xd0, yd1), _fnlGradCoord2D(seed, x1, y1, xd1, yd1), xs); + + return _fnlLerp(xf0, xf1, ys) * 1.4247691104677813f; +} + +static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + int z0 = _fnlFastFloor(z); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float zd0 = (float)(z - z0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + float zd1 = zd0 - 1; + + float xs = _fnlInterpQuintic(xd0); + float ys = _fnlInterpQuintic(yd0); + float zs = _fnlInterpQuintic(zd0); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + z0 *= PRIME_Z; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + int z1 = z0 + PRIME_Z; + + float xf00 = _fnlLerp(_fnlGradCoord3D(seed, x0, y0, z0, xd0, yd0, zd0), _fnlGradCoord3D(seed, x1, y0, z0, xd1, yd0, zd0), xs); + float xf10 = _fnlLerp(_fnlGradCoord3D(seed, x0, y1, z0, xd0, yd1, zd0), _fnlGradCoord3D(seed, x1, y1, z0, xd1, yd1, zd0), xs); + float xf01 = _fnlLerp(_fnlGradCoord3D(seed, x0, y0, z1, xd0, yd0, zd1), _fnlGradCoord3D(seed, x1, y0, z1, xd1, yd0, zd1), xs); + float xf11 = _fnlLerp(_fnlGradCoord3D(seed, x0, y1, z1, xd0, yd1, zd1), _fnlGradCoord3D(seed, x1, y1, z1, xd1, yd1, zd1), xs); + + float yf0 = _fnlLerp(xf00, xf10, ys); + float yf1 = _fnlLerp(xf01, xf11, ys); + + return _fnlLerp(yf0, yf1, zs) * 0.964921414852142333984375f; +} + +// Value Cubic + +static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y) +{ + int x1 = _fnlFastFloor(x); + int y1 = _fnlFastFloor(y); + + float xs = x - (float)x1; + float ys = y - (float)y1; + + x1 *= PRIME_X; + y1 *= PRIME_Y; + + int x0 = x1 - PRIME_X; + int y0 = y1 - PRIME_Y; + int x2 = x1 + PRIME_X; + int y2 = y1 + PRIME_Y; + int x3 = x1 + PRIME_X * 2; + int y3 = y1 + PRIME_Y * 2; + + return _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y0), _fnlValCoord2D(seed, x1, y0), _fnlValCoord2D(seed, x2, y0), _fnlValCoord2D(seed, x3, y0), + xs), + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y1), _fnlValCoord2D(seed, x1, y1), _fnlValCoord2D(seed, x2, y1), _fnlValCoord2D(seed, x3, y1), + xs), + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y2), _fnlValCoord2D(seed, x1, y2), _fnlValCoord2D(seed, x2, y2), _fnlValCoord2D(seed, x3, y2), + xs), + _fnlCubicLerp(_fnlValCoord2D(seed, x0, y3), _fnlValCoord2D(seed, x1, y3), _fnlValCoord2D(seed, x2, y3), _fnlValCoord2D(seed, x3, y3), + xs), + ys) * (1 / (1.5f * 1.5f)); +} + +static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int x1 = _fnlFastFloor(x); + int y1 = _fnlFastFloor(y); + int z1 = _fnlFastFloor(z); + + float xs = x - (float)x1; + float ys = y - (float)y1; + float zs = z - (float)z1; + + x1 *= PRIME_X; + y1 *= PRIME_Y; + z1 *= PRIME_Z; + + int x0 = x1 - PRIME_X; + int y0 = y1 - PRIME_Y; + int z0 = z1 - PRIME_Z; + int x2 = x1 + PRIME_X; + int y2 = y1 + PRIME_Y; + int z2 = z1 + PRIME_Z; + int x3 = x1 + PRIME_X * 2; + int y3 = y1 + PRIME_Y * 2; + int z3 = z1 + PRIME_Z * 2; + + return _fnlCubicLerp( + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z0), _fnlValCoord3D(seed, x1, y0, z0), _fnlValCoord3D(seed, x2, y0, z0), _fnlValCoord3D(seed, x3, y0, z0), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z0), _fnlValCoord3D(seed, x1, y1, z0), _fnlValCoord3D(seed, x2, y1, z0), _fnlValCoord3D(seed, x3, y1, z0), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z0), _fnlValCoord3D(seed, x1, y2, z0), _fnlValCoord3D(seed, x2, y2, z0), _fnlValCoord3D(seed, x3, y2, z0), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z0), _fnlValCoord3D(seed, x1, y3, z0), _fnlValCoord3D(seed, x2, y3, z0), _fnlValCoord3D(seed, x3, y3, z0), xs), + ys), + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z1), _fnlValCoord3D(seed, x1, y0, z1), _fnlValCoord3D(seed, x2, y0, z1), _fnlValCoord3D(seed, x3, y0, z1), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z1), _fnlValCoord3D(seed, x1, y1, z1), _fnlValCoord3D(seed, x2, y1, z1), _fnlValCoord3D(seed, x3, y1, z1), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z1), _fnlValCoord3D(seed, x1, y2, z1), _fnlValCoord3D(seed, x2, y2, z1), _fnlValCoord3D(seed, x3, y2, z1), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z1), _fnlValCoord3D(seed, x1, y3, z1), _fnlValCoord3D(seed, x2, y3, z1), _fnlValCoord3D(seed, x3, y3, z1), xs), + ys), + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z2), _fnlValCoord3D(seed, x1, y0, z2), _fnlValCoord3D(seed, x2, y0, z2), _fnlValCoord3D(seed, x3, y0, z2), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z2), _fnlValCoord3D(seed, x1, y1, z2), _fnlValCoord3D(seed, x2, y1, z2), _fnlValCoord3D(seed, x3, y1, z2), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z2), _fnlValCoord3D(seed, x1, y2, z2), _fnlValCoord3D(seed, x2, y2, z2), _fnlValCoord3D(seed, x3, y2, z2), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z2), _fnlValCoord3D(seed, x1, y3, z2), _fnlValCoord3D(seed, x2, y3, z2), _fnlValCoord3D(seed, x3, y3, z2), xs), + ys), + _fnlCubicLerp( + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z3), _fnlValCoord3D(seed, x1, y0, z3), _fnlValCoord3D(seed, x2, y0, z3), _fnlValCoord3D(seed, x3, y0, z3), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z3), _fnlValCoord3D(seed, x1, y1, z3), _fnlValCoord3D(seed, x2, y1, z3), _fnlValCoord3D(seed, x3, y1, z3), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z3), _fnlValCoord3D(seed, x1, y2, z3), _fnlValCoord3D(seed, x2, y2, z3), _fnlValCoord3D(seed, x3, y2, z3), xs), + _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z3), _fnlValCoord3D(seed, x1, y3, z3), _fnlValCoord3D(seed, x2, y3, z3), _fnlValCoord3D(seed, x3, y3, z3), xs), + ys), + zs) * (1 / 1.5f * 1.5f * 1.5f); +} + +// Value noise + +static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + + float xs = _fnlInterpHermite((float)(x - x0)); + float ys = _fnlInterpHermite((float)(y - y0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + + float xf0 = _fnlLerp(_fnlValCoord2D(seed, x0, y0), _fnlValCoord2D(seed, x1, y0), xs); + float xf1 = _fnlLerp(_fnlValCoord2D(seed, x0, y1), _fnlValCoord2D(seed, x1, y1), xs); + + return _fnlLerp(xf0, xf1, ys); +} + +static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z) +{ + int x0 = _fnlFastFloor(x); + int y0 = _fnlFastFloor(y); + int z0 = _fnlFastFloor(z); + + float xs = _fnlInterpHermite((float)(x - x0)); + float ys = _fnlInterpHermite((float)(y - y0)); + float zs = _fnlInterpHermite((float)(z - z0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + z0 *= PRIME_Z; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + int z1 = z0 + PRIME_Z; + + float xf00 = _fnlLerp(_fnlValCoord3D(seed, x0, y0, z0), _fnlValCoord3D(seed, x1, y0, z0), xs); + float xf10 = _fnlLerp(_fnlValCoord3D(seed, x0, y1, z0), _fnlValCoord3D(seed, x1, y1, z0), xs); + float xf01 = _fnlLerp(_fnlValCoord3D(seed, x0, y0, z1), _fnlValCoord3D(seed, x1, y0, z1), xs); + float xf11 = _fnlLerp(_fnlValCoord3D(seed, x0, y1, z1), _fnlValCoord3D(seed, x1, y1, z1), xs); + + float yf0 = _fnlLerp(xf00, xf10, ys); + float yf1 = _fnlLerp(xf01, xf11, ys); + + return _fnlLerp(yf0, yf1, zs); +} + +// Domain Warp + +// Forward declare +static void _fnlSingleDomainWarpBasicGrid2D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, out FNLfloat xp, out FNLfloat yp); +static void _fnlSingleDomainWarpBasicGrid3D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, out FNLfloat xp, out FNLfloat yp, out FNLfloat zp); +static void _fnlSingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, out FNLfloat xr, out FNLfloat yr, bool outGradOnly); +static void _fnlSingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, out FNLfloat xr, out FNLfloat yr, out FNLfloat zr, bool outGradOnly); + +static void _fnlDoSingleDomainWarp2D(fnl_state state, int seed, float amp, float freq, FNLfloat x, FNLfloat y, out FNLfloat xp, out FNLfloat yp) +{ + switch (state.domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + _fnlSingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, xp, yp, false); + break; + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + _fnlSingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, xp, yp, true); + break; + case FNL_DOMAIN_WARP_BASICGRID: + _fnlSingleDomainWarpBasicGrid2D(seed, amp, freq, x, y, xp, yp); + break; + } +} + +static void _fnlDoSingleDomainWarp3D(fnl_state state, int seed, float amp, float freq, FNLfloat x, FNLfloat y, FNLfloat z, out FNLfloat xp, out FNLfloat yp, out FNLfloat zp) +{ + switch (state.domain_warp_type) + { + case FNL_DOMAIN_WARP_OPENSIMPLEX2: + _fnlSingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, xp, yp, zp, false); + break; + case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED: + _fnlSingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, xp, yp, zp, true); + break; + case FNL_DOMAIN_WARP_BASICGRID: + _fnlSingleDomainWarpBasicGrid3D(seed, amp, freq, x, y, z, xp, yp, zp); + break; + } +} + +// Domain Warp Single Wrapper + +static void _fnlDomainWarpSingle2D(fnl_state state, inout FNLfloat x, inout FNLfloat y) +{ + int seed = state.seed; + float amp = state.domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state.frequency; + + FNLfloat xs = x; + FNLfloat ys = y; + _fnlTransformDomainWarpCoordinate2D(state, xs, ys); + + _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y); +} + +static void _fnlDomainWarpSingle3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z) +{ + int seed = state.seed; + float amp = state.domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state.frequency; + + FNLfloat xs = x; + FNLfloat ys = y; + FNLfloat zs = z; + _fnlTransformDomainWarpCoordinate3D(state, xs, ys, zs); + + _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z); +} + +// Domain Warp Fractal Progressive + +static void _fnlDomainWarpFractalProgressive2D(fnl_state state, inout FNLfloat x, inout FNLfloat y) +{ + int seed = state.seed; + float amp = state.domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state.frequency; + + for (int i = 0; i < state.octaves; i++) + { + FNLfloat xs = x; + FNLfloat ys = y; + _fnlTransformDomainWarpCoordinate2D(state, xs, ys); + + _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y); + + seed++; + amp *= state.gain; + freq *= state.lacunarity; + } +} + +static void _fnlDomainWarpFractalProgressive3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z) +{ + int seed = state.seed; + float amp = state.domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state.frequency; + + for (int i = 0; i < state.octaves; i++) + { + FNLfloat xs = x; + FNLfloat ys = y; + FNLfloat zs = z; + _fnlTransformDomainWarpCoordinate3D(state, xs, ys, zs); + + _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z); + + seed++; + amp *= state.gain; + freq *= state.lacunarity; + } +} + +// Domain Warp Fractal Independent + +static void _fnlDomainWarpFractalIndependent2D(fnl_state state, inout FNLfloat x, inout FNLfloat y) +{ + FNLfloat xs = x; + FNLfloat ys = y; + _fnlTransformDomainWarpCoordinate2D(state, xs, ys); + + int seed = state.seed; + float amp = state.domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state.frequency; + + for (int i = 0; i < state.octaves; i++) + { + _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y); + + seed++; + amp *= state.gain; + freq *= state.lacunarity; + } +} + +static void _fnlDomainWarpFractalIndependent3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z) +{ + FNLfloat xs = x; + FNLfloat ys = y; + FNLfloat zs = z; + _fnlTransformDomainWarpCoordinate3D(state, xs, ys, zs); + + int seed = state.seed; + float amp = state.domain_warp_amp * _fnlCalculateFractalBounding(state); + float freq = state.frequency; + + for (int i = 0; i < state.octaves; i++) + { + _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z); + + seed++; + amp *= state.gain; + freq *= state.lacunarity; + } +} + +// Domain Warp Basic Grid + +static void _fnlSingleDomainWarpBasicGrid2D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, out FNLfloat xp, out FNLfloat yp) +{ + FNLfloat xf = x * frequency; + FNLfloat yf = y * frequency; + + int x0 = _fnlFastFloor(xf); + int y0 = _fnlFastFloor(yf); + + float xs = _fnlInterpHermite((float)(xf - x0)); + float ys = _fnlInterpHermite((float)(yf - y0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + + int idx0 = _fnlHash2D(seed, x0, y0) & (255 << 1); + int idx1 = _fnlHash2D(seed, x1, y0) & (255 << 1); + + float lx0x = _fnlLerp(RAND_VECS_2D[idx0], RAND_VECS_2D[idx1], xs); + float ly0x = _fnlLerp(RAND_VECS_2D[idx0 | 1], RAND_VECS_2D[idx1 | 1], xs); + + idx0 = _fnlHash2D(seed, x0, y1) & (255 << 1); + idx1 = _fnlHash2D(seed, x1, y1) & (255 << 1); + + float lx1x = _fnlLerp(RAND_VECS_2D[idx0], RAND_VECS_2D[idx1], xs); + float ly1x = _fnlLerp(RAND_VECS_2D[idx0 | 1], RAND_VECS_2D[idx1 | 1], xs); + + xp += _fnlLerp(lx0x, lx1x, ys) * warpAmp; + yp += _fnlLerp(ly0x, ly1x, ys) * warpAmp; +} + +static void _fnlSingleDomainWarpBasicGrid3D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, out FNLfloat xp, out FNLfloat yp, out FNLfloat zp) +{ + FNLfloat xf = x * frequency; + FNLfloat yf = y * frequency; + FNLfloat zf = z * frequency; + + int x0 = _fnlFastFloor(xf); + int y0 = _fnlFastFloor(yf); + int z0 = _fnlFastFloor(zf); + + float xs = _fnlInterpHermite((float)(xf - x0)); + float ys = _fnlInterpHermite((float)(yf - y0)); + float zs = _fnlInterpHermite((float)(zf - z0)); + + x0 *= PRIME_X; + y0 *= PRIME_Y; + z0 *= PRIME_Z; + int x1 = x0 + PRIME_X; + int y1 = y0 + PRIME_Y; + int z1 = z0 + PRIME_Z; + + int idx0 = _fnlHash3D(seed, x0, y0, z0) & (255 << 2); + int idx1 = _fnlHash3D(seed, x1, y0, z0) & (255 << 2); + + float lx0x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + float ly0x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + float lz0x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + idx0 = _fnlHash3D(seed, x0, y1, z0) & (255 << 2); + idx1 = _fnlHash3D(seed, x1, y1, z0) & (255 << 2); + + float lx1x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + float ly1x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + float lz1x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + float lx0y = _fnlLerp(lx0x, lx1x, ys); + float ly0y = _fnlLerp(ly0x, ly1x, ys); + float lz0y = _fnlLerp(lz0x, lz1x, ys); + + idx0 = _fnlHash3D(seed, x0, y0, z1) & (255 << 2); + idx1 = _fnlHash3D(seed, x1, y0, z1) & (255 << 2); + + lx0x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + ly0x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + lz0x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + idx0 = _fnlHash3D(seed, x0, y1, z1) & (255 << 2); + idx1 = _fnlHash3D(seed, x1, y1, z1) & (255 << 2); + + lx1x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs); + ly1x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs); + lz1x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs); + + xp += _fnlLerp(lx0y, _fnlLerp(lx0x, lx1x, ys), zs) * warpAmp; + yp += _fnlLerp(ly0y, _fnlLerp(ly0x, ly1x, ys), zs) * warpAmp; + zp += _fnlLerp(lz0y, _fnlLerp(lz0x, lz1x, ys), zs) * warpAmp; +} + +// Domain Warp Simplex/OpenSimplex2 + +static void _fnlSingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, out FNLfloat xr, out FNLfloat yr, bool outGradOnly) +{ + const float SQRT3 = 1.7320508075688772935274463415059f; + const float G2 = (3 - SQRT3) / 6; + + x *= frequency; + y *= frequency; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * const FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = _fnlFastFloor(x); + int j = _fnlFastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PRIME_X; + j *= PRIME_Y; + + float vx, vy; + vx = vy = 0; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i, j, xo, yo); + else + _fnlGradCoordDual2D(seed, i, j, x0, y0, xo, yo); + vx += aaaa * xo; + vy += aaaa * yo; + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c > 0) + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + float cccc = (c * c) * (c * c); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i + PRIME_X, j + PRIME_Y, xo, yo); + else + _fnlGradCoordDual2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2, xo, yo); + vx += cccc * xo; + vy += cccc * yo; + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i, j + PRIME_Y, xo, yo); + else + _fnlGradCoordDual2D(seed, i, j + PRIME_Y, x1, y1, xo, yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + _fnlGradCoordOut2D(seed, i + PRIME_X, j, xo, yo); + else + _fnlGradCoordDual2D(seed, i + PRIME_X, j, x1, y1, xo, yo); + vx += bbbb * xo; + vy += bbbb * yo; + } + } + + xr += vx * warpAmp; + yr += vy * warpAmp; +} + +static void _fnlSingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, out FNLfloat xr, out FNLfloat yr, out FNLfloat zr, bool outGradOnly) +{ + x *= frequency; + y *= frequency; + z *= frequency; + + /* + * --- Rotation moved to TransformDomainWarpCoordinate method --- + * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = _fnlFastRound(x); + int j = _fnlFastRound(y); + int k = _fnlFastRound(z); + float x0 = (float)x - i; + float y0 = (float)y - j; + float z0 = (float)z - k; + + int xNSign = (int)(-x0 - 1.0f) | 1; + int yNSign = (int)(-y0 - 1.0f) | 1; + int zNSign = (int)(-z0 - 1.0f) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PRIME_X; + j *= PRIME_Y; + k *= PRIME_Z; + + float vx, vy, vz; + vx = vy = vz = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; l < 2; l++) + { + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo, zo; + if (outGradOnly) + _fnlGradCoordOut3D(seed, i, j, k, xo, yo, zo); + else + _fnlGradCoordDual3D(seed, i, j, k, x0, y0, z0, xo, yo, zo); + vx += aaaa * xo; + vy += aaaa * yo; + vz += aaaa * zo; + } + + float b = a + 1; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b -= xNSign * 2 * x1; + i1 -= xNSign * PRIME_X; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b -= yNSign * 2 * y1; + j1 -= yNSign * PRIME_Y; + } + else + { + z1 += zNSign; + b -= zNSign * 2 * z1; + k1 -= zNSign * PRIME_Z; + } + + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo, zo; + if (outGradOnly) + _fnlGradCoordOut3D(seed, i1, j1, k1, xo, yo, zo); + else + _fnlGradCoordDual3D(seed, i1, j1, k1, x1, y1, z1, xo, yo, zo); + vx += bbbb * xo; + vy += bbbb * yo; + vz += bbbb * zo; + } + + if (l == 1) + break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PRIME_X; + j += (yNSign >> 1) & PRIME_Y; + k += (zNSign >> 1) & PRIME_Z; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + xr += vx * warpAmp; + yr += vy * warpAmp; + zr += vz * warpAmp; +} + +// ==================== +// Public API +// ==================== + +fnl_state fnlCreateState(int seed) +{ + fnl_state newState; + newState.seed = seed; + newState.frequency = 0.01f; + newState.noise_type = FNL_NOISE_OPENSIMPLEX2; + newState.rotation_type_3d = FNL_ROTATION_NONE; + newState.fractal_type = FNL_FRACTAL_NONE; + newState.octaves = 3; + newState.lacunarity = 2.0f; + newState.gain = 0.5f; + newState.weighted_strength = 0.0f; + newState.ping_pong_strength = 2.0f; + newState.cellular_distance_func = FNL_CELLULAR_DISTANCE_EUCLIDEANSQ; + newState.cellular_return_type = FNL_CELLULAR_RETURN_TYPE_DISTANCE; + newState.cellular_jitter_mod = 1.0f; + newState.domain_warp_amp = 30.0f; + newState.domain_warp_type = FNL_DOMAIN_WARP_OPENSIMPLEX2; + return newState; +} + +float fnlGetNoise2D(fnl_state state, FNLfloat x, FNLfloat y) +{ + _fnlTransformNoiseCoordinate2D(state, x, y); + + switch (state.fractal_type) + { + default: + return _fnlGenNoiseSingle2D(state, state.seed, x, y); + case FNL_FRACTAL_FBM: + return _fnlGenFractalFBM2D(state, x, y); + case FNL_FRACTAL_RIDGED: + return _fnlGenFractalRidged2D(state, x, y); + case FNL_FRACTAL_PINGPONG: + return _fnlGenFractalPingPong2D(state, x, y); + } +} + +float fnlGetNoise3D(fnl_state state, FNLfloat x, FNLfloat y, FNLfloat z) +{ + _fnlTransformNoiseCoordinate3D(state, x, y, z); + + // Select a noise type + switch (state.fractal_type) + { + default: + return _fnlGenNoiseSingle3D(state, state.seed, x, y, z); + case FNL_FRACTAL_FBM: + return _fnlGenFractalFBM3D(state, x, y, z); + case FNL_FRACTAL_RIDGED: + return _fnlGenFractalRidged3D(state, x, y, z); + case FNL_FRACTAL_PINGPONG: + return _fnlGenFractalPingPong3D(state, x, y, z); + } +} + +void fnlDomainWarp2D(fnl_state state, inout FNLfloat x, inout FNLfloat y) +{ + switch (state.fractal_type) + { + default: + _fnlDomainWarpSingle2D(state, x, y); + break; + case FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE: + _fnlDomainWarpFractalProgressive2D(state, x, y); + break; + case FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT: + _fnlDomainWarpFractalIndependent2D(state, x, y); + break; + } +} + +void fnlDomainWarp3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout FNLfloat z) +{ + switch (state.fractal_type) + { + default: + _fnlDomainWarpSingle3D(state, x, y, z); + break; + case FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE: + _fnlDomainWarpFractalProgressive3D(state, x, y, z); + break; + case FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT: + _fnlDomainWarpFractalIndependent3D(state, x, y, z); + break; + } +} diff --git a/Java/FastNoiseLite.java b/Java/FastNoiseLite.java new file mode 100644 index 0000000..8e56fcc --- /dev/null +++ b/Java/FastNoiseLite.java @@ -0,0 +1,2609 @@ +// MIT License +// +// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com) +// Copyright(c) 2020 Contributors +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files(the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions : +// +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +// +// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll +// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo +// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd +// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx +// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx +// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd +// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo +// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo +// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo +// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo +// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo +// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo +// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl +// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c +// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c +// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc +// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll +// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo +// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd +// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk +// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000 +// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX +// +// VERSION: 1.0 +// https://github.com/Auburn/FastNoise + +// To switch between using floats or doubles for input position, +// perform a file-wide replace on the following strings (including /*FNLfloat*/) +// /*FNLfloat*/ float +// /*FNLfloat*/ double + +public class FastNoiseLite +{ + public enum NoiseType + { + OpenSimplex2, + OpenSimplex2S, + Cellular, + Perlin, + ValueCubic, + Value + }; + + public enum RotationType3D + { + None, + ImproveXYPlanes, + ImproveXZPlanes + }; + + public enum FractalType + { + None, + FBm, + Ridged, + PingPong, + DomainWarpProgressive, + DomainWarpIndependent + }; + + public enum CellularDistanceFunction + { + Euclidean, + EuclideanSq, + Manhattan, + Hybrid + }; + + public enum CellularReturnType + { + CellValue, + Distance, + Distance2, + Distance2Add, + Distance2Sub, + Distance2Mul, + Distance2Div + }; + + public enum DomainWarpType + { + OpenSimplex2, + OpenSimplex2Reduced, + BasicGrid + }; + + private enum TransformType3D + { + None, + ImproveXYPlanes, + ImproveXZPlanes, + DefaultOpenSimplex2 + }; + + private int mSeed = 1337; + private float mFrequency = 0.01f; + private NoiseType mNoiseType = NoiseType.OpenSimplex2; + private RotationType3D mRotationType3D = RotationType3D.None; + private TransformType3D mTransformType3D = TransformType3D.DefaultOpenSimplex2; + + private FractalType mFractalType = FractalType.None; + private int mOctaves = 3; + private float mLacunarity = 2.0f; + private float mGain = 0.5f; + private float mWeightedStrength = 0.0f; + private float mPingPongStength = 2.0f; + + private float mFractalBounding = 1 / 1.75f; + + private CellularDistanceFunction mCellularDistanceFunction = CellularDistanceFunction.EuclideanSq; + private CellularReturnType mCellularReturnType = CellularReturnType.Distance; + private float mCellularJitterModifier = 1.0f; + + private DomainWarpType mDomainWarpType = DomainWarpType.OpenSimplex2; + private TransformType3D mWarpTransformType3D = TransformType3D.DefaultOpenSimplex2; + private float mDomainWarpAmp = 1.0f; + + /// + /// Create new FastNoise object with default seed + /// + public FastNoiseLite() { } + + /// + /// Create new FastNoise object with specified seed + /// + public FastNoiseLite(int seed) + { + SetSeed(seed); + } + + /// + /// Sets seed used for all noise types + /// + /// + /// Default: 1337 + /// + public void SetSeed(int seed) { mSeed = seed; } + + /// + /// Sets frequency for all noise types + /// + /// + /// Default: 0.01 + /// + public void SetFrequency(float frequency) { mFrequency = frequency; } + + /// + /// Sets noise algorithm used for GetNoise(...) + /// + /// + /// Default: OpenSimplex2 + /// + public void SetNoiseType(NoiseType noiseType) + { + mNoiseType = noiseType; + UpdateTransformType3D(); + } + + /// + /// Sets domain rotation type for 3D Noise and 3D DomainWarp. + /// Can aid in reducing directional artifacts when sampling a 2D plane in 3D + /// + /// + /// Default: None + /// + public void SetRotationType3D(RotationType3D rotationType3D) + { + mRotationType3D = rotationType3D; + UpdateTransformType3D(); + UpdateWarpTransformType3D(); + } + + /// + /// Sets method for combining octaves in all fractal noise types + /// + /// + /// Default: None + /// Note: FractalType.DomainWarp... only affects DomainWarp(...) + /// + public void SetFractalType(FractalType fractalType) { mFractalType = fractalType; } + + /// + /// Sets octave count for all fractal noise types + /// + /// + /// Default: 3 + /// + public void SetFractalOctaves(int octaves) + { + mOctaves = octaves; + CalculateFractalBounding(); + } + + /// + /// Sets octave lacunarity for all fractal noise types + /// + /// + /// Default: 2.0 + /// + public void SetFractalLacunarity(float lacunarity) { mLacunarity = lacunarity; } + + /// + /// Sets octave gain for all fractal noise types + /// + /// + /// Default: 0.5 + /// + public void SetFractalGain(float gain) + { + mGain = gain; + CalculateFractalBounding(); + } + + /// + /// Sets octave weighting for all none DomainWarp fratal types + /// + /// + /// Default: 0.0 + /// Note: Keep between 0...1 to maintain -1...1 output bounding + /// + public void SetFractalWeightedStrength(float weightedStrength) { mWeightedStrength = weightedStrength; } + + /// + /// Sets strength of the fractal ping pong effect + /// + /// + /// Default: 2.0 + /// + public void SetFractalPingPongStrength(float pingPongStrength) { mPingPongStength = pingPongStrength; } + + + /// + /// Sets distance function used in cellular noise calculations + /// + /// + /// Default: Distance + /// + public void SetCellularDistanceFunction(CellularDistanceFunction cellularDistanceFunction) { mCellularDistanceFunction = cellularDistanceFunction; } + + /// + /// Sets return type from cellular noise calculations + /// + /// + /// Default: EuclideanSq + /// + public void SetCellularReturnType(CellularReturnType cellularReturnType) { mCellularReturnType = cellularReturnType; } + + /// + /// Sets the maximum distance a cellular point can move from it's grid position + /// + /// + /// Default: 1.0 + /// Note: Setting this higher than 1 will cause artifacts + /// + public void SetCellularJitter(float cellularJitter) { mCellularJitterModifier = cellularJitter; } + + + /// + /// Sets the warp algorithm when using DomainWarp(...) + /// + /// + /// Default: OpenSimplex2 + /// + public void SetDomainWarpType(DomainWarpType domainWarpType) + { + mDomainWarpType = domainWarpType; + UpdateWarpTransformType3D(); + } + + + /// + /// Sets the maximum warp distance from original position when using DomainWarp(...) + /// + /// + /// Default: 1.0 + /// + public void SetDomainWarpAmp(float domainWarpAmp) { mDomainWarpAmp = domainWarpAmp; } + + + /// + /// 2D noise at given position using current settings + /// + /// + /// Noise output bounded between -1...1 + /// + public float GetNoise(/*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + x *= mFrequency; + y *= mFrequency; + + switch (mNoiseType) + { + case OpenSimplex2: + case OpenSimplex2S: + { + final /*FNLfloat*/ float SQRT3 = (/*FNLfloat*/ float)1.7320508075688772935274463415059; + final /*FNLfloat*/ float F2 = 0.5f * (SQRT3 - 1); + /*FNLfloat*/ float t = (x + y) * F2; + x += t; + y += t; + } + break; + default: + break; + } + + switch (mFractalType) + { + default: + return GenNoiseSingle(mSeed, x, y); + case FBm: + return GenFractalFBm(x, y); + case Ridged: + return GenFractalRidged(x, y); + case PingPong: + return GenFractalPingPong(x, y); + } + } + + /// + /// 3D noise at given position using current settings + /// + /// + /// Noise output bounded between -1...1 + /// + public float GetNoise(/*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + x *= mFrequency; + y *= mFrequency; + z *= mFrequency; + + switch (mTransformType3D) + { + case ImproveXYPlanes: + { + /*FNLfloat*/ float xy = x + y; + /*FNLfloat*/ float s2 = xy * -(/*FNLfloat*/ float)0.211324865405187; + z *= (/*FNLfloat*/ float)0.577350269189626; + x += s2 - z; + y = y + s2 - z; + z += xy * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case ImproveXZPlanes: + { + /*FNLfloat*/ float xz = x + z; + /*FNLfloat*/ float s2 = xz * -(/*FNLfloat*/ float)0.211324865405187; + y *= (/*FNLfloat*/ float)0.577350269189626; + x += s2 - y; + z += s2 - y; + y += xz * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case DefaultOpenSimplex2: + { + final /*FNLfloat*/ float R3 = (/*FNLfloat*/ float)(2.0 / 3.0); + /*FNLfloat*/ float r = (x + y + z) * R3; // Rotation, not skew + x = r - x; + y = r - y; + z = r - z; + } + break; + default: + break; + } + + switch (mFractalType) + { + default: + return GenNoiseSingle(mSeed, x, y, z); + case FBm: + return GenFractalFBm(x, y, z); + case Ridged: + return GenFractalRidged(x, y, z); + case PingPong: + return GenFractalPingPong(x, y, z); + } + } + + + /// + /// 2D warps the input position using current domain warp settings + /// + /// + /// Example usage with GetNoise + /// DomainWarp(coord) + /// noise = GetNoise(x, y) + /// + public void DomainWarp(Vector2 coord) + { + switch (mFractalType) + { + default: + DomainWarpSingle(coord); + break; + case DomainWarpProgressive: + DomainWarpFractalProgressive(coord); + break; + case DomainWarpIndependent: + DomainWarpFractalIndependent(coord); + break; + } + } + + /// + /// 3D warps the input position using current domain warp settings + /// + /// + /// Example usage with GetNoise + /// DomainWarp(coord) + /// noise = GetNoise(x, y, z) + /// + public void DomainWarp(Vector3 coord) + { + switch (mFractalType) + { + default: + DomainWarpSingle(coord); + break; + case DomainWarpProgressive: + DomainWarpFractalProgressive(coord); + break; + case DomainWarpIndependent: + DomainWarpFractalIndependent(coord); + break; + } + } + + + private static final float[] Gradients2D = { + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 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-0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f, + 0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f, + 0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f, + -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f, + -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f, + -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f, + 0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f, + -0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f, + }; + + private static final float[] RandVecs2D = { + -0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f, + -0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, -0.892300288f, -0.4514423508f, -0.379844434f, -0.9250503802f, -0.9951650832f, 0.0982163789f, 0.7724397808f, -0.6350880136f, 0.7573283322f, -0.6530343002f, -0.9928004525f, -0.119780055f, + -0.0532665713f, 0.9985803285f, 0.9754253726f, -0.2203300762f, -0.7665018163f, 0.6422421394f, 0.991636706f, 0.1290606184f, -0.994696838f, 0.1028503788f, -0.5379205513f, -0.84299554f, 0.5022815471f, -0.8647041387f, 0.4559821461f, -0.8899889226f, + -0.8659131224f, -0.5001944266f, 0.0879458407f, -0.9961252577f, -0.5051684983f, 0.8630207346f, 0.7753185226f, -0.6315704146f, -0.6921944612f, 0.7217110418f, -0.5191659449f, -0.8546734591f, 0.8978622882f, -0.4402764035f, -0.1706774107f, 0.9853269617f, + -0.9353430106f, -0.3537420705f, -0.9992404798f, 0.03896746794f, -0.2882064021f, -0.9575683108f, -0.9663811329f, 0.2571137995f, -0.8759714238f, -0.4823630009f, -0.8303123018f, -0.5572983775f, 0.05110133755f, -0.9986934731f, -0.8558373281f, -0.5172450752f, + 0.09887025282f, 0.9951003332f, 0.9189016087f, 0.3944867976f, -0.2439375892f, -0.9697909324f, -0.8121409387f, -0.5834613061f, -0.9910431363f, 0.1335421355f, 0.8492423985f, -0.5280031709f, -0.9717838994f, -0.2358729591f, 0.9949457207f, 0.1004142068f, + 0.6241065508f, -0.7813392434f, 0.662910307f, 0.7486988212f, -0.7197418176f, 0.6942418282f, -0.8143370775f, -0.5803922158f, 0.104521054f, -0.9945226741f, -0.1065926113f, -0.9943027784f, 0.445799684f, -0.8951327509f, 0.105547406f, 0.9944142724f, + -0.992790267f, 0.1198644477f, -0.8334366408f, 0.552615025f, 0.9115561563f, -0.4111755999f, 0.8285544909f, -0.5599084351f, 0.7217097654f, -0.6921957921f, 0.4940492677f, -0.8694339084f, -0.3652321272f, -0.9309164803f, -0.9696606758f, 0.2444548501f, + 0.08925509731f, 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0.8367622488f, 0.5475663786f, -0.8675753916f, -0.4973056806f, -0.2022662628f, -0.9793305667f, 0.9399189937f, 0.3413975472f, 0.9877404807f, -0.1561049093f, -0.9034455656f, 0.4287028224f, 0.1269804218f, -0.9919052235f, -0.3819600854f, 0.924178821f, + 0.9754625894f, 0.2201652486f, -0.3204015856f, -0.9472818081f, -0.9874760884f, 0.1577687387f, 0.02535348474f, -0.9996785487f, 0.4835130794f, -0.8753371362f, -0.2850799925f, -0.9585037287f, -0.06805516006f, -0.99768156f, -0.7885244045f, -0.6150034663f, + 0.3185392127f, -0.9479096845f, 0.8880043089f, 0.4598351306f, 0.6476921488f, -0.7619021462f, 0.9820241299f, 0.1887554194f, 0.9357275128f, -0.3527237187f, -0.8894895414f, 0.4569555293f, 0.7922791302f, 0.6101588153f, 0.7483818261f, 0.6632681526f, + -0.7288929755f, -0.6846276581f, 0.8729032783f, -0.4878932944f, 0.8288345784f, 0.5594937369f, 0.08074567077f, 0.9967347374f, 0.9799148216f, -0.1994165048f, -0.580730673f, -0.8140957471f, -0.4700049791f, -0.8826637636f, 0.2409492979f, 0.9705377045f, + 0.9437816757f, -0.3305694308f, -0.8927998638f, -0.4504535528f, -0.8069622304f, 0.5906030467f, 0.06258973166f, 0.9980393407f, -0.9312597469f, 0.3643559849f, 0.5777449785f, 0.8162173362f, -0.3360095855f, -0.941858566f, 0.697932075f, -0.7161639607f, + -0.002008157227f, -0.9999979837f, -0.1827294312f, -0.9831632392f, -0.6523911722f, 0.7578824173f, -0.4302626911f, -0.9027037258f, -0.9985126289f, -0.05452091251f, -0.01028102172f, -0.9999471489f, -0.4946071129f, 0.8691166802f, -0.2999350194f, 0.9539596344f, + 0.8165471961f, 0.5772786819f, 0.2697460475f, 0.962931498f, -0.7306287391f, -0.6827749597f, -0.7590952064f, -0.6509796216f, -0.907053853f, 0.4210146171f, -0.5104861064f, -0.8598860013f, 0.8613350597f, 0.5080373165f, 0.5007881595f, -0.8655698812f, + -0.654158152f, 0.7563577938f, -0.8382755311f, -0.545246856f, 0.6940070834f, 0.7199681717f, 0.06950936031f, 0.9975812994f, 0.1702942185f, -0.9853932612f, 0.2695973274f, 0.9629731466f, 0.5519612192f, -0.8338697815f, 0.225657487f, -0.9742067022f, + 0.4215262855f, -0.9068161835f, 0.4881873305f, -0.8727388672f, -0.3683854996f, -0.9296731273f, -0.9825390578f, 0.1860564427f, 0.81256471f, 0.5828709909f, 0.3196460933f, -0.9475370046f, 0.9570913859f, 0.2897862643f, -0.6876655497f, -0.7260276109f, + -0.9988770922f, -0.047376731f, -0.1250179027f, 0.992154486f, -0.8280133617f, 0.560708367f, 0.9324863769f, -0.3612051451f, 0.6394653183f, 0.7688199442f, -0.01623847064f, -0.9998681473f, -0.9955014666f, -0.09474613458f, -0.81453315f, 0.580117012f, + 0.4037327978f, -0.9148769469f, 0.9944263371f, 0.1054336766f, -0.1624711654f, 0.9867132919f, -0.9949487814f, -0.100383875f, -0.6995302564f, 0.7146029809f, 0.5263414922f, -0.85027327f, -0.5395221479f, 0.841971408f, 0.6579370318f, 0.7530729462f, + 0.01426758847f, -0.9998982128f, -0.6734383991f, 0.7392433447f, 0.639412098f, -0.7688642071f, 0.9211571421f, 0.3891908523f, -0.146637214f, -0.9891903394f, -0.782318098f, 0.6228791163f, -0.5039610839f, -0.8637263605f, -0.7743120191f, -0.6328039957f, + }; + + private static final float[] Gradients3D = { + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0, + 1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0, + 1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0, + 1, 1, 0, 0, 0,-1, 1, 0, -1, 1, 0, 0, 0,-1,-1, 0 + }; + + private static final float[] RandVecs3D = { + -0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, 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-0.7788918132f, -0.6085091231f, 0, -0.2600384876f, -0.4755398075f, -0.8403819825f, 0, 0.572313509f, -0.7474340931f, -0.3373418503f, 0, -0.7174141009f, 0.1699017182f, -0.6756111411f, 0, -0.684180784f, 0.02145707593f, -0.7289967412f, 0, -0.2007447902f, 0.06555605789f, -0.9774476623f, 0, -0.1148803697f, -0.8044887315f, 0.5827524187f, 0, + -0.7870349638f, 0.03447489231f, 0.6159443543f, 0, -0.2015596421f, 0.6859872284f, 0.6991389226f, 0, -0.08581082512f, -0.10920836f, -0.9903080513f, 0, 0.5532693395f, 0.7325250401f, -0.396610771f, 0, -0.1842489331f, -0.9777375055f, -0.1004076743f, 0, 0.0775473789f, -0.9111505856f, 0.4047110257f, 0, 0.1399838409f, 0.7601631212f, -0.6344734459f, 0, 0.4484419361f, -0.845289248f, 0.2904925424f, 0 + }; + + + private static float FastMin(float a, float b) { return a < b ? a : b; } + + private static float FastMax(float a, float b) { return a > b ? a : b; } + + private static float FastAbs(float f) { return f < 0 ? -f : f; } + + private static float FastSqrt(float f) { return (float)Math.sqrt(f); } + + private static int FastFloor(/*FNLfloat*/ float f) { return f >= 0 ? (int)f : (int)f - 1; } + + private static int FastRound(/*FNLfloat*/ float f) { return f >= 0 ? (int)(f + 0.5f) : (int)(f - 0.5f); } + + private static float Lerp(float a, float b, float t) { return a + t * (b - a); } + + private static float InterpHermite(float t) { return t * t * (3 - 2 * t); } + + private static float InterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); } + + private static float CubicLerp(float a, float b, float c, float d, float t) + { + float p = (d - c) - (a - b); + return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b; + } + + private static float PingPong(float t) + { + t -= (int)(t * 0.5f) * 2; + return t < 1 ? t : 2 - t; + } + + private void CalculateFractalBounding() + { + float gain = FastAbs(mGain); + float amp = gain; + float ampFractal = 1.0f; + for (int i = 1; i < mOctaves; i++) + { + ampFractal += amp; + amp *= gain; + } + mFractalBounding = 1 / ampFractal; + } + + // Hashing + private static final int PrimeX = 501125321; + private static final int PrimeY = 1136930381; + private static final int PrimeZ = 1720413743; + + private static int Hash(int seed, int xPrimed, int yPrimed) + { + int hash = seed ^ xPrimed ^ yPrimed; + + hash *= 0x27d4eb2d; + return hash; + } + + private static int Hash(int seed, int xPrimed, int yPrimed, int zPrimed) + { + int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed; + + hash *= 0x27d4eb2d; + return hash; + } + + private static float ValCoord(int seed, int xPrimed, int yPrimed) + { + int hash = Hash(seed, xPrimed, yPrimed); + + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); + } + + private static float ValCoord(int seed, int xPrimed, int yPrimed, int zPrimed) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + + hash *= hash; + hash ^= hash << 19; + return hash * (1 / 2147483648.0f); + } + + private static float GradCoord(int seed, int xPrimed, int yPrimed, float xd, float yd) + { + int hash = Hash(seed, xPrimed, yPrimed); + hash ^= hash >> 15; + hash &= 127 << 1; + + float xg = Gradients2D[hash]; + float yg = Gradients2D[hash | 1]; + + return xd * xg + yd * yg; + } + + private static float GradCoord(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + hash ^= hash >> 15; + hash &= 63 << 2; + + float xg = Gradients3D[hash]; + float yg = Gradients3D[hash | 1]; + float zg = Gradients3D[hash | 2]; + + return xd * xg + yd * yg + zd * zg; + } + + + // Generic noise gen + + private float GenNoiseSingle(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + switch (mNoiseType) + { + case OpenSimplex2: + return SingleSimplex(seed, x, y); + case OpenSimplex2S: + return SingleOpenSimplex2S(seed, x, y); + case Cellular: + return SingleCellular(seed, x, y); + case Perlin: + return SinglePerlin(seed, x, y); + case ValueCubic: + return SingleValueCubic(seed, x, y); + case Value: + return SingleValue(seed, x, y); + default: + return 0; + } + } + + private float GenNoiseSingle(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + switch (mNoiseType) + { + case OpenSimplex2: + return SingleOpenSimplex2(seed, x, y, z); + case OpenSimplex2S: + return SingleOpenSimplex2S(seed, x, y, z); + case Cellular: + return SingleCellular(seed, x, y, z); + case Perlin: + return SinglePerlin(seed, x, y, z); + case ValueCubic: + return SingleValueCubic(seed, x, y, z); + case Value: + return SingleValue(seed, x, y, z); + default: + return 0; + } + } + + + // Noise Coordinate Transforms (frequency, and possible skew or rotation) + + private void UpdateTransformType3D() + { + switch (mRotationType3D) + { + case ImproveXYPlanes: + mTransformType3D = TransformType3D.ImproveXYPlanes; + break; + case ImproveXZPlanes: + mTransformType3D = TransformType3D.ImproveXZPlanes; + break; + default: + switch (mNoiseType) + { + case OpenSimplex2: + case OpenSimplex2S: + mTransformType3D = TransformType3D.DefaultOpenSimplex2; + break; + default: + mTransformType3D = TransformType3D.None; + break; + } + break; + } + } + + private void UpdateWarpTransformType3D() + { + switch (mRotationType3D) + { + case ImproveXYPlanes: + mWarpTransformType3D = TransformType3D.ImproveXYPlanes; + break; + case ImproveXZPlanes: + mWarpTransformType3D = TransformType3D.ImproveXZPlanes; + break; + default: + switch (mDomainWarpType) + { + case OpenSimplex2: + case OpenSimplex2Reduced: + mWarpTransformType3D = TransformType3D.DefaultOpenSimplex2; + break; + default: + mWarpTransformType3D = TransformType3D.None; + break; + } + break; + } + } + + + // Fractal FBm + + private float GenFractalFBm(/*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = GenNoiseSingle(seed++, x, y); + sum += noise * amp; + amp *= Lerp(1.0f, FastMin(noise + 1, 2) * 0.5f, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + private float GenFractalFBm(/*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = GenNoiseSingle(seed++, x, y, z); + sum += noise * amp; + amp *= Lerp(1.0f, (noise + 1) * 0.5f, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Fractal Ridged + + private float GenFractalRidged(/*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = FastAbs(GenNoiseSingle(seed++, x, y)); + sum += (noise * -2 + 1) * amp; + amp *= Lerp(1.0f, 1 - noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + private float GenFractalRidged(/*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = FastAbs(GenNoiseSingle(seed++, x, y, z)); + sum += (noise * -2 + 1) * amp; + amp *= Lerp(1.0f, 1 - noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Fractal PingPong + + private float GenFractalPingPong(/*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = PingPong((GenNoiseSingle(seed++, x, y) + 1) * mPingPongStength); + sum += (noise - 0.5f) * 2 * amp; + amp *= Lerp(1.0f, noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + private float GenFractalPingPong(/*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int seed = mSeed; + float sum = 0; + float amp = mFractalBounding; + + for (int i = 0; i < mOctaves; i++) + { + float noise = PingPong((GenNoiseSingle(seed++, x, y, z) + 1) * mPingPongStength); + sum += (noise - 0.5f) * 2 * amp; + amp *= Lerp(1.0f, noise, mWeightedStrength); + + x *= mLacunarity; + y *= mLacunarity; + z *= mLacunarity; + amp *= mGain; + } + + return sum; + } + + + // Simplex/OpenSimplex2 Noise + + private float SingleSimplex(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex. + + final float SQRT3 = 1.7320508075688772935274463415059f; + final float G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to switch statements before fractal evaluation --- + * final FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PrimeX; + j *= PrimeY; + + float n0, n1, n2; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a <= 0) n0 = 0; + else + { + n0 = (a * a) * (a * a) * GradCoord(seed, i, j, x0, y0); + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c <= 0) n2 = 0; + else + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + n2 = (c * c) * (c * c) * GradCoord(seed, i + PrimeX, j + PrimeY, x2, y2); + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) n1 = 0; + else + { + n1 = (b * b) * (b * b) * GradCoord(seed, i, j + PrimeY, x1, y1); + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b <= 0) n1 = 0; + else + { + n1 = (b * b) * (b * b) * GradCoord(seed, i + PrimeX, j, x1, y1); + } + } + + return (n0 + n1 + n2) * 99.83685446303647f; + } + + private float SingleOpenSimplex2(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + // 3D OpenSimplex2 case uses two offset rotated cube grids. + + /* + * --- Rotation moved to switch statements before fractal evaluation --- + * final FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastRound(x); + int j = FastRound(y); + int k = FastRound(z); + float x0 = (float)(x - i); + float y0 = (float)(y - j); + float z0 = (float)(z - k); + + int xNSign = (int)(-1.0f - x0) | 1; + int yNSign = (int)(-1.0f - y0) | 1; + int zNSign = (int)(-1.0f - z0) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + + float value = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; ; l++) + { + if (a > 0) + { + value += (a * a) * (a * a) * GradCoord(seed, i, j, k, x0, y0, z0); + } + + if (ax0 >= ay0 && ax0 >= az0) + { + float b = a + ax0 + ax0; + if (b > 1) + { + b -= 1; + value += (b * b) * (b * b) * GradCoord(seed, i - xNSign * PrimeX, j, k, x0 + xNSign, y0, z0); + } + } + else if (ay0 > ax0 && ay0 >= az0) + { + float b = a + ay0 + ay0; + if (b > 1) + { + b -= 1; + value += (b * b) * (b * b) * GradCoord(seed, i, j - yNSign * PrimeY, k, x0, y0 + yNSign, z0); + } + } + else + { + float b = a + az0 + az0; + if (b > 1) + { + b -= 1; + value += (b * b) * (b * b) * GradCoord(seed, i, j, k - zNSign * PrimeZ, x0, y0, z0 + zNSign); + } + } + + if (l == 1) break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PrimeX; + j += (yNSign >> 1) & PrimeY; + k += (zNSign >> 1) & PrimeZ; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + return value * 32.69428253173828125f; + } + + + // OpenSimplex2S Noise + + private float SingleOpenSimplex2S(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + // 2D OpenSimplex2S case is a modified 2D simplex noise. + + final /*FNLfloat*/ float SQRT3 = (/*FNLfloat*/ float)1.7320508075688772935274463415059; + final /*FNLfloat*/ float G2 = (3 - SQRT3) / 6; + + /* + * --- Skew moved to TransformNoiseCoordinate method --- + * final FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + i *= PrimeX; + j *= PrimeY; + int i1 = i + PrimeX; + int j1 = j + PrimeY; + + float t = (xi + yi) * (float)G2; + float x0 = xi - t; + float y0 = yi - t; + + float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0; + float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, i, j, x0, y0); + + float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0); + float x1 = x0 - (float)(1 - 2 * G2); + float y1 = y0 - (float)(1 - 2 * G2); + value += (a1 * a1) * (a1 * a1) * GradCoord(seed, i1, j1, x1, y1); + + // Nested conditionals were faster than compact bit logic/arithmetic. + float xmyi = xi - yi; + if (t > G2) + { + if (xi + xmyi > 1) + { + float x2 = x0 + (float)(3 * G2 - 2); + float y2 = y0 + (float)(3 * G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + (PrimeX << 1), j + PrimeY, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2); + } + } + + if (yi - xmyi > 1) + { + float x3 = x0 + (float)(3 * G2 - 1); + float y3 = y0 + (float)(3 * G2 - 2); + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j + (PrimeY << 1), x3, y3); + } + } + else + { + float x3 = x0 + (float)(G2 - 1); + float y3 = y0 + (float)G2; + float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3; + if (a3 > 0) + { + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j, x3, y3); + } + } + } + else + { + if (xi + xmyi < 0) + { + float x2 = x0 + (float)(1 - G2); + float y2 = y0 - (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i - PrimeX, j, x2, y2); + } + } + else + { + float x2 = x0 + (float)(G2 - 1); + float y2 = y0 + (float)G2; + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + PrimeX, j, x2, y2); + } + } + + if (yi < xmyi) + { + float x2 = x0 - (float)G2; + float y2 = y0 - (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j - PrimeY, x2, y2); + } + } + else + { + float x2 = x0 + (float)G2; + float y2 = y0 + (float)(G2 - 1); + float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2; + if (a2 > 0) + { + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2); + } + } + } + + return value * 18.24196194486065f; + } + + private float SingleOpenSimplex2S(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + // 3D OpenSimplex2S case uses two offset rotated cube grids. + + /* + * --- Rotation moved to TransformNoiseCoordinate method --- + * final FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + int k = FastFloor(z); + float xi = (float)(x - i); + float yi = (float)(y - j); + float zi = (float)(z - k); + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + int seed2 = seed + 1293373; + + int xNMask = (int)(-0.5f - xi); + int yNMask = (int)(-0.5f - yi); + int zNMask = (int)(-0.5f - zi); + + float x0 = xi + xNMask; + float y0 = yi + yNMask; + float z0 = zi + zNMask; + float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0; + float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, + i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x0, y0, z0); + + float x1 = xi - 0.5f; + float y1 = yi - 0.5f; + float z1 = zi - 0.5f; + float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1; + value += (a1 * a1) * (a1 * a1) * GradCoord(seed2, + i + PrimeX, j + PrimeY, k + PrimeZ, x1, y1, z1); + + float xAFlipMask0 = ((xNMask | 1) << 1) * x1; + float yAFlipMask0 = ((yNMask | 1) << 1) * y1; + float zAFlipMask0 = ((zNMask | 1) << 1) * z1; + float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f; + float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f; + float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f; + + boolean skip5 = false; + float a2 = xAFlipMask0 + a0; + if (a2 > 0) + { + float x2 = x0 - (xNMask | 1); + float y2 = y0; + float z2 = z0; + value += (a2 * a2) * (a2 * a2) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x2, y2, z2); + } + else + { + float a3 = yAFlipMask0 + zAFlipMask0 + a0; + if (a3 > 0) + { + float x3 = x0; + float y3 = y0 - (yNMask | 1); + float z3 = z0 - (zNMask | 1); + value += (a3 * a3) * (a3 * a3) * GradCoord(seed, + i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (~zNMask & PrimeZ), x3, y3, z3); + } + + float a4 = xAFlipMask1 + a1; + if (a4 > 0) + { + float x4 = (xNMask | 1) + x1; + float y4 = y1; + float z4 = z1; + value += (a4 * a4) * (a4 * a4) * GradCoord(seed2, + i + (xNMask & (PrimeX * 2)), j + PrimeY, k + PrimeZ, x4, y4, z4); + skip5 = true; + } + } + + boolean skip9 = false; + float a6 = yAFlipMask0 + a0; + if (a6 > 0) + { + float x6 = x0; + float y6 = y0 - (yNMask | 1); + float z6 = z0; + value += (a6 * a6) * (a6 * a6) * GradCoord(seed, + i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), x6, y6, z6); + } + else + { + float a7 = xAFlipMask0 + zAFlipMask0 + a0; + if (a7 > 0) + { + float x7 = x0 - (xNMask | 1); + float y7 = y0; + float z7 = z0 - (zNMask | 1); + value += (a7 * a7) * (a7 * a7) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), x7, y7, z7); + } + + float a8 = yAFlipMask1 + a1; + if (a8 > 0) + { + float x8 = x1; + float y8 = (yNMask | 1) + y1; + float z8 = z1; + value += (a8 * a8) * (a8 * a8) * GradCoord(seed2, + i + PrimeX, j + (yNMask & (PrimeY << 1)), k + PrimeZ, x8, y8, z8); + skip9 = true; + } + } + + boolean skipD = false; + float aA = zAFlipMask0 + a0; + if (aA > 0) + { + float xA = x0; + float yA = y0; + float zA = z0 - (zNMask | 1); + value += (aA * aA) * (aA * aA) * GradCoord(seed, + i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), xA, yA, zA); + } + else + { + float aB = xAFlipMask0 + yAFlipMask0 + a0; + if (aB > 0) + { + float xB = x0 - (xNMask | 1); + float yB = y0 - (yNMask | 1); + float zB = z0; + value += (aB * aB) * (aB * aB) * GradCoord(seed, + i + (~xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), xB, yB, zB); + } + + float aC = zAFlipMask1 + a1; + if (aC > 0) + { + float xC = x1; + float yC = y1; + float zC = (zNMask | 1) + z1; + value += (aC * aC) * (aC * aC) * GradCoord(seed2, + i + PrimeX, j + PrimeY, k + (zNMask & (PrimeZ << 1)), xC, yC, zC); + skipD = true; + } + } + + if (!skip5) + { + float a5 = yAFlipMask1 + zAFlipMask1 + a1; + if (a5 > 0) + { + float x5 = x1; + float y5 = (yNMask | 1) + y1; + float z5 = (zNMask | 1) + z1; + value += (a5 * a5) * (a5 * a5) * GradCoord(seed2, + i + PrimeX, j + (yNMask & (PrimeY << 1)), k + (zNMask & (PrimeZ << 1)), x5, y5, z5); + } + } + + if (!skip9) + { + float a9 = xAFlipMask1 + zAFlipMask1 + a1; + if (a9 > 0) + { + float x9 = (xNMask | 1) + x1; + float y9 = y1; + float z9 = (zNMask | 1) + z1; + value += (a9 * a9) * (a9 * a9) * GradCoord(seed2, + i + (xNMask & (PrimeX * 2)), j + PrimeY, k + (zNMask & (PrimeZ << 1)), x9, y9, z9); + } + } + + if (!skipD) + { + float aD = xAFlipMask1 + yAFlipMask1 + a1; + if (aD > 0) + { + float xD = (xNMask | 1) + x1; + float yD = (yNMask | 1) + y1; + float zD = z1; + value += (aD * aD) * (aD * aD) * GradCoord(seed2, + i + (xNMask & (PrimeX << 1)), j + (yNMask & (PrimeY << 1)), k + PrimeZ, xD, yD, zD); + } + } + + return value * 9.046026385208288f; + } + + + // Cellular Noise + + private float SingleCellular(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int xr = FastRound(x); + int yr = FastRound(y); + + float distance0 = Float.MAX_VALUE; + float distance1 = Float.MAX_VALUE; + int closestHash = 0; + + float cellularJitter = 0.43701595f * mCellularJitterModifier; + + int xPrimed = (xr - 1) * PrimeX; + int yPrimedBase = (yr - 1) * PrimeY; + + switch (mCellularDistanceFunction) + { + default: + case Euclidean: + case EuclideanSq: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY; + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case Manhattan: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = FastAbs(vecX) + FastAbs(vecY); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case Hybrid: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int hash = Hash(seed, xPrimed, yPrimed); + int idx = hash & (255 << 1); + + float vecX = (float)(xi - x) + RandVecs2D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs2D[idx | 1] * cellularJitter; + + float newDistance = (FastAbs(vecX) + FastAbs(vecY)) + (vecX * vecX + vecY * vecY); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + } + + if (mCellularDistanceFunction == CellularDistanceFunction.Euclidean && mCellularReturnType != CellularReturnType.CellValue) + { + distance0 = FastSqrt(distance0); + + if (mCellularReturnType != CellularReturnType.CellValue) + { + distance1 = FastSqrt(distance1); + } + } + + switch (mCellularReturnType) + { + case CellValue: + return closestHash * (1 / 2147483648.0f); + case Distance: + return distance0 - 1; + case Distance2: + return distance1 - 1; + case Distance2Add: + return (distance1 + distance0) * 0.5f - 1; + case Distance2Sub: + return distance1 - distance0 - 1; + case Distance2Mul: + return distance1 * distance0 * 0.5f - 1; + case Distance2Div: + return distance0 / distance1 - 1; + default: + return 0; + } + } + + private float SingleCellular(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int xr = FastRound(x); + int yr = FastRound(y); + int zr = FastRound(z); + + float distance0 = Float.MAX_VALUE; + float distance1 = Float.MAX_VALUE; + int closestHash = 0; + + float cellularJitter = 0.39614353f * mCellularJitterModifier; + + int xPrimed = (xr - 1) * PrimeX; + int yPrimedBase = (yr - 1) * PrimeY; + int zPrimedBase = (zr - 1) * PrimeZ; + + switch (mCellularDistanceFunction) + { + case Euclidean: + case EuclideanSq: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ; + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case Manhattan: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + case Hybrid: + for (int xi = xr - 1; xi <= xr + 1; xi++) + { + int yPrimed = yPrimedBase; + + for (int yi = yr - 1; yi <= yr + 1; yi++) + { + int zPrimed = zPrimedBase; + + for (int zi = zr - 1; zi <= zr + 1; zi++) + { + int hash = Hash(seed, xPrimed, yPrimed, zPrimed); + int idx = hash & (255 << 2); + + float vecX = (float)(xi - x) + RandVecs3D[idx] * cellularJitter; + float vecY = (float)(yi - y) + RandVecs3D[idx | 1] * cellularJitter; + float vecZ = (float)(zi - z) + RandVecs3D[idx | 2] * cellularJitter; + + float newDistance = (FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ); + + distance1 = FastMax(FastMin(distance1, newDistance), distance0); + if (newDistance < distance0) + { + distance0 = newDistance; + closestHash = hash; + } + zPrimed += PrimeZ; + } + yPrimed += PrimeY; + } + xPrimed += PrimeX; + } + break; + default: + break; + } + + if (mCellularDistanceFunction == CellularDistanceFunction.Euclidean && mCellularReturnType != CellularReturnType.CellValue) + { + distance0 = FastSqrt(distance0); + + if (mCellularReturnType != CellularReturnType.CellValue) + { + distance1 = FastSqrt(distance1); + } + } + + switch (mCellularReturnType) + { + case CellValue: + return closestHash * (1 / 2147483648.0f); + case Distance: + return distance0 - 1; + case Distance2: + return distance1 - 1; + case Distance2Add: + return (distance1 + distance0) * 0.5f - 1; + case Distance2Sub: + return distance1 - distance0 - 1; + case Distance2Mul: + return distance1 * distance0 * 0.5f - 1; + case Distance2Div: + return distance0 / distance1 - 1; + default: + return 0; + } + } + + + // Perlin Noise + + private float SinglePerlin(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + + float xs = InterpQuintic(xd0); + float ys = InterpQuintic(yd0); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + float xf0 = Lerp(GradCoord(seed, x0, y0, xd0, yd0), GradCoord(seed, x1, y0, xd1, yd0), xs); + float xf1 = Lerp(GradCoord(seed, x0, y1, xd0, yd1), GradCoord(seed, x1, y1, xd1, yd1), xs); + + return Lerp(xf0, xf1, ys) * 1.4247691104677813f; + } + + private float SinglePerlin(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + int z0 = FastFloor(z); + + float xd0 = (float)(x - x0); + float yd0 = (float)(y - y0); + float zd0 = (float)(z - z0); + float xd1 = xd0 - 1; + float yd1 = yd0 - 1; + float zd1 = zd0 - 1; + + float xs = InterpQuintic(xd0); + float ys = InterpQuintic(yd0); + float zs = InterpQuintic(zd0); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + float xf00 = Lerp(GradCoord(seed, x0, y0, z0, xd0, yd0, zd0), GradCoord(seed, x1, y0, z0, xd1, yd0, zd0), xs); + float xf10 = Lerp(GradCoord(seed, x0, y1, z0, xd0, yd1, zd0), GradCoord(seed, x1, y1, z0, xd1, yd1, zd0), xs); + float xf01 = Lerp(GradCoord(seed, x0, y0, z1, xd0, yd0, zd1), GradCoord(seed, x1, y0, z1, xd1, yd0, zd1), xs); + float xf11 = Lerp(GradCoord(seed, x0, y1, z1, xd0, yd1, zd1), GradCoord(seed, x1, y1, z1, xd1, yd1, zd1), xs); + + float yf0 = Lerp(xf00, xf10, ys); + float yf1 = Lerp(xf01, xf11, ys); + + return Lerp(yf0, yf1, zs) * 0.964921414852142333984375f; + } + + + // Value Cubic Noise + + private float SingleValueCubic(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int x1 = FastFloor(x); + int y1 = FastFloor(y); + + float xs = (float)(x - x1); + float ys = (float)(y - y1); + + x1 *= PrimeX; + y1 *= PrimeY; + int x0 = x1 - PrimeX; + int y0 = y1 - PrimeY; + int x2 = x1 + PrimeX; + int y2 = y1 + PrimeY; + int x3 = x1 + (PrimeX << 1); + int y3 = y1 + (PrimeY << 1); + + return CubicLerp( + CubicLerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), ValCoord(seed, x2, y0), ValCoord(seed, x3, y0), + xs), + CubicLerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), ValCoord(seed, x2, y1), ValCoord(seed, x3, y1), + xs), + CubicLerp(ValCoord(seed, x0, y2), ValCoord(seed, x1, y2), ValCoord(seed, x2, y2), ValCoord(seed, x3, y2), + xs), + CubicLerp(ValCoord(seed, x0, y3), ValCoord(seed, x1, y3), ValCoord(seed, x2, y3), ValCoord(seed, x3, y3), + xs), + ys) * (1 / (1.5f * 1.5f)); + } + + private float SingleValueCubic(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int x1 = FastFloor(x); + int y1 = FastFloor(y); + int z1 = FastFloor(z); + + float xs = (float)(x - x1); + float ys = (float)(y - y1); + float zs = (float)(z - z1); + + x1 *= PrimeX; + y1 *= PrimeY; + z1 *= PrimeZ; + + int x0 = x1 - PrimeX; + int y0 = y1 - PrimeY; + int z0 = z1 - PrimeZ; + int x2 = x1 + PrimeX; + int y2 = y1 + PrimeY; + int z2 = z1 + PrimeZ; + int x3 = x1 + (PrimeX << 1); + int y3 = y1 + (PrimeY << 1); + int z3 = z1 + (PrimeZ << 1); + + + return CubicLerp( + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), ValCoord(seed, x2, y0, z0), ValCoord(seed, x3, y0, z0), xs), + CubicLerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), ValCoord(seed, x2, y1, z0), ValCoord(seed, x3, y1, z0), xs), + CubicLerp(ValCoord(seed, x0, y2, z0), ValCoord(seed, x1, y2, z0), ValCoord(seed, x2, y2, z0), ValCoord(seed, x3, y2, z0), xs), + CubicLerp(ValCoord(seed, x0, y3, z0), ValCoord(seed, x1, y3, z0), ValCoord(seed, x2, y3, z0), ValCoord(seed, x3, y3, z0), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), ValCoord(seed, x2, y0, z1), ValCoord(seed, x3, y0, z1), xs), + CubicLerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), ValCoord(seed, x2, y1, z1), ValCoord(seed, x3, y1, z1), xs), + CubicLerp(ValCoord(seed, x0, y2, z1), ValCoord(seed, x1, y2, z1), ValCoord(seed, x2, y2, z1), ValCoord(seed, x3, y2, z1), xs), + CubicLerp(ValCoord(seed, x0, y3, z1), ValCoord(seed, x1, y3, z1), ValCoord(seed, x2, y3, z1), ValCoord(seed, x3, y3, z1), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z2), ValCoord(seed, x1, y0, z2), ValCoord(seed, x2, y0, z2), ValCoord(seed, x3, y0, z2), xs), + CubicLerp(ValCoord(seed, x0, y1, z2), ValCoord(seed, x1, y1, z2), ValCoord(seed, x2, y1, z2), ValCoord(seed, x3, y1, z2), xs), + CubicLerp(ValCoord(seed, x0, y2, z2), ValCoord(seed, x1, y2, z2), ValCoord(seed, x2, y2, z2), ValCoord(seed, x3, y2, z2), xs), + CubicLerp(ValCoord(seed, x0, y3, z2), ValCoord(seed, x1, y3, z2), ValCoord(seed, x2, y3, z2), ValCoord(seed, x3, y3, z2), xs), + ys), + CubicLerp( + CubicLerp(ValCoord(seed, x0, y0, z3), ValCoord(seed, x1, y0, z3), ValCoord(seed, x2, y0, z3), ValCoord(seed, x3, y0, z3), xs), + CubicLerp(ValCoord(seed, x0, y1, z3), ValCoord(seed, x1, y1, z3), ValCoord(seed, x2, y1, z3), ValCoord(seed, x3, y1, z3), xs), + CubicLerp(ValCoord(seed, x0, y2, z3), ValCoord(seed, x1, y2, z3), ValCoord(seed, x2, y2, z3), ValCoord(seed, x3, y2, z3), xs), + CubicLerp(ValCoord(seed, x0, y3, z3), ValCoord(seed, x1, y3, z3), ValCoord(seed, x2, y3, z3), ValCoord(seed, x3, y3, z3), xs), + ys), + zs) * (1 / (1.5f * 1.5f * 1.5f)); + } + + + // Value Noise + + private float SingleValue(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + + float xs = InterpHermite((float)(x - x0)); + float ys = InterpHermite((float)(y - y0)); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + float xf0 = Lerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), xs); + float xf1 = Lerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), xs); + + return Lerp(xf0, xf1, ys); + } + + private float SingleValue(int seed, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + int x0 = FastFloor(x); + int y0 = FastFloor(y); + int z0 = FastFloor(z); + + float xs = InterpHermite((float)(x - x0)); + float ys = InterpHermite((float)(y - y0)); + float zs = InterpHermite((float)(z - z0)); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + float xf00 = Lerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), xs); + float xf10 = Lerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), xs); + float xf01 = Lerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), xs); + float xf11 = Lerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), xs); + + float yf0 = Lerp(xf00, xf10, ys); + float yf1 = Lerp(xf01, xf11, ys); + + return Lerp(yf0, yf1, zs); + } + + + // Domain Warp + + private void DoSingleDomainWarp(int seed, float amp, float freq, /*FNLfloat*/ float x, /*FNLfloat*/ float y, Vector2 coord) + { + switch (mDomainWarpType) + { + case OpenSimplex2: + SingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, coord, false); + break; + case OpenSimplex2Reduced: + SingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, coord, true); + break; + case BasicGrid: + SingleDomainWarpBasicGrid(seed, amp, freq, x, y, coord); + break; + } + } + + private void DoSingleDomainWarp(int seed, float amp, float freq, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z, Vector3 coord) + { + switch (mDomainWarpType) + { + case OpenSimplex2: + SingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, coord, false); + break; + case OpenSimplex2Reduced: + SingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, coord, true); + break; + case BasicGrid: + SingleDomainWarpBasicGrid(seed, amp, freq, x, y, z, coord); + break; + } + } + + + // Domain Warp Single Wrapper + + private void DomainWarpSingle(Vector2 coord) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + /*FNLfloat*/ float xs = coord.x; + /*FNLfloat*/ float ys = coord.y; + switch (mDomainWarpType) + { + case OpenSimplex2: + case OpenSimplex2Reduced: + { + final /*FNLfloat*/ float SQRT3 = (/*FNLfloat*/ float)1.7320508075688772935274463415059; + final /*FNLfloat*/ float F2 = 0.5f * (SQRT3 - 1); + /*FNLfloat*/ float t = (xs + ys) * F2; + xs += t; ys += t; + } + break; + default: + break; + } + + DoSingleDomainWarp(seed, amp, freq, xs, ys, coord); + } + + private void DomainWarpSingle(Vector3 coord) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + /*FNLfloat*/ float xs = coord.x; + /*FNLfloat*/ float ys = coord.y; + /*FNLfloat*/ float zs = coord.z; + switch (mWarpTransformType3D) + { + case ImproveXYPlanes: + { + /*FNLfloat*/ float xy = xs + ys; + /*FNLfloat*/ float s2 = xy * -(/*FNLfloat*/ float)0.211324865405187; + zs *= (/*FNLfloat*/ float)0.577350269189626; + xs += s2 - zs; + ys = ys + s2 - zs; + zs += xy * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case ImproveXZPlanes: + { + /*FNLfloat*/ float xz = xs + zs; + /*FNLfloat*/ float s2 = xz * -(/*FNLfloat*/ float)0.211324865405187; + ys *= (/*FNLfloat*/ float)0.577350269189626; + xs += s2 - ys; zs += s2 - ys; + ys += xz * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case DefaultOpenSimplex2: + { + final /*FNLfloat*/ float R3 = (/*FNLfloat*/ float)(2.0 / 3.0); + /*FNLfloat*/ float r = (xs + ys + zs) * R3; // Rotation, not skew + xs = r - xs; + ys = r - ys; + zs = r - zs; + } + break; + default: + break; + } + + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, coord); + } + + + // Domain Warp Fractal Progressive + + private void DomainWarpFractalProgressive(Vector2 coord) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + /*FNLfloat*/ float xs = coord.x; + /*FNLfloat*/ float ys = coord.y; + switch (mDomainWarpType) + { + case OpenSimplex2: + case OpenSimplex2Reduced: + { + final /*FNLfloat*/ float SQRT3 = (/*FNLfloat*/ float)1.7320508075688772935274463415059; + final /*FNLfloat*/ float F2 = 0.5f * (SQRT3 - 1); + /*FNLfloat*/ float t = (xs + ys) * F2; + xs += t; ys += t; + } + break; + default: + break; + } + + DoSingleDomainWarp(seed, amp, freq, xs, ys, coord); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + private void DomainWarpFractalProgressive(Vector3 coord) + { + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + /*FNLfloat*/ float xs = coord.x; + /*FNLfloat*/ float ys = coord.y; + /*FNLfloat*/ float zs = coord.z; + switch (mWarpTransformType3D) + { + case ImproveXYPlanes: + { + /*FNLfloat*/ float xy = xs + ys; + /*FNLfloat*/ float s2 = xy * -(/*FNLfloat*/ float)0.211324865405187; + zs *= (/*FNLfloat*/ float)0.577350269189626; + xs += s2 - zs; + ys = ys + s2 - zs; + zs += xy * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case ImproveXZPlanes: + { + /*FNLfloat*/ float xz = xs + zs; + /*FNLfloat*/ float s2 = xz * -(/*FNLfloat*/ float)0.211324865405187; + ys *= (/*FNLfloat*/ float)0.577350269189626; + xs += s2 - ys; zs += s2 - ys; + ys += xz * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case DefaultOpenSimplex2: + { + final /*FNLfloat*/ float R3 = (/*FNLfloat*/ float)(2.0 / 3.0); + /*FNLfloat*/ float r = (xs + ys + zs) * R3; // Rotation, not skew + xs = r - xs; + ys = r - ys; + zs = r - zs; + } + break; + default: + break; + } + + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, coord); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + + // Domain Warp Fractal Independant + private void DomainWarpFractalIndependent(Vector2 coord) + { + /*FNLfloat*/ float xs = coord.x; + /*FNLfloat*/ float ys = coord.y; + switch (mDomainWarpType) + { + case OpenSimplex2: + case OpenSimplex2Reduced: + { + final /*FNLfloat*/ float SQRT3 = (/*FNLfloat*/ float)1.7320508075688772935274463415059; + final /*FNLfloat*/ float F2 = 0.5f * (SQRT3 - 1); + /*FNLfloat*/ float t = (xs + ys) * F2; + xs += t; ys += t; + } + break; + default: + break; + } + + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + DoSingleDomainWarp(seed, amp, freq, xs, ys, coord); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + private void DomainWarpFractalIndependent(Vector3 coord) + { + /*FNLfloat*/ float xs = coord.x; + /*FNLfloat*/ float ys = coord.y; + /*FNLfloat*/ float zs = coord.z; + switch (mWarpTransformType3D) + { + case ImproveXYPlanes: + { + /*FNLfloat*/ float xy = xs + ys; + /*FNLfloat*/ float s2 = xy * -(/*FNLfloat*/ float)0.211324865405187; + zs *= (/*FNLfloat*/ float)0.577350269189626; + xs += s2 - zs; + ys = ys + s2 - zs; + zs += xy * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case ImproveXZPlanes: + { + /*FNLfloat*/ float xz = xs + zs; + /*FNLfloat*/ float s2 = xz * -(/*FNLfloat*/ float)0.211324865405187; + ys *= (/*FNLfloat*/ float)0.577350269189626; + xs += s2 - ys; zs += s2 - ys; + ys += xz * (/*FNLfloat*/ float)0.577350269189626; + } + break; + case DefaultOpenSimplex2: + { + final /*FNLfloat*/ float R3 = (/*FNLfloat*/ float)(2.0 / 3.0); + /*FNLfloat*/ float r = (xs + ys + zs) * R3; // Rotation, not skew + xs = r - xs; + ys = r - ys; + zs = r - zs; + } + break; + default: + break; + } + + int seed = mSeed; + float amp = mDomainWarpAmp * mFractalBounding; + float freq = mFrequency; + + for (int i = 0; i < mOctaves; i++) + { + DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, coord); + + seed++; + amp *= mGain; + freq *= mLacunarity; + } + } + + + // Domain Warp Basic Grid + + private void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, /*FNLfloat*/ float x, /*FNLfloat*/ float y, Vector2 coord) + { + /*FNLfloat*/ float xf = x * frequency; + /*FNLfloat*/ float yf = y * frequency; + + int x0 = FastFloor(xf); + int y0 = FastFloor(yf); + + float xs = InterpHermite((float)(xf - x0)); + float ys = InterpHermite((float)(yf - y0)); + + x0 *= PrimeX; + y0 *= PrimeY; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + + int hash0 = Hash(seed, x0, y0) & (255 << 1); + int hash1 = Hash(seed, x1, y0) & (255 << 1); + + float lx0x = Lerp(RandVecs2D[hash0], RandVecs2D[hash1], xs); + float ly0x = Lerp(RandVecs2D[hash0 | 1], RandVecs2D[hash1 | 1], xs); + + hash0 = Hash(seed, x0, y1) & (255 << 1); + hash1 = Hash(seed, x1, y1) & (255 << 1); + + float lx1x = Lerp(RandVecs2D[hash0], RandVecs2D[hash1], xs); + float ly1x = Lerp(RandVecs2D[hash0 | 1], RandVecs2D[hash1 | 1], xs); + + coord.x += Lerp(lx0x, lx1x, ys) * warpAmp; + coord.y += Lerp(ly0x, ly1x, ys) * warpAmp; + } + + private void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z, Vector3 coord) + { + /*FNLfloat*/ float xf = x * frequency; + /*FNLfloat*/ float yf = y * frequency; + /*FNLfloat*/ float zf = z * frequency; + + int x0 = FastFloor(xf); + int y0 = FastFloor(yf); + int z0 = FastFloor(zf); + + float xs = InterpHermite((float)(xf - x0)); + float ys = InterpHermite((float)(yf - y0)); + float zs = InterpHermite((float)(zf - z0)); + + x0 *= PrimeX; + y0 *= PrimeY; + z0 *= PrimeZ; + int x1 = x0 + PrimeX; + int y1 = y0 + PrimeY; + int z1 = z0 + PrimeZ; + + int hash0 = Hash(seed, x0, y0, z0) & (255 << 2); + int hash1 = Hash(seed, x1, y0, z0) & (255 << 2); + + float lx0x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + float ly0x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + float lz0x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + hash0 = Hash(seed, x0, y1, z0) & (255 << 2); + hash1 = Hash(seed, x1, y1, z0) & (255 << 2); + + float lx1x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + float ly1x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + float lz1x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + float lx0y = Lerp(lx0x, lx1x, ys); + float ly0y = Lerp(ly0x, ly1x, ys); + float lz0y = Lerp(lz0x, lz1x, ys); + + hash0 = Hash(seed, x0, y0, z1) & (255 << 2); + hash1 = Hash(seed, x1, y0, z1) & (255 << 2); + + lx0x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + ly0x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + lz0x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + hash0 = Hash(seed, x0, y1, z1) & (255 << 2); + hash1 = Hash(seed, x1, y1, z1) & (255 << 2); + + lx1x = Lerp(RandVecs3D[hash0], RandVecs3D[hash1], xs); + ly1x = Lerp(RandVecs3D[hash0 | 1], RandVecs3D[hash1 | 1], xs); + lz1x = Lerp(RandVecs3D[hash0 | 2], RandVecs3D[hash1 | 2], xs); + + coord.x += Lerp(lx0y, Lerp(lx0x, lx1x, ys), zs) * warpAmp; + coord.y += Lerp(ly0y, Lerp(ly0x, ly1x, ys), zs) * warpAmp; + coord.z += Lerp(lz0y, Lerp(lz0x, lz1x, ys), zs) * warpAmp; + } + + + // Domain Warp Simplex/OpenSimplex2 + private void SingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, /*FNLfloat*/ float x, /*FNLfloat*/ float y, Vector2 coord, boolean outGradOnly) + { + final float SQRT3 = 1.7320508075688772935274463415059f; + final float G2 = (3 - SQRT3) / 6; + + x *= frequency; + y *= frequency; + + /* + * --- Skew moved to switch statements before fractal evaluation --- + * final FNLfloat F2 = 0.5f * (SQRT3 - 1); + * FNLfloat s = (x + y) * F2; + * x += s; y += s; + */ + + int i = FastFloor(x); + int j = FastFloor(y); + float xi = (float)(x - i); + float yi = (float)(y - j); + + float t = (xi + yi) * G2; + float x0 = (float)(xi - t); + float y0 = (float)(yi - t); + + i *= PrimeX; + j *= PrimeY; + + float vx, vy; + vx = vy = 0; + + float a = 0.5f - x0 * x0 - y0 * y0; + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo; + if (outGradOnly) + { + int hash = Hash(seed, i, j) & (255 << 1); + xo = RandVecs2D[hash]; + yo = RandVecs2D[hash | 1]; + } + else + { + int hash = Hash(seed, i, j); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + float xg = Gradients2D[index1]; + float yg = Gradients2D[index1 | 1]; + float value = x0 * xg + y0 * yg; + float xgo = RandVecs2D[index2]; + float ygo = RandVecs2D[index2 | 1]; + xo = value * xgo; + yo = value * ygo; + } + vx += aaaa * xo; + vy += aaaa * yo; + } + + float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a); + if (c > 0) + { + float x2 = x0 + (2 * (float)G2 - 1); + float y2 = y0 + (2 * (float)G2 - 1); + float cccc = (c * c) * (c * c); + float xo, yo; + if (outGradOnly) + { + int hash = Hash(seed, i + PrimeX, j + PrimeY) & (255 << 1); + xo = RandVecs2D[hash]; + yo = RandVecs2D[hash | 1]; + } + else + { + int hash = Hash(seed, i + PrimeX, j + PrimeY); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + float xg = Gradients2D[index1]; + float yg = Gradients2D[index1 | 1]; + float value = x2 * xg + y2 * yg; + float xgo = RandVecs2D[index2]; + float ygo = RandVecs2D[index2 | 1]; + xo = value * xgo; + yo = value * ygo; + } + vx += cccc * xo; + vy += cccc * yo; + } + + if (y0 > x0) + { + float x1 = x0 + (float)G2; + float y1 = y0 + ((float)G2 - 1); + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + { + int hash = Hash(seed, i, j + PrimeY) & (255 << 1); + xo = RandVecs2D[hash]; + yo = RandVecs2D[hash | 1]; + } + else + { + int hash = Hash(seed, i, j + PrimeY); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + float xg = Gradients2D[index1]; + float yg = Gradients2D[index1 | 1]; + float value = x1 * xg + y1 * yg; + float xgo = RandVecs2D[index2]; + float ygo = RandVecs2D[index2 | 1]; + xo = value * xgo; + yo = value * ygo; + } + vx += bbbb * xo; + vy += bbbb * yo; + } + } + else + { + float x1 = x0 + ((float)G2 - 1); + float y1 = y0 + (float)G2; + float b = 0.5f - x1 * x1 - y1 * y1; + if (b > 0) + { + float bbbb = (b * b) * (b * b); + float xo, yo; + if (outGradOnly) + { + int hash = Hash(seed, i + PrimeX, j) & (255 << 1); + xo = RandVecs2D[hash]; + yo = RandVecs2D[hash | 1]; + } + else + { + int hash = Hash(seed, i + PrimeX, j); + int index1 = hash & (127 << 1); + int index2 = (hash >> 7) & (255 << 1); + float xg = Gradients2D[index1]; + float yg = Gradients2D[index1 | 1]; + float value = x1 * xg + y1 * yg; + float xgo = RandVecs2D[index2]; + float ygo = RandVecs2D[index2 | 1]; + xo = value * xgo; + yo = value * ygo; + } + vx += bbbb * xo; + vy += bbbb * yo; + } + } + + coord.x += vx * warpAmp; + coord.y += vy * warpAmp; + } + + private void SingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, /*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z, Vector3 coord, boolean outGradOnly) + { + x *= frequency; + y *= frequency; + z *= frequency; + + /* + * --- Rotation moved to switch statements before fractal evaluation --- + * final FNLfloat R3 = (FNLfloat)(2.0 / 3.0); + * FNLfloat r = (x + y + z) * R3; // Rotation, not skew + * x = r - x; y = r - y; z = r - z; + */ + + int i = FastRound(x); + int j = FastRound(y); + int k = FastRound(z); + float x0 = (float)x - i; + float y0 = (float)y - j; + float z0 = (float)z - k; + + int xNSign = (int)(-x0 - 1.0f) | 1; + int yNSign = (int)(-y0 - 1.0f) | 1; + int zNSign = (int)(-z0 - 1.0f) | 1; + + float ax0 = xNSign * -x0; + float ay0 = yNSign * -y0; + float az0 = zNSign * -z0; + + i *= PrimeX; + j *= PrimeY; + k *= PrimeZ; + + float vx, vy, vz; + vx = vy = vz = 0; + + float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0); + for (int l = 0; ; l++) + { + if (a > 0) + { + float aaaa = (a * a) * (a * a); + float xo, yo, zo; + if (outGradOnly) + { + int hash = Hash(seed, i, j, k) & (255 << 2); + xo = RandVecs3D[hash]; + yo = RandVecs3D[hash | 1]; + zo = RandVecs3D[hash | 2]; + } + else + { + int hash = Hash(seed, i, j, k); + int index1 = hash & (63 << 2); + int index2 = (hash >> 6) & (255 << 2); + float xg = Gradients3D[index1]; + float yg = Gradients3D[index1 | 1]; + float zg = Gradients3D[index1 | 2]; + float value = x0 * xg + y0 * yg + z0 * zg; + float xgo = RandVecs3D[index2]; + float ygo = RandVecs3D[index2 | 1]; + float zgo = RandVecs3D[index2 | 2]; + xo = value * xgo; + yo = value * ygo; + zo = value * zgo; + } + vx += aaaa * xo; + vy += aaaa * yo; + vz += aaaa * zo; + } + + float b = a; + int i1 = i; + int j1 = j; + int k1 = k; + float x1 = x0; + float y1 = y0; + float z1 = z0; + + if (ax0 >= ay0 && ax0 >= az0) + { + x1 += xNSign; + b = b + ax0 + ax0; + i1 -= xNSign * PrimeX; + } + else if (ay0 > ax0 && ay0 >= az0) + { + y1 += yNSign; + b = b + ay0 + ay0; + j1 -= yNSign * PrimeY; + } + else + { + z1 += zNSign; + b = b + az0 + az0; + k1 -= zNSign * PrimeZ; + } + + if (b > 1) + { + b -= 1; + float bbbb = (b * b) * (b * b); + float xo, yo, zo; + if (outGradOnly) + { + int hash = Hash(seed, i1, j1, k1) & (255 << 2); + xo = RandVecs3D[hash]; + yo = RandVecs3D[hash | 1]; + zo = RandVecs3D[hash | 2]; + } + else + { + int hash = Hash(seed, i1, j1, k1); + int index1 = hash & (63 << 2); + int index2 = (hash >> 6) & (255 << 2); + float xg = Gradients3D[index1]; + float yg = Gradients3D[index1 | 1]; + float zg = Gradients3D[index1 | 2]; + float value = x1 * xg + y1 * yg + z1 * zg; + float xgo = RandVecs3D[index2]; + float ygo = RandVecs3D[index2 | 1]; + float zgo = RandVecs3D[index2 | 2]; + xo = value * xgo; + yo = value * ygo; + zo = value * zgo; + } + vx += bbbb * xo; + vy += bbbb * yo; + vz += bbbb * zo; + } + + if (l == 1) break; + + ax0 = 0.5f - ax0; + ay0 = 0.5f - ay0; + az0 = 0.5f - az0; + + x0 = xNSign * ax0; + y0 = yNSign * ay0; + z0 = zNSign * az0; + + a += (0.75f - ax0) - (ay0 + az0); + + i += (xNSign >> 1) & PrimeX; + j += (yNSign >> 1) & PrimeY; + k += (zNSign >> 1) & PrimeZ; + + xNSign = -xNSign; + yNSign = -yNSign; + zNSign = -zNSign; + + seed += 1293373; + } + + coord.x += vx * warpAmp; + coord.y += vy * warpAmp; + coord.z += vz * warpAmp; + } + + public static class Vector2 + { + public /*FNLfloat*/ float x; + public /*FNLfloat*/ float y; + public Vector2(/*FNLfloat*/ float x, /*FNLfloat*/ float y) + { + this.x = x; + this.y = y; + } + } + + public static class Vector3 + { + public /*FNLfloat*/ float x; + public /*FNLfloat*/ float y; + public /*FNLfloat*/ float z; + public Vector3(/*FNLfloat*/ float x, /*FNLfloat*/ float y, /*FNLfloat*/ float z) + { + this.x = x; + this.y = y; + this.z = z; + } + } +} \ No newline at end of file diff --git a/LICENSE b/LICENSE index 5ee8678..dd6df2c 100644 --- a/LICENSE +++ b/LICENSE @@ -1,6 +1,7 @@ MIT License -Copyright (c) 2017 Jordan Peck +Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com) +Copyright(c) 2020 Contributors Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal diff --git a/PreviewApp/FastNoiseLite.csproj b/PreviewApp/FastNoiseLite.csproj new file mode 100644 index 0000000..7dc04ef --- /dev/null +++ b/PreviewApp/FastNoiseLite.csproj @@ -0,0 +1,13 @@ + + + WinExe + netcoreapp3.1 + + + + + + + + + \ No newline at end of file diff --git a/PreviewApp/FastNoiseLiteGUI.cs b/PreviewApp/FastNoiseLiteGUI.cs new file mode 100644 index 0000000..7796ae9 --- /dev/null +++ b/PreviewApp/FastNoiseLiteGUI.cs @@ -0,0 +1,778 @@ +using System; +using System.Diagnostics; +using System.Text.RegularExpressions; +using System.Threading.Tasks; +using Eto.Drawing; +using Eto.Forms; + +// Switch between using floats or doubles for input position (Match with FastNoiseLite.cs) +using FNfloat = System.Single; +//using FNfloat = System.Double; + +class Program +{ + [STAThread] + public static void Main(string[] args) + { + new Application().Run(new FastNoiseLiteGUI()); + } +} + +public class FastNoiseLiteGUI : Form +{ + private Button GenerateButton; + private Button UpButton; + private Button DownButton; + private Button ScrollButton; + + private NumericStepper PreviewWidth; + private NumericStepper PreviewHeight; + private CheckBox Invert; + private CheckBox Is3D; + private CheckBox VisualiseDomainWarp; + + private DropDown NoiseType; + private DropDown RotationType3D; + private NumericStepper Seed; + private NumericStepper Frequency; + + private DropDown FractalType; + private NumericStepper FractalOctaves; + private NumericStepper FractalLacunarity; + private NumericStepper FractalGain; + private NumericStepper FractalWeightedStrength; + private NumericStepper FractalPingPongStrength; + + private DropDown CellularDistanceFunction; + private DropDown CellularReturnType; + private NumericStepper CellularJitter; + + private DropDown DomainWarp; + private DropDown DomainWarpRotationType3D; + private NumericStepper DomainWarpAmplitude; + private NumericStepper DomainWarpFrequency; + + private DropDown DomainWarpFractal; + private NumericStepper DomainWarpFractalOctaves; + private NumericStepper DomainWarpFractalLacunarity; + private NumericStepper DomainWarpFractalGain; + + private Bitmap Bitmap; + private ImageView Image; + private int[] ImageData; + + private Label Time; + private Label Min; + private Label Max; + private Label Mean; + private Label ExtraInfo; + + private bool isScrolling = false; + private float zPos = 0; + private Size previewStartSize = new Size(768, 768); + private Size windowSizeOffset = new Size(334, 52); + + public FastNoiseLiteGUI() + { + Title = "FastNoise Lite GUI"; + Resizable = false; + + ImageData = new int[1]; + + // Create main layout, makes controls and result appear side by side + var mainLayout = new StackLayout(); + mainLayout.Orientation = Orientation.Horizontal; + mainLayout.Spacing = 5; + mainLayout.Padding = new Padding(10); + mainLayout.HorizontalContentAlignment = HorizontalAlignment.Left; + + // Control panel + var controlPanel = new StackLayout(); + controlPanel.Orientation = Orientation.Vertical; + controlPanel.Spacing = 5; + + Font bold = new Font(new Label().Font.Family, new Label().Font.Size, FontStyle.Bold); + + { + // Generate, Up, Down + { + var layout = new StackLayout() + { + Orientation = Orientation.Horizontal, + Spacing = 2 + }; + + GenerateButton = new Button(); + GenerateButton.Text = "Generate"; + GenerateButton.Click += Generate; + GenerateButton.Width = 90; + layout.Items.Add(GenerateButton); + + UpButton = new Button(); + UpButton.Text = "Up"; + UpButton.Enabled = false; + UpButton.Click += OnUp; + UpButton.Width = 70; + layout.Items.Add(UpButton); + + DownButton = new Button(); + DownButton.Text = "Down"; + DownButton.Enabled = false; + DownButton.Click += OnDown; + DownButton.Width = 70; + layout.Items.Add(DownButton); + + ScrollButton = new Button(); + ScrollButton.Text = "Scroll"; + ScrollButton.Enabled = false; + ScrollButton.Click += OnScroll; + ScrollButton.Width = 70; + layout.Items.Add(ScrollButton); + + controlPanel.Items.Add(layout); + } + + // Control table + var table = new TableLayout(); + table.Spacing = new Size(5, 5); + + // Preview controls + { + // Preview size dropdown + { + var stack = new StackLayout(); + stack.Orientation = Orientation.Horizontal; + stack.Spacing = 2; + PreviewWidth = new NumericStepper { Value = previewStartSize.Width, Increment = 128 }; + PreviewWidth.ValueChanged += Generate; + stack.Items.Add(new StackLayoutItem(PreviewWidth)); + PreviewHeight = new NumericStepper { Value = previewStartSize.Height, Increment = 128 }; + PreviewHeight.ValueChanged += Generate; + stack.Items.Add(new StackLayoutItem(PreviewHeight)); + + AddToTableWithLabel(table, stack, "Preview Size:"); + } + + // Invert + Invert = new CheckBox(); + Invert.CheckedChanged += Generate; + AddToTableWithLabel(table, Invert, "Invert:"); + + // 3D + Is3D = new CheckBox(); + Is3D.CheckedChanged += OnUIUpdate; + AddToTableWithLabel(table, Is3D, "3D:"); + + // Visualise Domain Warp + VisualiseDomainWarp = new CheckBox(); + VisualiseDomainWarp.CheckedChanged += OnUIUpdate; + AddToTableWithLabel(table, VisualiseDomainWarp, "Visualise Domain Warp:"); + } + + table.Rows.Add(new TableRow { Cells = { new Label { Text = "General:", Font = bold } } }); + + // General properties + { + // Noise Type + { + NoiseType = new DropDown(); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.NoiseType))) + { + NoiseType.Items.Add(FormatReadable(name)); + } + NoiseType.SelectedIndex = (int)FastNoiseLite.NoiseType.OpenSimplex2; + NoiseType.SelectedIndexChanged += OnUIUpdate; + AddToTableWithLabel(table, NoiseType, "Noise Type:"); + } + + // Rotation Type 3D + { + RotationType3D = new DropDown(); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.RotationType3D))) + { + RotationType3D.Items.Add(FormatReadable(name)); + } + RotationType3D.SelectedIndex = (int)FastNoiseLite.RotationType3D.None; + RotationType3D.SelectedIndexChanged += OnUIUpdate; + AddToTableWithLabel(table, RotationType3D, "Rotation Type 3D:"); + } + + // Seed + Seed = new NumericStepper { Value = 1337 }; + Seed.ValueChanged += Generate; + AddToTableWithLabel(table, Seed, "Seed:"); + + // Frequency + Frequency = new NumericStepper { Value = 0.02, DecimalPlaces = 3, Increment = 0.005 }; + Frequency.ValueChanged += Generate; + AddToTableWithLabel(table, Frequency, "Frequency:"); + } + + // Add fractal label + table.Rows.Add(new TableRow { Cells = { new Label { Text = "Fractal:", Font = bold } } }); + + { + // Fractal type + { + FractalType = new DropDown(); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.FractalType))) + { + if (name.StartsWith("DomainWarp")) break; + FractalType.Items.Add(FormatReadable(name)); + } + FractalType.SelectedIndex = (int)FastNoiseLite.FractalType.FBm; + FractalType.SelectedIndexChanged += OnUIUpdate; + AddToTableWithLabel(table, FractalType, "Type:"); + } + + // Octaves + FractalOctaves = new NumericStepper { Value = 5 }; + FractalOctaves.ValueChanged += Generate; + AddToTableWithLabel(table, FractalOctaves, "Octaves:"); + + // Lacunarity + FractalLacunarity = new NumericStepper { Value = 2.0, DecimalPlaces = 2, Increment = 0.1 }; + FractalLacunarity.ValueChanged += Generate; + AddToTableWithLabel(table, FractalLacunarity, "Lacunarity:"); + + // Gain + FractalGain = new NumericStepper { Value = 0.5, DecimalPlaces = 2, Increment = 0.1 }; + FractalGain.ValueChanged += Generate; + AddToTableWithLabel(table, FractalGain, "Gain:"); + + // Weighted Strength + FractalWeightedStrength = new NumericStepper { Value = 0.0, DecimalPlaces = 2, Increment = 0.1 }; + FractalWeightedStrength.ValueChanged += Generate; + AddToTableWithLabel(table, FractalWeightedStrength, "Weighted Strength:"); + + // Ping Pong Strength + FractalPingPongStrength = new NumericStepper { Value = 2.0, DecimalPlaces = 2, Increment = 0.1 }; + FractalPingPongStrength.ValueChanged += Generate; + AddToTableWithLabel(table, FractalPingPongStrength, "Ping Pong Strength:"); + } + + // Add fractal label + table.Rows.Add(new TableRow { Cells = { new Label { Text = "Cellular:", Font = bold } } }); + + { + // Distance Function + { + CellularDistanceFunction = new DropDown(); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.CellularDistanceFunction))) + { + CellularDistanceFunction.Items.Add(FormatReadable(name)); + } + CellularDistanceFunction.SelectedIndex = (int)FastNoiseLite.CellularDistanceFunction.EuclideanSq; + CellularDistanceFunction.SelectedIndexChanged += Generate; + AddToTableWithLabel(table, CellularDistanceFunction, "Distance Function:"); + } + + // Return Type + { + CellularReturnType = new DropDown(); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.CellularReturnType))) + { + CellularReturnType.Items.Add(FormatReadable(name)); + } + CellularReturnType.SelectedIndex = (int)FastNoiseLite.CellularReturnType.Distance; + CellularReturnType.SelectedIndexChanged += Generate; + AddToTableWithLabel(table, CellularReturnType, "Return Type:"); + } + + // Jitter + CellularJitter = new NumericStepper() { Value = 1.0, DecimalPlaces = 2, Increment = 0.1 }; + CellularJitter.ValueChanged += Generate; + AddToTableWithLabel(table, CellularJitter, "Jitter:"); + } + + // Add fractal label + table.Rows.Add(new TableRow { Cells = { new Label { Text = "Domain Warp:", Font = bold } } }); + + { + // Domain Warp Dropdown + { + DomainWarp = new DropDown(); + DomainWarp.Items.Add("None"); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.DomainWarpType))) + { + DomainWarp.Items.Add(FormatReadable(name)); + } + DomainWarp.SelectedIndex = 0; + DomainWarp.SelectedIndexChanged += OnUIUpdate; + AddToTableWithLabel(table, DomainWarp, "Type:"); + } + + // Domain Warp Rotation Type 3D + { + DomainWarpRotationType3D = new DropDown(); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.RotationType3D))) + { + DomainWarpRotationType3D.Items.Add(FormatReadable(name)); + } + DomainWarpRotationType3D.SelectedIndex = (int)FastNoiseLite.RotationType3D.None; + DomainWarpRotationType3D.SelectedIndexChanged += OnUIUpdate; + AddToTableWithLabel(table, DomainWarpRotationType3D, "Rotation Type 3D:"); + } + + // Amplitude + DomainWarpAmplitude = new NumericStepper { Value = 30.0, DecimalPlaces = 2, Increment = 5 }; + DomainWarpAmplitude.ValueChanged += Generate; + AddToTableWithLabel(table, DomainWarpAmplitude, "Amplitude:"); + + // Frequency + DomainWarpFrequency = new NumericStepper { Value = 0.005, DecimalPlaces = 3, Increment = 0.005 }; + DomainWarpFrequency.ValueChanged += Generate; + AddToTableWithLabel(table, DomainWarpFrequency, "Frequency:"); + } + + // Add domain warp fractal label + table.Rows.Add(new TableRow { Cells = { new Label { Text = "Domain Warp Fractal:", Font = bold } } }); + + { + // Domain Warp Fractal Dropdown + { + DomainWarpFractal = new DropDown(); + DomainWarpFractal.Items.Add("None"); + foreach (var name in Enum.GetNames(typeof(FastNoiseLite.FractalType))) + { + if (!name.StartsWith("DomainWarp")) continue; + DomainWarpFractal.Items.Add(FormatReadable(name), name); + } + DomainWarpFractal.SelectedIndex = 0; + DomainWarpFractal.SelectedIndexChanged += OnUIUpdate; + AddToTableWithLabel(table, DomainWarpFractal, "Fractal Type:"); + } + + // Octaves + DomainWarpFractalOctaves = new NumericStepper { Value = 5 }; + DomainWarpFractalOctaves.ValueChanged += Generate; + AddToTableWithLabel(table, DomainWarpFractalOctaves, "Octaves:"); + + // Lacunarity + DomainWarpFractalLacunarity = new NumericStepper { Value = 2.0, DecimalPlaces = 2, Increment = 0.1 }; + DomainWarpFractalLacunarity.ValueChanged += Generate; + AddToTableWithLabel(table, DomainWarpFractalLacunarity, "Lacunarity:"); + + // Gain + DomainWarpFractalGain = new NumericStepper { Value = 0.5, DecimalPlaces = 2, Increment = 0.1 }; + DomainWarpFractalGain.ValueChanged += Generate; + AddToTableWithLabel(table, DomainWarpFractalGain, "Gain:"); + } + + // Add table to the controls panel + controlPanel.Items.Add(table); + + // Add save and github buttons + { + var stack = new StackLayout(); + stack.Orientation = Orientation.Horizontal; + stack.Spacing = 5; + stack.Padding = new Padding(10); + + var save = new Button { Text = "Save" }; + save.Click += Save; + stack.Items.Add(new StackLayoutItem(save)); + + var github = new Button { Text = "GitHub" }; + github.Click += (sender, e) => { Process.Start(new ProcessStartInfo("https://github.com/Auburns/FastNoise") { UseShellExecute = true }); }; + stack.Items.Add(new StackLayoutItem(github)); + + controlPanel.Items.Add(stack); + } + } + + // Add control panel to layout + mainLayout.Items.Add(controlPanel); + + // Add output panel + { + var layout = new StackLayout(); + layout.Orientation = Orientation.Vertical; + + // Info + { + var infoPane = new StackLayout(); + infoPane.Orientation = Orientation.Horizontal; + infoPane.Spacing = 15; + + // First info column + { + var column = new StackLayout(); + column.Orientation = Orientation.Vertical; + + // Time + Time = new Label { Text = "Time (ms): N/A" }; + column.Items.Add(new StackLayoutItem(Time)); + + // Mean + Mean = new Label { Text = "Mean: N/A" }; + column.Items.Add(new StackLayoutItem(Mean)); + + infoPane.Items.Add(column); + } + + // Second info column + { + var column = new StackLayout(); + column.Orientation = Orientation.Vertical; + + // Time + Min = new Label { Text = "Min: N/A" }; + column.Items.Add(new StackLayoutItem(Min)); + + // Mean + Max = new Label { Text = "Max: N/A" }; + column.Items.Add(new StackLayoutItem(Max)); + + infoPane.Items.Add(column); + } + + // Third entry + { + ExtraInfo = new Label(); + infoPane.Items.Add(ExtraInfo); + } + + layout.Items.Add(new StackLayoutItem(infoPane)); + } + + Image = new ImageView(); + //var imageScroll = new Scrollable(); + //imageScroll.Content = Image; + layout.Items.Add(new StackLayoutItem(Image)); + mainLayout.Items.Add(layout); + } + + // Display the layout + Content = mainLayout; + + // Ensure UI state is valid then it generates + OnUIUpdate(); + } + + async private void Generate(object sender = null, EventArgs e = null) + { + if (isScrolling && sender != ScrollButton) return; + + do + { + // Create noise generators + var genNoise = new FastNoiseLite(); + var warpNoise = new FastNoiseLite(); + + int w = (int)PreviewWidth.Value; + int h = (int)PreviewHeight.Value; + + if (w <= 0 || h <= 0) + { + return; + } + + genNoise.SetNoiseType((FastNoiseLite.NoiseType)NoiseType.SelectedIndex); + genNoise.SetRotationType3D((FastNoiseLite.RotationType3D)RotationType3D.SelectedIndex); + genNoise.SetSeed((int)Seed.Value); + genNoise.SetFrequency((float)Frequency.Value); + genNoise.SetFractalType((FastNoiseLite.FractalType)FractalType.SelectedIndex); + genNoise.SetFractalOctaves((int)FractalOctaves.Value); + genNoise.SetFractalLacunarity((float)FractalLacunarity.Value); + genNoise.SetFractalGain((float)FractalGain.Value); + genNoise.SetFractalWeightedStrength((float)FractalWeightedStrength.Value); + genNoise.SetFractalPingPongStrength((float)FractalPingPongStrength.Value); + + genNoise.SetCellularDistanceFunction((FastNoiseLite.CellularDistanceFunction)CellularDistanceFunction.SelectedIndex); + genNoise.SetCellularReturnType((FastNoiseLite.CellularReturnType)CellularReturnType.SelectedIndex); + genNoise.SetCellularJitter((float)CellularJitter.Value); + + warpNoise.SetSeed((int)Seed.Value); + warpNoise.SetDomainWarpType((FastNoiseLite.DomainWarpType)DomainWarp.SelectedIndex - 1); + warpNoise.SetRotationType3D((FastNoiseLite.RotationType3D)DomainWarpRotationType3D.SelectedIndex); + warpNoise.SetDomainWarpAmp((float)DomainWarpAmplitude.Value); + warpNoise.SetFrequency((float)DomainWarpFrequency.Value); + warpNoise.SetFractalType((FastNoiseLite.FractalType)Enum.Parse(typeof(FastNoiseLite.FractalType), DomainWarpFractal.SelectedKey)); + warpNoise.SetFractalOctaves((int)DomainWarpFractalOctaves.Value); + warpNoise.SetFractalLacunarity((float)DomainWarpFractalLacunarity.Value); + warpNoise.SetFractalGain((float)DomainWarpFractalGain.Value); + + if (ImageData.Length != w * h) + { + ImageData = new int[w * h]; + } + + float noise; + float minN = float.MaxValue; + float maxN = float.MinValue; + float avg = 0; + + bool get3d = Is3D.Checked == true; // Stupid! + bool invert = Invert.Checked == true; + + // Timer + Stopwatch sw = new Stopwatch(); + + int index = 0; + if (VisualiseDomainWarp.Checked != true) + { + var noiseValues = new float[w * h]; + bool warp = DomainWarp.SelectedIndex > 0; + + sw.Start(); + for (var y = h / -2; y < h / 2; y++) + { + for (var x = w / -2; x < w / 2; x++) + { + FNfloat xf = x; + FNfloat yf = y; + FNfloat zf = zPos; + + + if (get3d) + { + if (warp) + warpNoise.DomainWarp(ref xf, ref yf, ref zf); + + noise = genNoise.GetNoise(xf, yf, zf); + } + else + { + if (warp) + warpNoise.DomainWarp(ref xf, ref yf); + + noise = genNoise.GetNoise(xf, yf); + } + + avg += noise; + maxN = Math.Max(maxN, noise); + minN = Math.Min(minN, noise); + noiseValues[index++] = noise; + } + } + sw.Stop(); + + avg /= index - 1; + float scale = 255 / (maxN - minN); + + for (var i = 0; i < noiseValues.Length; i++) + { + int value = (int)MathF.Round(Math.Clamp((noiseValues[i] - minN) * scale, 0, 255)); + + if (invert) + value = 255 - value; + + ImageData[i] = value; + ImageData[i] |= value << 8; + ImageData[i] |= value << 16; + } + } + else + { + var noiseValues = new float[w * h * 3]; + + sw.Start(); + for (var y = -h / 2; y < h / 2; y++) + { + for (var x = -w / 2; x < w / 2; x++) + { + FNfloat xf = x; + FNfloat yf = y; + FNfloat zf = zPos; + + if (get3d) + warpNoise.DomainWarp(ref xf, ref yf, ref zf); + else + warpNoise.DomainWarp(ref xf, ref yf); + + xf -= x; + yf -= y; + zf -= zPos; + + avg += (float)(xf + yf); + maxN = Math.Max(maxN, (float)Math.Max(xf, yf)); + minN = Math.Min(minN, (float)Math.Min(xf, yf)); + + noiseValues[index++] = (float)xf; + noiseValues[index++] = (float)yf; + + if (get3d) + { + avg += (float)zf; + maxN = Math.Max(maxN, (float)zf); + minN = Math.Min(minN, (float)zf); + noiseValues[index++] = (float)zf; + } + } + } + sw.Stop(); + + if (get3d) + avg /= (index - 1) * 3; + else avg /= (index - 1) * 2; + + index = 0; + float scale = 1 / (maxN - minN); + + for (var i = 0; i < ImageData.Length; i++) + { + Color color = new Color(); + + if (get3d) + { + color.R = (noiseValues[index++] - minN) * scale; + color.G = (noiseValues[index++] - minN) * scale; + color.B = (noiseValues[index++] - minN) * scale; + } + else + { + var vx = (noiseValues[index++] - minN) / (maxN - minN) - 0.5f; + var vy = (noiseValues[index++] - minN) / (maxN - minN) - 0.5f; + + ColorHSB hsb = new ColorHSB(); + + hsb.H = MathF.Atan2(vy, vx) * (180 / MathF.PI) + 180; + hsb.B = Math.Min(1.0f, MathF.Sqrt(vx * vx + vy * vy) * 2); + hsb.S = 0.9f; + + color = hsb.ToColor(); + } + + if (Invert.Checked == true) + { + color.Invert(); + } + + ImageData[i] = color.ToArgb(); + } + } + + // Set image + Bitmap = new Bitmap(w, h, PixelFormat.Format32bppRgb, ImageData); + Image.Image = Bitmap; + + // Set info labels + Time.Text = "Time (ms): " + sw.ElapsedMilliseconds.ToString(); + Mean.Text = "Mean: " + avg.ToString(); + Min.Text = "Min: " + minN.ToString(); + Max.Text = "Max: " + maxN.ToString(); + + // Sets the client (inner) size of the window for your content + ClientSize = new Size(Math.Max((int)PreviewWidth.Value, 768), Math.Max((int)PreviewHeight.Value, 768)) + windowSizeOffset; + + if (isScrolling) + { + await Task.Delay(50); + try + { + zPos += ((float)Frequency.Value) * 100.0f; + } + catch (Exception ex) { MessageBox.Show("Frequency error: " + ex.ToString()); } + } + } + while (isScrolling); + } + + private void OnUp(object sender, EventArgs e) + { + try + { + zPos += ((float)Frequency.Value) * 100.0f; + Generate(sender, e); + } + catch (Exception ex) { MessageBox.Show("Frequency error: " + ex.ToString()); } + } + + private void OnDown(object sender, EventArgs e) + { + try + { + zPos -= ((float)Frequency.Value) * 100.0f; + Generate(sender, e); + } + catch (Exception ex) { MessageBox.Show("Frequency error: " + ex.ToString()); } + } + + private void OnScroll(object sender, EventArgs e) + { + isScrolling = !isScrolling; + if (isScrolling) Generate(sender, e); + } + + private void OnUIUpdate(object sender = null, EventArgs e = null) + { + // 3D controls + var is3d = Is3D.Checked == true; + UpButton.Enabled = DownButton.Enabled = ScrollButton.Enabled = is3d; + + // Warp + var warpVis = VisualiseDomainWarp.Checked == true; + NoiseType.Enabled = !warpVis; + FractalType.Enabled = !warpVis; + Frequency.Enabled = !warpVis; + + if (warpVis) + { + if (is3d) + ExtraInfo.Text = "Visualisation of domain warp:\r\nRed = X offset, Green = Y offset, Blue = Z offset"; + else ExtraInfo.Text = "Visualisation of domain warp:\r\nHue = Angle, Brightness = Magnitude"; + } + else ExtraInfo.Text = ""; + + // Fractal options + var fractalEnabled = (!warpVis && FractalType.SelectedIndex > 0); + FractalOctaves.Enabled = fractalEnabled; + FractalLacunarity.Enabled = fractalEnabled; + FractalGain.Enabled = fractalEnabled; + FractalWeightedStrength.Enabled = fractalEnabled; + FractalPingPongStrength.Enabled = (fractalEnabled && FractalType.SelectedKey == "Ping Pong"); + + // Domain Warp Fractal options + var domainWarpFractalEnabled = (DomainWarp.SelectedIndex > 0 && DomainWarpFractal.SelectedIndex > 0); + DomainWarpFractalOctaves.Enabled = domainWarpFractalEnabled; + DomainWarpFractalLacunarity.Enabled = domainWarpFractalEnabled; + DomainWarpFractalGain.Enabled = domainWarpFractalEnabled; + + // Cellular + var cellular = NoiseType.SelectedKey.Contains("Cellular") && !warpVis; + CellularDistanceFunction.Enabled = cellular; + CellularReturnType.Enabled = cellular; + CellularJitter.Enabled = cellular; + + // Domain Warp + var warp = DomainWarp.SelectedIndex > 0; + DomainWarpFractal.Enabled = warp; + DomainWarpAmplitude.Enabled = warp; + DomainWarpFrequency.Enabled = warp; + + // 3D Domain Rotation + RotationType3D.Enabled = !warpVis && is3d; + DomainWarpRotationType3D.Enabled = warp && is3d; + + Generate(sender, e); + } + + private void Save(object sender, EventArgs e) + { + var save = new SaveFileDialog(); + save.Filters.Add(new FileFilter("PNG File", ".png")); + var res = save.ShowDialog(null); + if (res == DialogResult.Ok) + { + Bitmap.Save(save.FileName, ImageFormat.Png); + } + } + + // Helper + private void AddToTableWithLabel(TableLayout parent, Control me, string label) + { + parent.Rows.Add(new TableRow + { + Cells = { + new TableCell(new Label { Text = label, TextAlignment = TextAlignment.Right }), + new TableCell(me) + } + }); + } + + private string FormatReadable(string enumName) + { + return Regex.Replace(Regex.Replace(enumName, "([a-z])([A-Z0-9])", "$1 $2"), "([a-z0-9])([A-Z][a-z])", "$1 $2"); + } +} diff --git a/PreviewApp/README.md b/PreviewApp/README.md new file mode 100644 index 0000000..40d4716 --- /dev/null +++ b/PreviewApp/README.md @@ -0,0 +1,21 @@ +# FastNoise Lite Preview App + +This is the FastNoise Lite preview app, it allows you to generate visual representations of the noise generated by the library, exposing every parameter through the GUI. + +## Build Instructions + +I recommend the use of Visual Studio Code or Visual Studio 2019 for building this project. However I am providing CLI build instructions also for those who prefer the command line. + +### Visual Studio Code + +In VS Code, you must configure VS Code ready for working with C# ([See Microsoft's own guide](https://code.visualstudio.com/Docs/languages/csharp)). Then you will be able to open this directory in VS Code and simply press F5 to run in debug. + +### Visual Studio 2019 + +Make sure .Net Core 3.1 support is installed for Visual Studio using the Visual Studio installer. + +### CLI + +- To run the project in debug mode run: `dotnet run` +- To build the project in debug or release mode run: `dotnet build -c Debug/Release` +- To generate an executable run: `dotnet publish -c Debug/Release` \ No newline at end of file diff --git a/README.md b/README.md index 36c804e..d268cfd 100644 --- a/README.md +++ b/README.md @@ -1,89 +1,86 @@ [![discord](https://img.shields.io/discord/703636892901441577?style=flat-square&logo=discord "Discord")](https://discord.gg/SHVaVfV) -# FastNoise +# FastNoise Lite -FastNoise is an open source noise generation library with a large collection of different noise algorithms. This library has been designed for realtime usage from the ground up, so has been optimised for speed without sacrificing noise quality. +FastNoise Lite is an extremely portable open source noise generation library with a large selection of noise algorithms. This library focuses on high performance while avoiding platform/language specific features, allowing for easy ports to as many possible languages. -This project started when my search to find a good noise library for procedural terrain generation concluded without an obvious choice. I enjoyed the options and customisation of Accidental Noise Library and the speed of LibNoise, so many of the techniques from these libraries and the knowledge I gained from reading through their source has gone into creating FastNoise. +This project is an evolution of the original FastNoise library and shares the same goal: An easy to use library that can quickly be integrated into a project and provides performant modern noise generation. -I have now also created [FastNoise SIMD](https://github.com/Auburns/FastNoiseSIMD), which utilises SIMD CPU instructions to gain huge performance boosts. It is slightly less flexible and cannot be converted to other languages, but if you can I would highly suggest using this for heavy noise generation loads. +If you are looking for a more extensive noise generation library consider using [FastNoise2](https://github.com/Auburn/FastNoise2). It provides large performance gains thanks to SIMD and uses a node graph structure to allow complex noise configurations with lots of flexibility. -### Features -- Value Noise 2D, 3D -- Perlin Noise 2D, 3D -- Simplex Noise 2D, 3D, 4D -- Cubic Noise 2D, 3D -- Gradient Perturb 2D, 3D +## Features + +- 2D & 3D +- OpenSimplex2 Noise +- OpenSimplex2S Noise +- Cellular (Voronoi) Noise +- Perlin Noise +- Value Noise +- Value Cubic Noise +- OpenSimplex2-based Domain Warp +- Basic Grid Gradient Domain Warp - Multiple fractal options for all of the above -- Cellular (Voronoi) Noise 2D, 3D -- White Noise 2D, 3D, 4D -- Supports floats or doubles +- Supports floats and/or doubles -### Wiki -Usage and documentation available in wiki +### Supported Languages -[Wiki Link](https://github.com/Auburns/FastNoise/wiki) +- C# +- C++ +- C +- Java +- HLSL -### Related repositories - - [FastNoise C#](https://github.com/Auburns/FastNoise_CSharp) - - [FastNoise Java](https://github.com/Auburns/FastNoise_Java) - - [FastNoise SIMD](https://github.com/Auburns/FastNoiseSIMD) - - [FastNoise Unity](https://www.assetstore.unity3d.com/en/#!/content/70706) - - [Unreal FastNoise](https://github.com/midgen/UnrealFastNoise) +## FastNoise Preview App -Credit to [CubicNoise](https://github.com/jobtalle/CubicNoise) for the cubic noise algorithm +A compact testing application is available for testing all features included in FastNoise Lite with a visual representation. This can be used for development purposes and testing noise settings. -## FastNoise Preview +Download links can be found in the [Releases](https://github.com/Auburns/FastNoise/releases). Build instructions can also be found in the PreviewApp directory. -I have written a compact testing application for all the features included in FastNoise with a visual representation. I use this for development purposes and testing noise settings used in terrain generation. +![FastNoise GUI](https://user-images.githubusercontent.com/1349548/93670916-b19b3a00-fa96-11ea-9990-e866bc3d719e.png) -Download links can be found in the [Releases Section](https://github.com/Auburns/FastNoise/releases). +## Performance Comparisons -![FastNoise Preview](http://i.imgur.com/uG7Vepc.png) +Benchmarked using C++ version with [NoiseBenchmarking](https://github.com/Auburn/NoiseBenchmarking) +- CPU: Intel 7820X @ 4.9Ghz +- OS: Win10 x64 +- Compiler: clang-cl 10.0.0 -m64 /O2 -# Performance Comparisons -Using default noise settings on FastNoise and matching those settings across the other libraries where possible. +Million points of noise generated per second (higher = better) -Timings below are x1000 ns to generate 32x32x32 points of noise on a single thread. +| 3D | Value | Perlin | (*Open)Simplex | Cellular | +|--------------------|--------|--------|----------------|----------| +| FastNoise Lite | 64.13 | 47.93 | 36.83* | 12.49 | +| FastNoise (Legacy) | 49.34 | 37.75 | 44.74 | 13.27 | +| FastNoise 2 (AVX2) | 494.49 | 261.10 | 268.44 | 52.43 | +| libnoise | | 27.35 | | 0.65 | +| stb perlin | | 34.32 | | | -- CPU: Intel Xeon Skylake @ 2.0Ghz -- Compiler: Intel 17.0 x64 +| 2D | Value | Perlin | Simplex | Cellular | +|--------------------|--------|--------|---------|----------| +| FastNoise Lite | 114.01 | 92.83 | 71.30 | 39.15 | +| FastNoise (Legacy) | 102.12 | 87.99 | 65.29 | 36.84 | +| FastNoise 2 (AVX2) | 776.33 | 624.27 | 466.03 | 194.30 | -| Noise Type | FastNoise | FastNoiseSIMD AVX2 | LibNoise | FastNoise 2D | -|-------------|-----------|--------------------|----------|--------------| -| White Noise | 141 | 9 | | 111 | -| Value | 642 | 152 | | 361 | -| Perlin | 1002 | 324 | 1368 | 473 | -| Simplex | 1194 | 294 | | 883 | -| Cellular | 2979 | 1283 | 58125 | 1074 | -| Cubic | 2979 | 952 | | 858 | +## Credits: -Comparision of fractal performance [here](https://github.com/Auburns/FastNoiseSIMD/wiki/In-depth-SIMD-level). +- [OpenSimplex2](https://github.com/KdotJPG/OpenSimplex2) for the OpenSimplex2 noise algorithm +- [@KdotJPG](https://github.com/KdotJPG) for implementing all the OpenSimplex alogrithms and the Java port +- [CubicNoise](https://github.com/jobtalle/CubicNoise) for the Value (Cubic) noise algorithm +- [@Rover656](https://github.com/Rover656) for creating the preview GUI and porting FastNoise Lite to C and HLSL. # Examples -## Cellular Noise -![Cellular Noise](http://i.imgur.com/quAic8M.png) - -![Cellular Noise](http://i.imgur.com/gAd9Y2t.png) - -![Cellular Noise](http://i.imgur.com/7kJd4fA.png) - -## Fractal Noise -![Fractal Noise](http://i.imgur.com/XqSD7eR.png) -## Value Noise -![Value Noise](http://i.imgur.com/X2lbFZR.png) +![Ridged Fractal](https://user-images.githubusercontent.com/1349548/93671180-b2cd6680-fa98-11ea-9026-0fb58b346c23.png) -## White Noise -![White Noise](http://i.imgur.com/QIlYvyQ.png) +![Cellular](https://user-images.githubusercontent.com/1349548/93670968-12c30d80-fa97-11ea-87ee-452173e784e0.png) -## Gradient Perturb -![Gradient Perturb](http://i.imgur.com/gOjc1u1.png) +![Cellular Fractal](https://user-images.githubusercontent.com/1349548/93671060-dfcd4980-fa97-11ea-9792-da7df5cc7fa9.png) -![Gradient Perturb](http://i.imgur.com/ui045Bk.png) +![Cellular Warped](https://user-images.githubusercontent.com/1349548/93671113-3470c480-fa98-11ea-9da8-a279538ef7c2.png) -![Gradient Perturb](http://i.imgur.com/JICFypT.png) +![Value Warped](https://user-images.githubusercontent.com/1349548/93671571-ff667100-fa9b-11ea-934c-1f1ab1f8d3f4.png) +![Cellular Scrolling](https://user-images.githubusercontent.com/1349548/93672159-97665980-faa0-11ea-9fcc-f5309b1a3a4b.gif) -# Any suggestions or questions welcome +![OpenSimplex2 Warp](https://user-images.githubusercontent.com/1349548/93671333-f674a000-fa99-11ea-8a34-1338b104dd82.png)