purescript-transformation-matrix

Spatial matrix transformations for 4x4 affine matrices used in 3D graphics.

My goal is to build a pure functional set of libraries to perform the heavy lifting of creating, transforming, and interacting with 3D objects. The results of these operations can then be passed to a lightweight WebGL renderer (threejs or other) that is used only for display purposes. The purescript-transformation-matrix library will be the linear algebraic component of this set of libraries. The manipulation of geometries, materials, and meshes will be a separate library.

While this project is heavily inspired by threejs I have found my self frustrated with threejs for several reasons. Here are a few of those reasons:

1. Linear alegbraic operations are scattered across class inheritance structures making it difficult to find and reason about.
2. Pure mathematical logic is tightly coupled with threejs specific object logic.
3. Vectors and matrices are modified in place making it hard to keep track of modifications to their values.
4. Source code lacks types.

I believe that investing in a homegrown, pure functional, 3D graphics library is worth the time and effort and hope that you think so too! Code contributions are always welcome :)

In the context of threejs, this library:

1. Provides a direct API for linear algebraic operations used in 3D graphics
2. Does not tighly couple linear alebraic operations with higher order 3D graphic data types
3. Is not a FFI wrapper over threejs [1] [2] [3]

In the context of existing Purescript matrix libraries, this library:

1. Is specific to the matrix operations and dimensions used in 3D graphics (spatial/affine transformations, 4x4 matrices, 3x1 vectors)
2. Is not a general purpose matrix algebra library [1] [2]
3. Is runtime safe and does not use unsafe functions [1] [2]
4. Is not reliant on the user to make sure that their matrix functions are passed matrices of compatible dimensions

import Data.TransformationMatrix.Matrix4 
    ( Matrix4(..)
    , translate )

matrix = Matrix4
    1.0 0.0 0.0 1.0
    0.0 1.0 0.0 2.0
    0.0 0.0 1.0 3.0
    0.0 0.0 0.0 1.0

translation = Vector3 2.0 3.0 4.0

result = translate translation matrix
-- result == Matrix4
--   1.0 0.0 0.0 3.0
--   0.0 1.0 0.0 5.0
--   0.0 0.0 1.0 7.0
--   0.0 0.0 0.0 1.0

import Data.TransformationMatrix.Matrix4 
    ( Matrix4(..)
    , scale )

matrix = Matrix4
    1.0 0.0 0.0 1.0
    0.0 1.0 0.0 2.0
    0.0 0.0 1.0 3.0
    0.0 0.0 0.0 1.0

multiplier = 2.0

result = scale multiplier matrix
-- result == Matrix4
--   2.0 0.0 0.0 1.0
--   0.0 2.0 0.0 2.0
--   0.0 0.0 2.0 3.0
--   0.0 0.0 0.0 1.0