juicy-gcode-0.1.0.4: src/Transformation.hs

module Transformation ( TransformationMatrix
                      , identityMatrix
                      , transformPoint
                      , transformDrawOp
                      , applyTransformations
                      ) where

import qualified Graphics.Svg as SVG
import Data.Matrix as M
import Types                      
                      
type TransformationMatrix = Matrix Double
             
identityMatrix :: TransformationMatrix
identityMatrix = identity 3

fromElements :: [Double] -> TransformationMatrix
fromElements [a,b,c,d,e,f] = fromList 3 3 [a,c,e,b,d,f,0,0,1]
fromElements _ = error "Malformed transformation matrix"

transformPoint :: TransformationMatrix -> Point -> Point
transformPoint m (x,y) = (a * x + c * y + e, b * x + d * y + f)
   where
     (a:c:e:b:d:f:_) = M.toList m
     
transformDrawOp :: TransformationMatrix -> DrawOp -> DrawOp
transformDrawOp m (DMoveTo p) = DMoveTo (transformPoint m p)
transformDrawOp m (DLineTo p) = DLineTo (transformPoint m p)
transformDrawOp m (DBezierTo c1 c2 p2) = DBezierTo (transformPoint m c1) (transformPoint m c2) (transformPoint m p2)
     
applyTransformations :: TransformationMatrix -> Maybe [SVG.Transformation] -> TransformationMatrix
applyTransformations m Nothing = m
applyTransformations m (Just ts) = foldl applyTransformation m ts

radiansPerDegree :: Double
radiansPerDegree = pi / 180.0

-- https://developer.mozilla.org/en/docs/Web/SVG/Attribute/transform
applyTransformation :: Matrix Double -> SVG.Transformation -> Matrix Double
applyTransformation m (SVG.TransformMatrix a b c d e f) = multStd m (fromElements [a,b,c,d,e,f])
applyTransformation m (SVG.Translate x y) = multStd m (fromElements [1,0,0,1,x,y])
applyTransformation m (SVG.Scale sx mbSy) = multStd m (fromElements [sx,0,0,maybe sx id mbSy,0,0])
applyTransformation m (SVG.Rotate a Nothing) 
    = multStd m (fromElements [cos(r),sin(r),-sin(r),cos(r),0,0])
    where
        r = a * radiansPerDegree
applyTransformation m (SVG.Rotate a (Just (x, y))) = applyTransformations m (Just [SVG.Translate x y , SVG.Rotate a Nothing , SVG.Translate (-x) (-y)])
applyTransformation m (SVG.SkewX a) = multStd m (fromElements [1,0,tan(a*radiansPerDegree),1,0,0])
applyTransformation m (SVG.SkewY a) = multStd m (fromElements [1,tan(a*radiansPerDegree),0,1,0,0])
applyTransformation m (SVG.TransformUnknown) = m