40 lines
1.2 KiB
Haskell
40 lines
1.2 KiB
Haskell
module Geometry.Bezier
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where
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import Geometry.Data
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import Geometry.Vector
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{- | A synonym describing a quadratic Bezier curve as three 'Point2's: start,
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control and end.
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-}
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type BQuad = (Point2,Point2,Point2)
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{- | Split a quadratic Bezier curve into two at a fractional point along the
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curve.
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If the fraction is not between 0 and 1, this will create backwards curves.
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-}
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splitBezierquad :: BQuad -> Float -> (BQuad,BQuad)
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splitBezierquad (a,b,c) z
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= ( ( a
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, (z *.* b) -.- ((z-1) *.* a)
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, (z**2 *.* c) +.+ ((z-1)**2 *.* a) -.- (2*z*(z-1) *.* b)
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)
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, ( (z**2 *.* c) +.+ ((z-1)**2 *.* a) -.- (2*z*(z-1) *.* b)
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, (z *.* c) -.- ((z-1) *.* b)
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, c
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)
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)
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{- | Split a quadratic Bezier curve into a given number of straight lines, and
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return the list of points defining these lines.
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-}
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bQuadToLine :: BQuad -> Int -> [Point2]
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bQuadToLine (a,_,c) 0 = [a,c]
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bQuadToLine x i = let (l,r) = splitBezierquad x 0.5
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in bQuadToLine l (i-1) ++ bQuadToLine r (i-1)
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{- | Transform a quadratic Bezier curve into a function.
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-}
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bQuadToF :: (Point2,Point2,Point2) -> Float -> Point2
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bQuadToF (c,b,a) t = t *.* (t *.* a +.+ (1-t) *.* b) +.+
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(1-t) *.* (t *.* b +.+ (1-t) *.* c)
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