151 lines
6.1 KiB
Haskell
151 lines
6.1 KiB
Haskell
module Geometry.Intersect
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where
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import Geometry.Data
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import Control.Applicative
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-- | If two lines intersect, return 'Just' that point.
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intersectLineLine' :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
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{-# INLINE intersectLineLine' #-}
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intersectLineLine' (x1,y1) (x2,y2) (x3,y3) (x4,y4)
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| den == 0 = Nothing
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| otherwise = Just (x1 + (x2-x1)*t'/den, y1 + (y2-y1)*t'/den)
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where
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den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
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t' = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
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-- | If two segments intersect, return 'Just' that point.
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intersectSegSeg' :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
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{-# INLINE intersectSegSeg' #-}
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intersectSegSeg' (x1,y1) (x2,y2) (x3,y3) (x4,y4)
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| den == 0 = Nothing
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| den > 0 && (t' < 0 || u' < 0 || t' > den || u' > den)
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= Nothing
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| den < 0 && (t' > 0 || u' > 0 || t' < den || u' < den)
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= Nothing
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| otherwise = Just (x1 + (x2-x1)*t'/den, y1 + (y2-y1)*t'/den)
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where
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den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
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t' = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
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u' = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
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-- | Intended to intersect a segment with a half-line-segment, ie a segment
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-- extending infinitely in one direction.
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intersectSegLineFrom' :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
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{-# INLINE intersectSegLineFrom' #-}
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intersectSegLineFrom' (x1,y1) (x2,y2) (x3,y3) (x4,y4)
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| den == 0 = Nothing
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| den > 0 && ( t' < 0 || u' < 0 || t' > den )
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= Nothing
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| den < 0 && ( t' > 0 || u' > 0 || t' < den )
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= Nothing
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| otherwise = Just (x1 + (x2-x1)*t'/den, y1 + (y2-y1)*t'/den)
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where
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den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
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t' = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
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u' = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
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-- | Similar to 'intersectSegLineFrom'', but this version is probably not correct...
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intersectSegLineext :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
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{-# INLINE intersectSegLineext #-}
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intersectSegLineext (x1,y1) (x2,y2) (x3,y3) (x4,y4)
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| den == 0 = Nothing
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| den > 0 && ( t' < 0 || u' < den || t' > den )
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= Nothing
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| den < 0 && ( t' > 0 || u' > - den || t' < den )
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= Nothing
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| otherwise = Just (x1 + (x2-x1)*t'/den, y1 + (y2-y1)*t'/den)
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where
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den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
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t' = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
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u' = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
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-- | Intersect a segment with a line.
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intersectSegLine' :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
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{-# INLINE intersectSegLine' #-}
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intersectSegLine' (x1,y1) (x2,y2) (x3,y3) (x4,y4)
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| den == 0 = Nothing
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| den > 0 && (t' < 0 || t' > den)
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= Nothing
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| den < 0 && (t' > 0 || t' < den)
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= Nothing
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| otherwise = Just (x1 + (x2-x1)*t'/den, y1 + (y2-y1)*t'/den)
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where
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den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
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t' = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
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u' = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
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-- | Due to floating point issues, 'intersectSegSeg'' is not always
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-- accurate---'myIntersectSegSeg'
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-- fixes at least some of
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-- the problem cases by transforming the points into rationals and then doing the
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-- intersection.
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-- This version is, probably, slower---both testing and benchmarking should be
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-- done.
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myIntersectSegSeg a@(ax,ay) b@(bx,by) c@(cx,cy) d@(dx,dy) = case ratIntersectLineLine a b c d of
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Nothing -> Nothing
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Just (x,y) -> if inbetween x && inbetween' y
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then Just (x,y)
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else Nothing
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where inbetween x = ((ax <= x && x <= bx) || (bx <= x && x <= ax)) &&
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((cx <= x && x <= dx) || (dx <= x && x <= cx))
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inbetween' y = ((ay <= y && y <= by) || (by <= y && y <= ay)) &&
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((cy <= y && y <= dy) || (dy <= y && y <= cy))
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-- | Polymorphic intersection of fractional line points.
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myIntersectLineLine :: (Eq a,Fractional a) => (a,a) -> (a,a) -> (a,a) -> (a,a) -> Maybe (a,a)
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myIntersectLineLine a@(ax,ay) b c@(cx,cy) d
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| linGrad a b == Nothing = fmap ((,) ax) $ axisInt (c *-* (ax,0)) (d *-* (ax,0))
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| linGrad c d == Nothing = fmap ((,) cx) $ axisInt (a *-* (cx,0)) (b *-* (cx,0))
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| otherwise
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= case linGrad a b ^-^ linGrad c d of
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Just 0 -> Nothing
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_ -> liftA2 (,) newx
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((linGrad a b ^*^ newx) ^+^ axisInt a b)
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where (^-^) = liftA2 (-)
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(^+^) = liftA2 (+)
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(^/^) = liftA2 (/)
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(^*^) = liftA2 (*)
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newx = (axisInt c d ^-^ axisInt a b) ^/^ (linGrad a b ^-^ linGrad c d)
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(*-*) (ax,ay) (bx,by) = (ax-bx,ay-by)
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-- | Transforms floating points to rationals then performs line intersection.
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ratIntersectLineLine :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
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ratIntersectLineLine a b c d = fmap toNumPoint2 $ myIntersectLineLine (toRatPoint2 a) (toRatPoint2 b) (toRatPoint2 c) (toRatPoint2 d)
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where toRatPoint2 (x,y) = (toRational x, toRational y)
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toNumPoint2 (x,y) = (fromRational x, fromRational y)
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f = toRatPoint2 . roundPoint2
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-- | Round the floats within a 'Point2' to the nearest integer.
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-- Rounding jumps after intervals of .5:
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--
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-- >>> roundPoint (0.5,0.5001)
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-- (0.0,1.0)
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--
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-- but is symmetric around 0:
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--
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-- >>> roundPoint2 (0.5,-0.5)
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-- (0.0,0.0)
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--
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roundPoint2 :: Point2 -> Point2
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roundPoint2 (x,y) = (fromIntegral $ round x,fromIntegral $ round y)
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-- | Given two points, finds the linear gradient if it is non-infinite.
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linGrad :: (Eq a,Fractional a) => (a,a) -> (a,a) -> Maybe a
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linGrad (x,y) (a,b) | x-a == 0 = Nothing
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| otherwise = Just $ (y-b)/(x-a)
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-- | Given two points, finds the intersection with the y axis if it exists.
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axisInt :: (Eq a,Fractional a) => (a,a) -> (a,a) -> Maybe a
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axisInt p (a,b) = pure b ^-^ (pure a ^*^ linGrad p (a,b))
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where (^-^) = liftA2 (-)
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(^*^) = liftA2 (*)
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-- | Placeholder, undefined.
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intersectSegsSeg :: [Point2] -> Point2 -> Point2 -> Maybe Point2
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intersectSegsSeg = undefined
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-- | Placeholder: should intersect a segment with a bezier curve.
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intersectSegBezquad :: Point2 -> Point2 -> Point2 -> Point2 -> Point2 -> [Point2]
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intersectSegBezquad = undefined
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