{-# LANGUAGE CPP #-} ----------------------------------------------------------------------------- -- | -- Module : Diagrams.Transform.Matrix -- Copyright : (c) 2014 diagrams team (see LICENSE) -- License : BSD-style (see LICENSE) -- Maintainer : diagrams-discuss@googlegroups.com -- -- Functions for converting between 'Transformation's and matricies. -- ----------------------------------------------------------------------------- module Diagrams.Transform.Matrix where #if __GLASGOW_HASKELL__ < 710 import Control.Applicative #endif import Control.Arrow ((&&&)) import Control.Lens import Data.Distributive import qualified Data.Foldable as F import Data.Functor.Rep import Diagrams.Core.Transform as D import Diagrams.ThreeD.Types import Diagrams.TwoD.Types import Linear.Matrix import Linear.Vector -- | Build a matrix from a 'Transformation', ignoring the translation. mkMat :: (HasBasis v, Num n) => Transformation v n -> v (v n) mkMat t = distribute . tabulate \$ apply t . unit . el -- | Build a 3D transformation matrix in homogeneous coordinates from -- a 'Transformation V3'. mkMatHomo :: Num n => Transformation V3 n -> M44 n mkMatHomo t = mkTransformationMat (mkMat t) (transl t) -- | Make a 2D transformation from a 2x2 transform matrix and a -- translation vector. Does not check if the matrix is not invertible -- (in which case the 'T2' will be invalid). fromMat22 :: Floating n => M22 n -> V2 n -> T2 n fromMat22 m v = flip (fromMatWithInv m) v \$ inv22 m -- | Make a 3D transformation from a 3x3 transform matrix and a -- translation vector. Does not check if the matrix is not invertible -- (in which case the 'T3' will be invalid). fromMat33 :: Floating n => M33 n -> V3 n -> T3 n fromMat33 m v = flip (fromMatWithInv m) v \$ inv33 m -- | Build a transform with a maxtrix along with its inverse. fromMatWithInv :: (Additive v, Distributive v, F.Foldable v, Num n) => v (v n) -- ^ matrix -> v (v n) -- ^ inverse -> v n -- ^ translation -> Transformation v n fromMatWithInv m m_ v = Transformation ((*! m) <-> (*! m_)) ((*! distribute m) <-> (*! distribute m_)) v -- | Prism onto a 2D transformation from a 2x2 transform matrix and -- translation vector. Does not check if the matrix is invertible (in -- which case the 'T2' will be invalid). mat22 :: Floating n => Iso' (M22 n, V2 n) (T2 n) mat22 = iso (uncurry fromMat22) (mkMat &&& transl) -- | Prism onto a 2D transformation from a 2x2 transform matrix and -- translation vector (in which case the 'T3' will be invalid). mat33 :: Floating n => Iso' (M33 n, V3 n) (T3 n) mat33 = iso (uncurry fromMat33) (mkMat &&& transl)