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perspectiveone.py
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#!/usr/bin/env python3
# -*- encoding: utf-8 -*-
'''
@File : perspectiveone.py
@Time : 2020/12/11 21:45:11
@Author : Kearney
@Version : 0.0.0
@Contact : 191615342@qq.com
@License : GPL 3.0
@Desc : 一点透视、两点透视
画布横轴x向右增大，纵轴y向下增大
ref: https://blog.csdn.net/mylovestart/article/details/8352105
https://wenku.baidu.com/view/ce28831e0508763230121275.html
https://www.cnblogs.com/Penglimei/p/9750390.html
'''
import pygame
import sys
import numpy as np
import math
# 长方体的八个点(x, y ,z, 1)，其他点数的立体图形需要修改draw的参数
points = [[0, 0, 200, 1], [200, 0, 200, 1], [200, 0, 0, 1], [0, 0, 0, 1],
[0, 200, 200, 1], [200, 200, 200, 1], [200, 200, 0, 1],
[0, 200, 0, 1]]
onepoint = [] # 一点透视后的二维坐标
twopoint = [] # 两点透视后的二维坐标
threepoint = [] # 三点透视后的二维坐标
# 一点透视参数
L = 100 # 平移位置L, M, N
M = 100
N = 100
D = 300 # 视距
# 两点透视参数
P = 2
R = 3
xita = math.pi / 180 * 65 # 角度xita
Q = 1.5 # 三点透视参数
five = math.pi / 180 * 80 # 角度five，三点透视参数
# 一点透视变换矩阵
transMatrix = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1 / D], [L, M, 0, 1 + (N / D)]],
dtype='float32')
# 一点透视：将三维坐标映射到二维
for e in range(0, len(points)):
tmp = np.matmul(np.array(points[e], dtype='float32'), transMatrix)
tmp = tmp / tmp[3] # 齐次化
onepoint.append(tmp.tolist()[:2])
# 两点透视变换矩阵
twoMatrix = np.array(
[[math.cos(xita), 0, 0,
(P * math.cos(xita) - R * math.sin(xita))], [0, 1, 0, 0],
[math.sin(xita), 0, 0, (P * math.sin(xita) + R * math.cos(xita))],
[(L * math.cos(xita) + N * math.sin(xita)), M, 0,
(P * (L * math.cos(xita) + N * math.sin(xita))) +
(R * (N * math.cos(xita) + L * math.sin(xita))) + 1]],
dtype='float32')
# 两点透视降维变换
for e in range(0, len(points)):
tmp = np.matmul(np.array(points[e], dtype='float32'), twoMatrix)
tmp = tmp / tmp[3] # 齐次化
tmp = tmp * 500 # 非必须：放大，太小看不见
tmp[0] += 200 # 非必须：整体向右平移，不然和一位透视挡在一起了
twopoint.append(tmp.tolist()[:2])
# 三点透视变换矩阵
# 平移到LMN
mtranslation = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [L, M, N, 1]], dtype='float32')
# 沿y轴旋转
mrotatey = np.array([[math.cos(xita), 0, -math.sin(xita), 0], [0, 1, 0, 0],
[math.sin(xita), 0, math.cos(xita), 0], [0, 0, 0, 1]],
dtype='float32')
# 沿x轴旋转
mrotatex = np.array(
[[1, 0, 0, 0], [0, math.cos(five), math.sin(five), 0],
[0, -math.sin(five), math.cos(five), 0], [0, 0, 0, 1]],
dtype='float32')
# 透视
mperspective = np.array(
[[1, 0, 0, P], [0, 1, 0, Q], [0, 0, 1, R], [0, 0, 0, 1]], dtype='float32')
# 向xoy平面做正投影
mprojectionxy = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]], dtype='float32')
threeMatrix = np.matmul(
np.matmul(np.matmul(np.matmul(mtranslation, mrotatey), mrotatex),
mperspective), mprojectionxy)
# 三点透视降维变换
for e in range(0, len(points)):
tmp = np.matmul(np.array(points[e], dtype='float32'), threeMatrix)
tmp = tmp / tmp[3] # 齐次化
tmp = tmp * 800 # 非必须：放大，太小看不见
tmp[0] += 600 # 非必须：整体向右平移，不然和一点透视挡在一起了
tmp[1] += 100 # 非必须：整体向下平移，不然和一点透视挡在一起了
threepoint.append(tmp.tolist()[:2])
LINECOLOR = (29, 244, 255) # 颜色设置
BACKYCOLOR = (255, 212, 238)
LINEWIDTH = 3 # 线宽
pygame.init()
screen = pygame.display.set_mode((920, 640))
while True:
screen.fill(BACKYCOLOR)
# 一点透视的图
pygame.draw.lines(screen, LINECOLOR, False, onepoint, LINEWIDTH) # 懒人划线
pygame.draw.line(screen, BACKYCOLOR, onepoint[3], onepoint[4],
LINEWIDTH) # 遮瑕
# 补全剩下的线条
pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[3], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[4], onepoint[7], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[1], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[1], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[0], onepoint[4], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[3], onepoint[7], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[2], onepoint[6], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, onepoint[1], onepoint[5], LINEWIDTH)
# 两点透视的图
pygame.draw.lines(screen, LINECOLOR, False, twopoint, LINEWIDTH)
pygame.draw.line(screen, BACKYCOLOR, twopoint[3], twopoint[4], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[3], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[4], twopoint[7], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[1], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[1], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[0], twopoint[4], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[3], twopoint[7], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[2], twopoint[6], LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, twopoint[1], twopoint[5], LINEWIDTH)
pygame.draw.lines(screen, LINECOLOR, False, threepoint, LINEWIDTH)
pygame.draw.line(screen, BACKYCOLOR, threepoint[3], threepoint[4],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[3],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[4], threepoint[7],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[1],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[1],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[0], threepoint[4],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[3], threepoint[7],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[2], threepoint[6],
LINEWIDTH)
pygame.draw.line(screen, LINECOLOR, threepoint[1], threepoint[5],
LINEWIDTH)
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
sys.exit(0)
pygame.display.update()