Transform2D

A library for performing 2D matrix transformations. It is used primarily with the groupTransform function from Graphics.Collage and allows you to do things like rotation, scaling, translation, shearing, and reflection.

Note that all the matrices in this library are 3x3 matrices of homogeneous coordinates, used for affine transformations. Since the bottom row as always 0 0 1 in these matrices, it is omitted in the diagrams below.

Transforms

identity : Transform2D

Create an identity transform. Transforming by the identity does not change anything, but it can come in handy as a default or base case.

    / 1 0 0 \
    \ 0 1 0 /

matrix : Float -> Float -> Float -> Float -> Float -> Float -> Transform2D

Create a transformation matrix. This lets you create transforms such as scales, shears, reflections, and translations.

matrix a b c d x y


    / a b x \
    \ c d y /

Note that x and y are the translation values.

rotation : Float -> Transform2D

Create a rotation matrix. Given an angle t, it creates a counterclockwise rotation matrix:

rotation t


    / cos t  -sin t  0 \
    \ sin t   cos t  0 /

translation : Float -> Float -> Transform2D

Create a transformation matrix for translation.

translation x y


    / 1 0 x \
    \ 0 1 y /

scale : Float -> Transform2D

Creates a transformation matrix for scaling by a all directions.

scale s


  / s 0 0 \
  \ 0 s 0 /

scaleX : Float -> Transform2D

Create a transformation for horizontal scaling.

scaleY : Float -> Transform2D

Create a transformation for vertical scaling.

Multiplication

multiply : Transform2D -> Transform2D -> Transform2D

Multiply two transforms together.

multiply m n


    / ma mb mx \     / na nb nx \
    | mc md my |  .  | nc nd ny |
    \  0  0  1 /     \  0  0  1 /

elm-lang/core/1.1.1

Transform2D

Transforms

Multiplication

Modules