----------------------------------------------------------------------------- -- | -- Module : Graphics.Rendering.Cairo.Matrix -- Copyright : (c) Paolo Martini 2005 -- License : BSD-style (see cairo/COPYRIGHT) -- -- Maintainer : p.martini@neuralnoise.com -- Stability : experimental -- Portability : portable -- -- Matrix math ----------------------------------------------------------------------------- module Graphics.Rendering.Cairo.Matrix ( Matrix(Matrix) , MatrixPtr , identity , translate , scale , rotate , transformDistance , transformPoint , scalarMultiply , adjoint , invert ) where import Foreign hiding (rotate) import Foreign.C -- | Representation of a 2-D affine transformation. -- -- The Matrix type represents a 2x2 transformation matrix along with a -- translation vector. @Matrix a1 a2 b1 b2 c1 c2@ describes the -- transformation of a point with coordinates x,y that is defined by -- -- > / x' \ = / a1 b1 \ / x \ + / c1 \ -- > \ y' / \ a2 b2 / \ y / \ c2 / -- -- or -- -- > x' = a1 * x + b1 * y + c1 -- > y' = a2 * x + b2 * y + c2 data Matrix = Matrix { xx :: !Double, yx :: !Double, xy :: !Double, yy :: !Double, x0 :: !Double, y0 :: !Double } deriving (Show, Eq) {#pointer *cairo_matrix_t as MatrixPtr -> Matrix#} instance Storable Matrix where sizeOf _ = {#sizeof cairo_matrix_t#} alignment _ = alignment (undefined :: CDouble) peek p = do xx <- {#get cairo_matrix_t->xx#} p yx <- {#get cairo_matrix_t->yx#} p xy <- {#get cairo_matrix_t->xy#} p yy <- {#get cairo_matrix_t->yy#} p x0 <- {#get cairo_matrix_t->x0#} p y0 <- {#get cairo_matrix_t->y0#} p return \$ Matrix (realToFrac xx) (realToFrac yx) (realToFrac xy) (realToFrac yy) (realToFrac x0) (realToFrac y0) poke p (Matrix xx yx xy yy x0 y0) = do {#set cairo_matrix_t->xx#} p (realToFrac xx) {#set cairo_matrix_t->yx#} p (realToFrac yx) {#set cairo_matrix_t->xy#} p (realToFrac xy) {#set cairo_matrix_t->yy#} p (realToFrac yy) {#set cairo_matrix_t->x0#} p (realToFrac x0) {#set cairo_matrix_t->y0#} p (realToFrac y0) return () instance Num Matrix where (*) (Matrix xx yx xy yy x0 y0) (Matrix xx' yx' xy' yy' x0' y0') = Matrix (xx * xx' + yx * xy') (xx * yx' + yx * yy') (xy * xx' + yy * xy') (xy * yx' + yy * yy') (x0 * xx' + y0 * xy' + x0') (x0 * yx' + y0 * yy' + y0') (+) = pointwise2 (+) (-) = pointwise2 (-) negate = pointwise negate abs = pointwise abs signum = pointwise signum -- this definition of fromInteger means that 2*m = scale 2 m -- and it means 1 = identity fromInteger n = Matrix (fromInteger n) 0 0 (fromInteger n) 0 0 {-# INLINE pointwise #-} pointwise f (Matrix xx yx xy yy x0 y0) = Matrix (f xx) (f yx) (f xy) (f yy) (f x0) (f y0) {-# INLINE pointwise2 #-} pointwise2 f (Matrix xx yx xy yy x0 y0) (Matrix xx' yx' xy' yy' x0' y0') = Matrix (f xx xx') (f yx yx') (f xy xy') (f yy yy') (f x0 x0') (f y0 y0') identity :: Matrix identity = Matrix 1 0 0 1 0 0 translate :: Double -> Double -> Matrix -> Matrix translate tx ty m = m * (Matrix 1 0 0 1 tx ty) scale :: Double -> Double -> Matrix -> Matrix scale sx sy m = m * (Matrix sx 0 0 sy 0 0) rotate :: Double -> Matrix -> Matrix rotate r m = m * (Matrix c s (-s) c 0 0) where s = sin r c = cos r transformDistance :: Matrix -> (Double,Double) -> (Double,Double) transformDistance (Matrix xx yx xy yy _ _) (dx,dy) = newX `seq` newY `seq` (newX,newY) where newX = xx * dx + xy * dy newY = yx * dx + yy * dy transformPoint :: Matrix -> (Double,Double) -> (Double,Double) transformPoint (Matrix xx yx xy yy x0 y0) (dx,dy) = newX `seq` newY `seq` (newX,newY) where newX = xx * dx + xy * dy + x0 newY = yx * dx + yy * dy + y0 scalarMultiply :: Double -> Matrix -> Matrix scalarMultiply scalar = pointwise (*scalar) adjoint :: Matrix -> Matrix adjoint (Matrix a b c d tx ty) = Matrix d (-b) (-c) a (c*ty - d*tx) (b*tx - a*ty) invert :: Matrix -> Matrix invert m@(Matrix xx yx xy yy _ _) = scalarMultiply (recip det) \$ adjoint m where det = xx*yy - yx*xy