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Lemmih 2020-08-27 15:32:19 +00:00
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<pre>
<span class="decl"><span class="nottickedoff">never executed</span> <span class="tickonlytrue">always true</span> <span class="tickonlyfalse">always false</span></span>
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<pre>
<span class="lineno"> 1 </span>{-# LANGUAGE BangPatterns #-}
<span class="lineno"> 2 </span>{-|
<span class="lineno"> 3 </span> 2D transformation matrices capable of translating, scaling,
<span class="lineno"> 4 </span> rotating, and skewing.
<span class="lineno"> 5 </span>-}
<span class="lineno"> 6 </span>module Reanimate.Transform
<span class="lineno"> 7 </span> ( identity
<span class="lineno"> 8 </span> , transformPoint
<span class="lineno"> 9 </span> , mkMatrix
<span class="lineno"> 10 </span> , toTransformation
<span class="lineno"> 11 </span> ) where
<span class="lineno"> 12 </span>
<span class="lineno"> 13 </span>-- XXX: Use Linear.Matrix instead of Data.Matrix to drop the 'matrix' dependency.
<span class="lineno"> 14 </span>import Data.List
<span class="lineno"> 15 </span>import Data.Matrix (Matrix)
<span class="lineno"> 16 </span>import qualified Data.Matrix as M
<span class="lineno"> 17 </span>import Data.Maybe
<span class="lineno"> 18 </span>import Graphics.SvgTree
<span class="lineno"> 19 </span>import Linear.V2
<span class="lineno"> 20 </span>
<span class="lineno"> 21 </span>-- | Identity matrix.
<span class="lineno"> 22 </span>--
<span class="lineno"> 23 </span>-- @transformPoints identity x = x@
<span class="lineno"> 24 </span>identity :: Matrix Coord
<span class="lineno"> 25 </span><span class="decl"><span class="istickedoff">identity = M.identity 3</span></span>
<span class="lineno"> 26 </span>
<span class="lineno"> 27 </span>fromList :: [Coord] -&gt; Matrix Coord
<span class="lineno"> 28 </span><span class="decl"><span class="istickedoff">fromList [a,b,c,d,e,f] = M.fromList 3 3 [a,c,e,b,d,f,0,0,1]</span>
<span class="lineno"> 29 </span><span class="spaces"></span><span class="istickedoff">fromList _ = <span class="nottickedoff">error &quot;Reanimate.Transform.fromList: bad input&quot;</span></span></span>
<span class="lineno"> 30 </span>
<span class="lineno"> 31 </span>-- | Apply a transformation matrix to a 2D point.
<span class="lineno"> 32 </span>transformPoint :: Matrix Coord -&gt; RPoint -&gt; RPoint
<span class="lineno"> 33 </span><span class="decl"><span class="istickedoff">transformPoint m (V2 x y) = V2 (a*x +c*y + e) (b*x + d*y +f)</span>
<span class="lineno"> 34 </span><span class="spaces"> </span><span class="istickedoff">where</span>
<span class="lineno"> 35 </span><span class="spaces"> </span><span class="istickedoff">!a = M.unsafeGet 1 1 m</span>
<span class="lineno"> 36 </span><span class="spaces"> </span><span class="istickedoff">!c = M.unsafeGet 1 2 m</span>
<span class="lineno"> 37 </span><span class="spaces"> </span><span class="istickedoff">!e = M.unsafeGet 1 3 m</span>
<span class="lineno"> 38 </span><span class="spaces"> </span><span class="istickedoff">!b = M.unsafeGet 2 1 m</span>
<span class="lineno"> 39 </span><span class="spaces"> </span><span class="istickedoff">!d = M.unsafeGet 2 2 m</span>
<span class="lineno"> 40 </span><span class="spaces"> </span><span class="istickedoff">!f = M.unsafeGet 2 3 m</span></span>
<span class="lineno"> 41 </span> -- (a:c:e:b:d:f:_) = M.toList m
<span class="lineno"> 42 </span>
<span class="lineno"> 43 </span>-- | Convert multiple SVG transformations into a single transformation matrix.
<span class="lineno"> 44 </span>mkMatrix :: Maybe [Transformation] -&gt; Matrix Coord
<span class="lineno"> 45 </span><span class="decl"><span class="istickedoff">mkMatrix Nothing = identity</span>
<span class="lineno"> 46 </span><span class="spaces"></span><span class="istickedoff">mkMatrix (Just ts) = foldl' (*) identity (map transformationMatrix ts)</span></span>
<span class="lineno"> 47 </span>
<span class="lineno"> 48 </span>-- | Convert an SVG transformation into a transformation matrix.
<span class="lineno"> 49 </span>transformationMatrix :: Transformation -&gt; Matrix Coord
<span class="lineno"> 50 </span><span class="decl"><span class="istickedoff">transformationMatrix transformation =</span>
<span class="lineno"> 51 </span><span class="spaces"> </span><span class="istickedoff">case transformation of</span>
<span class="lineno"> 52 </span><span class="spaces"> </span><span class="istickedoff">TransformMatrix a b c d e f -&gt; <span class="nottickedoff">fromList [a,b,c,d,e,f]</span></span>
<span class="lineno"> 53 </span><span class="spaces"> </span><span class="istickedoff">Translate x y -&gt; <span class="nottickedoff">translate x y</span></span>
<span class="lineno"> 54 </span><span class="spaces"> </span><span class="istickedoff">Scale sx mbSy -&gt; fromList [sx,0,0,fromMaybe <span class="nottickedoff">sx</span> mbSy,0,0]</span>
<span class="lineno"> 55 </span><span class="spaces"> </span><span class="istickedoff">Rotate a Nothing -&gt; <span class="nottickedoff">rotate a</span></span>
<span class="lineno"> 56 </span><span class="spaces"> </span><span class="istickedoff">Rotate a (Just (x,y)) -&gt; <span class="nottickedoff">translate x y * rotate a * translate (-x) (-y)</span></span>
<span class="lineno"> 57 </span><span class="spaces"> </span><span class="istickedoff">SkewX a -&gt; <span class="nottickedoff">fromList [1,0,tan (a*pi/180),1,0,0]</span></span>
<span class="lineno"> 58 </span><span class="spaces"> </span><span class="istickedoff">SkewY a -&gt; <span class="nottickedoff">fromList [1,tan (a*pi/180),0,1,0,0]</span></span>
<span class="lineno"> 59 </span><span class="spaces"> </span><span class="istickedoff">TransformUnknown -&gt; <span class="nottickedoff">identity</span></span>
<span class="lineno"> 60 </span><span class="spaces"> </span><span class="istickedoff">where</span>
<span class="lineno"> 61 </span><span class="spaces"> </span><span class="istickedoff"><span class="nottickedoff">translate x y = fromList [1,0,0,1,x,y]</span></span>
<span class="lineno"> 62 </span><span class="spaces"> </span><span class="istickedoff"><span class="nottickedoff">rotate a = fromList [cos r,sin r,-sin r,cos r,0,0]</span></span>
<span class="lineno"> 63 </span><span class="spaces"> </span><span class="istickedoff"><span class="nottickedoff">where r = a * pi / 180</span></span></span>
<span class="lineno"> 64 </span>
<span class="lineno"> 65 </span>-- | Convert a transformation matrix back into an SVG transformation.
<span class="lineno"> 66 </span>toTransformation :: Matrix Coord -&gt; Transformation
<span class="lineno"> 67 </span><span class="decl"><span class="nottickedoff">toTransformation m = TransformMatrix a b c d e f</span>
<span class="lineno"> 68 </span><span class="spaces"> </span><span class="nottickedoff">where</span>
<span class="lineno"> 69 </span><span class="spaces"> </span><span class="nottickedoff">[a,c,e,b,d,f,_,_,_] = M.toList m</span></span>
</pre>
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