Z-order curve / Morton code for Erlang

erlzord is an implementation of the Z-order curve, or Morton code, for Erlang and Elixir.

Any number of dimensions is supported and there is no limit on the bitsize of output values.

The test cases were generated based on an existing Python implementation from the rubik project.

How to use

Erlang

1. Import as a dependency

rebar.config

{deps, [
    % [...]
    {erlzord, "~> 2.0"}
]}.

your_application.app.src

{applications, [
    kernel,
    stdlib,
    % [...]
    erlzord
]}

2. Encode and decode your vectors

2d points

Config = erlzord:config(#{
    dimensions => 2,
    min_component => -1000,
    max_component => +1000
}),

1595729 = erlzord:encode({245, -456}, Config),
{245,-456} = erlzord:decode(1595729, Config).

3d points

Config = erlzord:config(#{
    dimensions => 3,
    min_component => 0,
    max_component => 100
}),

123788 = erlzord:encode({42, 52, 21}, Config),
{42,52,21} = erlzord:decode_tuple(123788, Config).

10d points

Config = erlzord:config(#{
    dimensions => 10,
    min_component => 0,
    max_component => 700
}),

740763791023146735114306653082 =
    erlzord:encode([400,543,632,445,565,0,674,491,403,555], Config),

[400,543,632,445,565,0,674,491,403,555] =
    erlzord:decode_list(740763791023146735114306653082, Config).

Elixir

1. Import as a dependency

mix.exs

  defp deps do
    [
      # [...]
      {:erlzord, "~> 2.0"}
    ]
  end

2. Encode and decode your vectors

2d points

config = :erlzord.config(%{
    dimensions: 2,
    min_component: -1000,
    max_component: +1000
})

1595729 = :erlzord.encode({245,-456}, config)
{245,-456} = :erlzord.decode(1595729, Config)

3d points

config = :erlzord.config(%{
    dimensions: 3,
    min_component: 0,
    max_component: 100
}),

123788 = :erlzord.encode({42,52,21}, config)
{42,52,21} = :erlzord.decode_tuple(123788, config)

10d points

config = erlzord:config(%{
    dimensions: 10,
    min_component: 0,
    max_component: 700
}),

740763791023146735114306653082 =
    :erlzord.encode([400,543,632,445,565,0,674,491,403,555], config)

[400,543,632,445,565,0,674,491,403,555] =
    :erlzord.decode_list(740763791023146735114306653082, Config)

API Reference

The API reference can be found on HexDocs.

License

MIT License

Copyright (c) 2017-2024 Guilherme Andrade

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.