module Transform2D ( Transform2D
, identity, matrix, multiply
, rotation, translation
, scale, scaleX, scaleY
) where
{-| A library for performing [2D matrix transformations][affine].
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][affine]. Since the bottom row as
always `0 0 1` in these matrices, it is omitted in the diagrams below.
[affine]: http://en.wikipedia.org/wiki/Transformation_matrix#Affine_transformations
# Transforms
@docs identity, matrix, rotation, translation, scale, scaleX, scaleY
# Multiplication
@docs multiply
-}
import Native.Transform2D
type Transform2D = 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 /
-}
identity : Transform2D
identity = Native.Transform2D.identity
{-| 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.
-}
matrix : Float -> Float -> Float -> Float -> Float -> Float -> Transform2D
matrix = Native.Transform2D.matrix
{-| Create a [rotation matrix](http://en.wikipedia.org/wiki/Rotation_matrix).
Given an angle t, it creates a counterclockwise rotation matrix:
rotation t
/ cos t -sin t 0 \
\ sin t cos t 0 /
-}
rotation : Float -> Transform2D
rotation = Native.Transform2D.rotation
{-| Create a transformation matrix for translation.
translation x y
/ 1 0 x \
\ 0 1 y /
-}
translation : Float -> Float -> Transform2D
translation x y = matrix 1 0 0 1 x y
{-| Creates a transformation matrix for scaling by a all directions.
scale s
/ s 0 0 \
\ 0 s 0 /
-}
scale : Float -> Transform2D
scale s = matrix s 0 0 s 0 0
{-| Create a transformation for horizontal scaling. -}
scaleX : Float -> Transform2D
scaleX x = matrix x 0 0 1 0 0
{-| Create a transformation for vertical scaling. -}
scaleY : Float -> Transform2D
scaleY y = matrix 1 0 0 y 0 0
{-| 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 /
-}
multiply : Transform2D -> Transform2D -> Transform2D
multiply = Native.Transform2D.multiply