126 lines
4.8 KiB
Haskell
126 lines
4.8 KiB
Haskell
{-# LANGUAGE BangPatterns #-}
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module Geometry.Polygon where
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import Geometry.Data
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import Geometry.LHS
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import Geometry.Vector
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import ListHelp
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import Data.Maybe
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--import Data.List
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import qualified Control.Foldl as L
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-- | Draw an anticlockwise rectangle based on maximal N E S W values.
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rectNESW :: Float -> Float -> Float -> Float -> [Point2]
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rectNESW !a !b !c !d = [V2 b a,V2 b c,V2 d c,V2 d a]
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-- | Draw a clockwise rectangle based on maximal N S E W values.
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--rectNSEW :: Float -> Float -> Float -> Float -> [Point2]
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--rectNSEW !n !s !e !w = rectNESW n e s w
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-- | Draw an anticlockwise rectangle based on maximal N S W E values.
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rectNSWE :: Float -> Float -> Float -> Float -> [Point2]
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rectNSWE !n !s !w !e = [V2 w n, V2 w s, V2 e s, V2 e n]
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-- | Draw an anticlockwise rectangle around the origin with given height and width
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rectWH :: Float -> Float -> [Point2]
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rectWH w h = rectNSWE h (-h) (-w) w
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isotriBWH :: Point2 -> Float -> Float -> [Point2]
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isotriBWH (V2 x y) w h = [V2 (x-w) y, V2 (x+w) y, V2 x (y+h)]
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-- trapezion
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trapezionBWHW :: Point2 -> Float -> Float -> Float -> [Point2]
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trapezionBWHW (V2 x y) w1 h w2 =
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[ V2 (x-w1) y
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, V2 (x+w1) y
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, V2 (x+w2) (y+h)
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, V2 (x-w2) (y+h)]
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rectXH :: Float -> Float -> [Point2]
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rectXH x h = rectNSWE h (-h) 0 x
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rectXY :: Float -> Float -> [Point2]
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rectXY x y = rectNSWE y 0 0 x
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square :: Float -> [Point2]
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square n = rectWH n n
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mirrorXAxis :: [Point2] -> [Point2]
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mirrorXAxis ps = orderPolygon $ ps ++ mapMaybe f ps
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where
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f (V2 _ 0) = Nothing
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f (V2 x y) = Just $ V2 x (-y)
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-- | Test whether a point is in a polygon or on the polygon border.
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-- Supposes the points in the
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-- polygon are listed in anticlockwise order.
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pointInOrOnPolygon :: Point2 -> [Point2] -> Bool
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pointInOrOnPolygon !p (x:xs) = all (\l -> not (uncurry isRHS l p)) $ zip (x:xs) (xs ++ [x])
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pointInOrOnPolygon _ _ = undefined
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-- | Test whether a point is strictly inside a polygon.
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-- Supposes the points in the polygon are listed in anticlockwise order.
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pointInPolygon :: Point2 -> [Point2] -> Bool
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pointInPolygon !p (x:xs) = all (\l -> uncurry isLHS l p) $ zip (x:xs) (xs ++ [x])
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pointInPolygon _ [] = False
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orderPolygonAround
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:: Point2 -- ^ point to order around
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-> [Point2]
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-> [Point2]
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orderPolygonAround _ [] = []
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orderPolygonAround cen ps = sortOn (\p -> argV (p -.- cen)) ps
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orderAroundFirstReverse :: [Point2] -> [Point2]
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orderAroundFirstReverse [] = []
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orderAroundFirstReverse (a:as) = a : reverse (orderPolygonAround a as)
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orderAroundFirst :: [Point2] -> [Point2]
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orderAroundFirst [] = []
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orderAroundFirst (a:as) = a : orderPolygonAround a as
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-- | Reorder points to be anticlockwise around their center.
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orderPolygon :: [Point2] -> [Point2]
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orderPolygon [] = []
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--orderPolygon ps = orderPolygonAround (1/ fromIntegral (length ps) *.* foldr1 (+.+) ps) ps
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orderPolygon ps = orderPolygonAround (centroid ps) ps
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-- | Adds a point to a convex polygon.
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-- If the point is inside, returns the original.
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-- Points ordered anticlockwise, input not checked.
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addPointPolygon :: Point2 -> [Point2] -> [Point2]
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addPointPolygon p ps
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| pointInOrOnPolygon p ps = ps
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| otherwise = orderPolygon $ p : ps
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-- | Creates the convex hull of a set of points.
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-- Need to verify whether or not this is ordered
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convexHull :: [Point2] -> [Point2]
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convexHull (x:y:z:xs) = grahamScan $ orderAroundFirst $ sortOn (\(V2 a b) -> (b,a)) (x:y:z:xs)
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convexHull _ = error "Tried to create the convex hull of two or fewer points"
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-- | Creates the convex hull of a set of points.
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-- assumes no repetition of points: try nubbing!
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convexHullSafe :: [Point2] -> [Point2]
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--convexHullSafe (x:y:z:xs) = grahamScan $ orderAroundFirst $ sortOn (\(V2 a b) -> (b,a)) (x:y:z:xs)
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convexHullSafe (x:y:z:xs) = grahamScan $ orderAroundFirst $ sortOn (\(V2 a b) -> (b,a)) (x:y:z:xs)
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convexHullSafe _ = []
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grahamScan :: [Point2] -> [Point2]
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grahamScan = foldr push []
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where
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push point stack = grahamEliminate (point:stack)
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-- | Remove second element if top three elements are not counterclockwise.
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-- Repeat if necessary. See
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-- https://codereview.stackexchange.com/questions/206019/graham-scan-algorithm-in-haskell
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grahamEliminate :: [Point2] -> [Point2]
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grahamEliminate (x:y:z:xs)
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| not $ isLHS x y z = grahamEliminate (x:z:xs)
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grahamEliminate xs = xs
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centroid :: Foldable t => t Point2 -> Point2
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centroid = L.fold $ (/) <$> L.Fold (+.+) (V2 0 0) id <*> L.genericLength
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centroidNum :: (Fractional a ,Foldable t) => t a -> a
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centroidNum = L.fold $ (/) <$> L.Fold (+) 0 id <*> L.genericLength
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shrinkPolyOnEdges :: Float -> [Point2] -> [Point2]
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shrinkPolyOnEdges x (p:q:ps) = map (shrinkVert x) . slideWindow 3 $ (p:q:ps) ++ [p,q]
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shrinkPolyOnEdges _ _ = error "too few vertices in polygon"
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shrinkVert :: Float -> [Point2] -> Point2
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shrinkVert d [x,y,z] = x +.+ (d *.* normalizeV (x -.- y)) +.+ (d *.* normalizeV (z -.- y))
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shrinkVert _ _ = error "wrong number of vertices"
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