Transformations

Transformations is an Elixir library for translating, rotating, reflecting, scaling, shearing, projecting, orthogonalizing, and superimposing arrays of 3D homogeneous coordinates as well as for converting between rotation matrices, Euler angles, and quaternions. Also includes an Arcball control object and functions to decompose transformation matrices.

Installation

If available in Hex, the package can be installed by adding transformations to your list of dependencies in mix.exs:

def deps do
  [
    {:transformations, "~> 0.1.0"}
  ]
end

Usage

Create a matrix

matrix(mtx)

The following transformations are currently available:

transition(mtx, xt, yt, zt)

where xt, yt and zt are the x, y and z coordinates for the transform

scale(mtx, xs, ys, zs)

where xs, ys and zs are the scale factors along the x, y and z axes

rotatex(mtx, angle)

rotatey(mtx, angle)

rotatez(mtx, angle)

where angle refers to the angle of rotation along the specified axes

shearx(mtx, sy, sz)

sheary(mtx, sx, sz)

shearz(mtx, sx, sy)

where sx, sy and sz refer to the shear coefficients along each axis

mirrorx(mtx)

mirrors around the yz plane or the x-axis

mirrory(mtx)

mirrors around the xz plane or the y-axis

mirrorz(mtx)

mirrors around the xy plane or the z-axis

projectx(mtx)

projects down to the yz plane

projecty(mtx)

projects down to the xz plane

projectz(mtx)

projects down to the xy plane

Examples

Transformations can be applied to points as well as shapes. Points are specified as a 4 x 1 matrix while shapes are specified as a 4 x n matrix. Transformations are also 4 x 1 and 4 x n matrices respectively.

    iex(1)> point = Transformations.matrix([[1],[1],[1],[1]])
    #Matrex[4×1]
    ┌     ┐
    │ 1.0 │
    │ 1.0 │
    │ 1.0 │
    │ 1.0 │
    └     ┘
    iex(2)> point |> Transformations.scale(1,2,3)
    #Matrex[4×1]
    ┌     ┐
    │ 1.0 │
    │ 2.0 │
    │ 3.0 │
    │ 1.0 │
    └     ┘
    iex(3)> point |> Transformations.scale(1,2,3) |> Transformations.transition(3,4,7)
    #Matrex[4×1]
    ┌      ┐
    │  4.0 │
    │  6.0 │
    │ 10.0 │
    │  1.0 │
    └      ┘
    iex(4)> shape = Transformations.matrix([
        [0,1,1,0,0,1,1,0],
        [0,0,0,0,1,1,1,1],
        [0,0,1,1,0,0,1,1],
        [1,1,1,1,1,1,1,1]
    ])
    #Matrex[4×8]
    ┌                                                              ┐
    │  0.0     1.0     1.0     0.0     0.0     1.0     1.0     0.0 │
    │  0.0     0.0     0.0     0.0     1.0     1.0     1.0     1.0 │
    │  0.0     0.0     1.0     1.0     0.0     0.0     1.0     1.0 │
    │  1.0     1.0     1.0     1.0     1.0     1.0     1.0     1.0 │
    └                                                                 ┘
    iex(5)> shape |> Transformations.scale(1,2,3) |> Transformations.transition(3,4,7)            
    #Matrex[4×8]         
    ┌                                                              ┐
    │  3.0     4.0     4.0     3.0     3.0     4.0     4.0     3.0 │
    │  4.0     4.0     4.0     4.0     6.0     6.0     6.0     6.0 │
    │  7.0     7.0    10.0    10.0     7.0     7.0    10.0    10.0 │
    │  1.0     1.0     1.0     1.0     1.0     1.0     1.0     1.0 │
    └                                                              ┘

Generating documentation

    mix docs