Matrix.hs

{-# LANGUAGE  MultiParamTypeClasses, FunctionalDependencies, 
    TypeSynonymInstances #-}
module Graphics.SceneGraph.Matrix where

-- Warning: Because this matrix is going to get passed directly to GL we convert to GL space
-- here. 

import Graphics.Rendering.OpenGL hiding (Matrix)
import Graphics.SceneGraph.Vector
import Data.List
import Numeric.LinearAlgebra -- (inv, (><),toLists,Matrix,Vector,mul,fromLists,toList,fromList )

type MatrixD = Matrix GLdouble

identityMatrix :: MatrixD
identityMatrix = fromLists [ [1,0,0,0], [0,1,0,0], [0,0,1,0],[0,0,0,1]]

asMatrix :: VectorD -> MatrixD
asMatrix vec = let v = toList vec
               in fromLists [ [1, 0, 0, v!!0],[ 0, 1, 0, v!!2],[ 0, 0, 1 , (-(v!!1))],[ 0, 0, 0, 1] ]

translateM :: VectorD -> MatrixD -> MatrixD 
translateM v m = (asMatrix v) `multiply` m


translatePostM :: VectorD -> MatrixD -> MatrixD 
translatePostM v m = m `multiply` (asMatrix v)

scaleM :: VectorD -> MatrixD -> MatrixD
scaleM vec m = let v = toList vec
             in m `multiply` (fromLists  [ [ v!!0,0,0,0],[ 0, v!!2,0,0],[ 0, 0, (-(v!!1)),0],[ 0, 0, 0, 1] ])

-- | Build rotational transform matrix for rotate of ''theta'' around a vector.
rotateM' :: ((Element a)) => a -> Vector a -> Matrix a
rotateM' theta v = fromLists [ [ t*x*x  + c, t*x*y-s*z, t*x*z + s*y, 0],
                    [ t*x*y+s*z, t*y*y + c, t*y*z - s*x , 0], 
                    [ t*x*z-s*y, t*y*z + s*x, t*z*z+c, 0],
                    [0,0,0,1]]
                  where t = 1 - cos theta
                        c = cos theta
                        s = sin theta
                        [x',y',z'] = toList v
                        [x,y,z] = [x',z',(-y')]
           
rotateM theta v m = (rotateM' theta v) `multiply` m 

rotatePostM theta v m = m `multiply` (rotateM' theta v)
                    

mulV :: MatrixD  -> VectorD -> VectorD 
mulV m v = head $ toColumns $ m `multiply` (asColumn v)