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{-# LANGUAGE BangPatterns #-}
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{-|
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Module : Geometry
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Description : Geometry helpers
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This module provides geometry functions that manipulate pairs of floats.
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Conventions:
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Seg refers to a segment, typically defined by two points, and will typically not extend beyond either of these points.
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Line refers to a line defined by two points, and extends beyond the two points.
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-}
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module Geometry
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( module Geometry
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, module Geometry.Data
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@@ -17,46 +26,61 @@ import Data.List
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import Data.Maybe
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import Control.Applicative
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-- TODO add bang patterns
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alongLineBy :: Float -> Point2 -> Point2 -> Point2
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alongLineBy !x !a !b = a +.+ y *.* normalizeV (b -.- a)
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-- | Return a point a distance away from a first point towards a second point.
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-- Does not go past the second point.
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alongSegBy :: Float -> Point2 -> Point2 -> Point2
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alongSegBy !x !a !b = a +.+ y *.* normalizeV (b -.- a)
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where
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y = min x $ dist a b
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closestPointOnLine :: Point2 -> Point2 -> Point2 -> Point2
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-- | Given a line and a point return the point on the line closest to the
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-- point.
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closestPointOnLine
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:: Point2 -- ^ First line point.
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-> Point2 -- ^ Second line point.
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-> Point2 -- ^ Point not on line.
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-> Point2
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{-# INLINE closestPointOnLine #-}
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closestPointOnLine !a !b !p = a +.+ u *.* (b -.- a)
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closestPointOnLine !a !b !p = a +.+ u *.* (b -.- a)
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where u = closestPointOnLineParam a b p
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closestPointOnLineParam :: Point2 -> Point2 -> Point2 -> Float
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-- | Given a line and a point return a value corresponding to how far along the
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-- line the point is.
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closestPointOnLineParam
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:: Point2 -- ^ First line point.
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-> Point2 -- ^ Second line point.
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-> Point2 -- ^ Point not on line.
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-> Float
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{-# INLINE closestPointOnLineParam #-}
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closestPointOnLineParam !a !b !p
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= (p -.- a) `dotV` (b -.- a) / (b -.- a) `dotV` (b -.- a)
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-- the following helper draws a rectangle based on maximal N E S W values
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-- | Draw a 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 = [(b,a),(b,c),(d,c),(d,a) ]
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-- | Draw a 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 a 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 = [ (w,n), (w,s), (e,s), (e,n)]
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-- -- the following filters points in a polygon: supposes the points in the
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-- polygon are listed in anticlockwise order
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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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-- | 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 [] = False
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pointInPolygon !p (x:xs) = all (\l -> uncurry (errorIsLHS 1) l p) $ zip (x:xs) (xs ++ [x])
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-- | Debug version of 'pointInPolygon'.
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errorPointInPolygon :: Int -> Point2 -> [Point2] -> Bool
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errorPointInPolygon !i !p xs
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| length xs == 1 = error "one point polygon"
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@@ -64,43 +88,53 @@ errorPointInPolygon !i !p xs
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| nub xs == xs = pointInPolygon p xs
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| otherwise = error $ "errorPointInPolygon "++ show i
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-- | Debug version of 'normalizeV'.
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errorNormalizeV :: Int -> Point2 -> Point2
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errorNormalizeV !i !(0,0) = error $ "problem with function: errorNormalizeV "++show i
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errorNormalizeV !i !p = normalizeV p
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-- | Debug version of 'angleVV'.
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errorAngleVV :: Int -> Point2 -> Point2 -> Float
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errorAngleVV !i !(0,0) _ = error $ "problem with function: errorAngleVV "++show i
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errorAngleVV !i _ !(0,0) = error $ "problem with function: errorAngleVV "++show i
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errorAngleVV !i !p !p' = angleVV p p'
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-- | Debug version of 'isLHS'.
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errorIsLHS :: Int -> Point2 -> Point2 -> Point2 -> Bool
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errorIsLHS !i !x !y
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| x == y = error $ "problem with function: errorIsLHS " ++show i
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| otherwise = isLHS x y
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-- | Debug version of 'closestPointOnLine'
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errorClosestPointOnLine :: Int -> Point2 -> Point2 -> Point2 -> Point2
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errorClosestPointOnLine !i !x !y
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| x == y = error $ "problem with function: errorClosestPointOnLine " ++show i
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| otherwise = closestPointOnLine x y
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-- | Debug version of 'closestPointOnLineParam'
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errorClosestPointOnLineParam :: Int -> Point2 -> Point2 -> Point2 -> Float
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errorClosestPointOnLineParam !i !x! y! z
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| x == y = dist x z
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| otherwise = closestPointOnLineParam x y z
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-- | Normalize a vector to be unit length.
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-- For (0,0) return (0,0).
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safeNormalizeV :: Point2 -> Point2
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safeNormalizeV !(0,0) = (0,0)
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safeNormalizeV !p = normalizeV p
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-- tests whether a point is on the LHS of a line
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isLHS :: Point2 -> Point2 -> Point2 -> Bool
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-- | Test whether a point is on the LHS of a line.
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-- Returns False if the line is of zero length.
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isLHS
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:: Point2 -- ^ First line point.
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-> Point2 -- ^ Second line point.
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-> Point2 -- ^ Point not on line.
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-> Bool
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{-# INLINE isLHS #-}
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isLHS' :: (Float, Float) -> (Float, Float) -> Point2 -> Bool
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isLHS' !l1 !l2 !p
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| l1 == l2 = False
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| otherwise = closestPointOnLineParam l1 (l1 +.+ vNormal (l2 -.- l1)) p < 0
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isLHS !(x,y) !(x',y') !(x'',y'')
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isLHS
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!(x,y)
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!(x',y')
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!(x'',y'')
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| (x,y) == (x',y') = False
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| otherwise = a1 * b2 - a2 * b1 > 0
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where
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@@ -109,9 +143,18 @@ isLHS !(x,y) !(x',y') !(x'',y'')
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b1 = x'' - x
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b2 = y'' - y
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isRHS :: Point2 -> Point2 -> Point2 -> Bool
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-- | Test whether a point is on the LHS of a line.
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-- Returns False if the line is of zero length.
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isRHS
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:: Point2 -- ^ First line point.
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-> Point2 -- ^ Second line point.
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-> Point2 -- ^ Point not on line.
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-> Bool
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{-# INLINE isRHS #-}
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isRHS !(x,y) !(x',y') !(x'',y'')
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isRHS
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!(x,y)
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!(x',y')
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!(x'',y'')
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| (x,y) == (x',y') = False
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| otherwise = a1 * b2 - a2 * b1 < 0
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where
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@@ -120,54 +163,69 @@ isRHS !(x,y) !(x',y') !(x'',y'')
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b1 = x'' - x
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b2 = y'' - y
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-- reorders points to be anticlockwise around their center
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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 = sortBy (compare `on` \p -> argV (p -.- cen)) ps
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where
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cen = 1/ fromIntegral (length ps) *.* foldr1 (+.+) ps
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-- | Return distance between two points.
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dist :: Point2 -> Point2 -> Float
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{-# INLINE dist #-}
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dist !p1 !p2 = magV (p2 -.- p1)
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-- | Return midpoint between two points.
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pHalf :: Point2 -> Point2 -> Point2
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pHalf !a !b = 0.5 *.* (a +.+ b)
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circOnLine' :: Point2 -> Point2 -> Point2 -> Float -> Bool
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circOnLine' !p1 !p2 !c !rad = isJustTrue (fmap (\p -> magV (p -.- c) < rad) y)
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-- | Test whether a circle is on a segment by intersecting a new normal segment through the
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-- center of the circle with the segment itself.
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-- Returns False if the circle center is beyond the enpoints of the
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-- segment.
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circOnSegNoEndpoints :: Point2 -> Point2 -> Point2 -> Float -> Bool
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{-# INLINE circOnSegNoEndpoints #-}
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circOnSegNoEndpoints !p1 !p2 !c !rad = isJustTrue (fmap (\p -> magV (p -.- c) < rad) y)
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where
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y = intersectSegLine' p1 p2 c (c +.+ vNormal (p1 -.- p2))
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isJustTrue (Just True) = True
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isJustTrue _ = False
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-- this should probably be circOnSeg
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circOnLine :: Point2 -> Point2 -> Point2 -> Float -> Bool
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{-# INLINE circOnLine #-}
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circOnLine !p1 !p2 !c !rad = magV (p1 -.- c) <= rad || magV (p2 -.- c) <= rad
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-- | Test whether a circle is on a segment by intersecting a normal and testing
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-- the distance to the endpoints of the segment.
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circOnSeg :: Point2 -> Point2 -> Point2 -> Float -> Bool
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{-# INLINE circOnSeg #-}
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circOnSeg !p1 !p2 !c !rad = magV (p1 -.- c) <= rad || magV (p2 -.- c) <= rad
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|| isJustTrue (fmap (\p -> magV (p -.- c) < rad) y)
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where
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y = intersectSegLine' p1 p2 c (c +.+ vNormal (p1 -.- p2))
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isJustTrue (Just True) = True
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isJustTrue _ = False
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-- | Find the difference between two Nums.
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difference :: (Ord a, Num a) => a -> a -> a
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difference x y
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| x > y = x - y
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| otherwise = y - x
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-- | Given vector line direction and a vector movement,
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-- reflects the movement accoring to the line.
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reflectIn :: Point2 -> Point2 -> Point2
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reflectIn line vec =
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let angle = 2 * angleBetween line vec
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in rotateV angle vec
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-- | Find angle between two points.
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-- Not normalised, ranges from -2*pi to 2*pi.
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angleBetween :: Point2 -> Point2 -> Float
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angleBetween v1 v2 = argV v1 - argV v2
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-- | Return a list containing two copies of a pair.
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doublePair :: (a,a) -> [(a,a)]
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doublePair (x,y) = [(x,y),(y,x)]
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-- | Test whether two polygons intersect by testing the intersection of each
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-- consecutive pair of points.
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polysIntersect :: [Point2] -> [Point2] -> Bool
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polysIntersect (p:ps) (q:qs)
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= any isJust $ (\(a,b) (c,d) -> myIntersectSegSeg a b c d) <$> pairs1 <*> pairs2
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@@ -178,25 +236,33 @@ polysIntersect (p:ps) (q:qs)
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polysIntersect [] _ = False
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polysIntersect _ [] = False
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-- | Test whether any polygons from a first list intersect with any polygons from
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-- a second list.
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anyPolyssIntersect :: [[Point2]] -> [[Point2]] -> Bool
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anyPolyssIntersect x y = or $ polysIntersect <$> x <*> y
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-- | Return n equidistant points on a circle with a radius of 600.
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nRays :: Int -> [Point2]
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nRays n = take n $ iterate (rotateV (2*pi/fromIntegral n)) (600,0)
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-- | Return n equidistant points on a circle with a radius of x.
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nRaysRad :: Int -> Float -> [Point2]
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nRaysRad n x = take n $ iterate (rotateV (2*pi/fromIntegral n)) (x,0)
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-- angles go from 0 to 2pi, need to work out what is left of another
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-- | Test whether an angle is to the left of another angle, according to the
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-- smallest change in rotation between them.
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isLeftOfA :: Float -> Float -> Bool
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isLeftOfA angle1 angle2 =
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(angle1 - angle2 < pi && angle1 > angle2)
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|| (angle2 - angle1 > pi && angle2 > angle1)
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-- | Test whether a vector is to the left of another, according to the smallest
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-- change of rotation between them.
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isLeftOf :: Point2 -> Point2 -> Bool
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isLeftOf x y = isLeftOfA (argV x) (argV y)
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-- diffAngles has an issue...
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-- | Find the difference between two angles.
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-- Possibly not correct...
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diffAngles :: Float -> Float -> Float
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diffAngles x y
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| diff > pi = diffAngles (x - 2*pi) y
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@@ -209,10 +275,10 @@ diffAngles x y
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differenceAngles = diffAngles
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angleDifference = diffAngles
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-- given a triangle where we know the length of a first side,
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-- | Given a triangle where we know the length of a first side,
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-- the length of a second side, and the angle between the first side and the
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-- third side, finds the length of the third side
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-- not this doesn't necessarily find ALL solutions, asin is a map not a function
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-- third side, finds the length of the third side.
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-- Note this doesn't necessarily find ALL solutions, asin is a map not a function.
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ssaTri :: Float -> Float -> Float -> Float
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ssaTri ab bc a
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| sin a == 0 = 0
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@@ -222,12 +288,10 @@ ssaTri ab bc a
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b = pi - (a + c)
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in sin b * bc / sin a
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-- fix points: we now fix the triangle in the coordinate system, and return a
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-- third unknown point:
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-- the point which lies between pa and pc' on a line from b of length bc
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-- note that there are likely two such points, this seems to return the point
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-- closer to pc'
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-- | Given two points of a triangle and a third point, return
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-- the point which lies between pa and pc' on a line from pb of length bc.
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-- Note that there are likely two such points, this should return the point
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-- closer to pc'.
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ssaTriPoint :: Point2 -> Point2 -> Point2 -> Float -> Point2
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ssaTriPoint pa pb pc' bc
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= let ab = magV (pa -.- pb)
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@@ -235,13 +299,15 @@ ssaTriPoint pa pb pc' bc
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ac = ssaTri ab bc a
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in pa +.+ (ac *.* errorNormalizeV 47 (pc' -.- pa))
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-- the above SHOULD return a Maybe Point...
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-- | Safe version of 'ssaTriPoint'.
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ssaTriPoint' :: Point2 -> Point2 -> Point2 -> Float -> Maybe Point2
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ssaTriPoint' pa pb pc' bc
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| dist pb (closestPointOnSeg pa pc' pb) >= bc
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= Nothing
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| otherwise
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= Just $ ssaTriPoint pa pb pc' bc
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-- | A potential correction of 'ssaTriPoint'.
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-- This should be tested and benchmarked.
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ssaTriPointCorrect :: Point2 -> Point2 -> Point2 -> Float -> Maybe Point2
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ssaTriPointCorrect pa pb pc' bc
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| param <= 1 && param >= 0 = Just p
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@@ -250,42 +316,42 @@ ssaTriPointCorrect pa pb pc' bc
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p = ssaTriPoint pa pb pc' bc
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param = closestPointOnLineParam pa pc' p
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-- | Given a segment and external point, find the closest point on the segment.
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closestPointOnSeg :: Point2 -> Point2 -> Point2 -> Point2
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closestPointOnSeg segP1 segP2 p
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| errorClosestPointOnLineParam 3 segP1 segP2 p <= 0 = segP1
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| errorClosestPointOnLineParam 4 segP1 segP2 p >= 1 = segP2
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| otherwise = errorClosestPointOnLine 2 segP1 segP2 p
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-- | Return Just a point if it is inside a circle, Nothing otherwise.
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pointInCircle :: Point2 -> Float -> Point2 -> Maybe Point2
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pointInCircle p r c
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| p == c = Just p
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| magV (p -.- c) < r = Just p
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| otherwise = Nothing
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--determines if a moving point intersects with a circle,
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--if so, returns a point on circle that intersects with the line passing
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--throught the circle : HOPEFULLY THE CORRECT OF THE TWO!
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-- | Determines if a moving point intersects with a circle,
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-- if so, returns a point on circle that intersects with the line passing
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-- throught the circle : HOPEFULLY THE CORRECT OF THE TWO!
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collidePointCirc :: Point2 -> Point2 -> Float -> Point2 -> Maybe Point2
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collidePointCirc p1 p2 rad c = ssaTriPoint' p2 c p1 rad
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-- changes the point to a measure of the distance
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-- | As 'collidePointCirc', but changes the point to a measure of the distance.
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collidePointCirc' :: Point2 -> Point2 -> Float -> Point2 -> Maybe Float
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collidePointCirc' p1 p2 rad c = fmap (\x -> magV (x -.- p1))
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(collidePointCirc p1 p2 rad c)
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--returns both the point and the measure of the distance
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-- | As 'collidePointCirc', but returns both the point and the measure of the distance.
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collidePointCirc'' :: Point2 -> Point2 -> Float -> Point2 -> Maybe (Point2,Float)
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collidePointCirc'' p1 p2 rad c = (,) <$> collidePointCirc p1 p2 rad c
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<*> collidePointCirc' p1 p2 rad c
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-- | As 'collidePointCirc', but uses the supposedly correct version of ssaTriPoint.
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collidePointCircCorrect :: Point2 -> Point2 -> Float -> Point2 -> Maybe Point2
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collidePointCircCorrect p1 p2 rad c = ssaTriPointCorrect p2 c p1 rad
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-- finds the height of a triangle using herons formula
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-- the base is the line between the first two points
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-- | Finds the height of a triangle using herons formula.
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-- The base is the line between the first two points.
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heron :: Point2 -> Point2 -> Point2 -> Float
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heron x y z
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| x == y = 0
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@@ -296,7 +362,8 @@ heron x y z
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s = (a+b+c)/2
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area = sqrt(s*(s-a)*(s-b)*(s-c))
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in 2*area/a
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-- multiplies reflection in normal by factor
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-- | Multiplies reflection in normal by factor.
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reflectInParam :: Float -> Point2 -> Point2 -> Point2
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reflectInParam x line vec =
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let angle = 2 * angleBetween line vec
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|
@@ -304,16 +371,17 @@ reflectInParam x line vec =
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p = x *.* errorClosestPointOnLine 3 (0,0) (vNormal line) rAng
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in rAng -.- p
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--reflectIn' :: Point2 -> Point2 -> Point2 -> Point2 -> Point2
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--reflectIn' l1 l2 v1 v2 = v1 +.+ reflectIn (l1 -.- l2) (v2 -.- v1)
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reflectIn' :: Point2 -> Point2 -> Point2 -> Point2 -> Point2
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reflectIn' l1 l2 v1 v2 = v1 +.+ reflectIn (l1 -.- l2) (v2 -.- v1)
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isOnLine :: Point2 -> Point2 -> Point2 -> Bool
|
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|
|
isOnLine l1 l2 p =
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|
|
errorClosestPointOnLineParam 10 l1 (l1 +.+ vNormal (l2 -.- l1)) p == 0
|
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|
|
&& errorClosestPointOnLineParam 11 l1 l2 p <= 1
|
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|
|
&& errorClosestPointOnLineParam 12 l1 l2 p >= 0
|
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|
|
--isOnSeg :: Point2 -> Point2 -> Point2 -> Bool
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|
|
--isOnSeg l1 l2 p =
|
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|
|
-- errorClosestPointOnLineParam 10 l1 (l1 +.+ vNormal (l2 -.- l1)) p == 0
|
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|
|
-- && errorClosestPointOnLineParam 11 l1 l2 p <= 1
|
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|
|
-- && errorClosestPointOnLineParam 12 l1 l2 p >= 0
|
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|
|
-- | Divide a segment into a list of points with a maximal distance between
|
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|
|
-- them.
|
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|
|
|
-- the take 5000 here is a hack, otherwise divideLine seems to sometimes
|
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|
|
|
-- generate an infinite list, and I don't know why
|
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|
|
|
divideLine :: Float -> Point2 -> Point2 -> [Point2]
|
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|
|
@@ -327,6 +395,7 @@ divideLine x a b =
|
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|
|
numPoints = max 1 $ ceiling $ d / x
|
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|
|
ns = [0 .. numPoints]
|
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|
|
|
|
|
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|
|
-- | As 'divideLine', but must return an odd number of points.
|
|
|
|
|
divideLineOddNumPoints :: Float -> Point2 -> Point2 -> [Point2]
|
|
|
|
|
--divideLine x a b = map (\i -> a +.+ (i / (fromIntegral numPoints)) *.* (b -.- a))
|
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|
|
divideLineOddNumPoints x a b = take 5000
|
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|
|
@@ -339,29 +408,8 @@ divideLineOddNumPoints x a b = take 5000
|
|
|
|
|
| otherwise = numPoints' + 1
|
|
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|
|
ns = [0 .. numPoints]
|
|
|
|
|
|
|
|
|
|
-- pulled the following from the haskell wiki
|
|
|
|
|
-- it seems to produce an infinite loop sometimes
|
|
|
|
|
-- fuck that, don't trust random code on the internet
|
|
|
|
|
bresenham :: (Int,Int) -> (Int,Int) -> [(Int,Int)]
|
|
|
|
|
{-# INLINE bresenham #-}
|
|
|
|
|
bresenham pa@(xa,ya) pb@(xb,yb) = map maySwitch . unfoldr go $ (x1,y1,0)
|
|
|
|
|
where
|
|
|
|
|
steep = abs (yb - ya) > abs (xb - xa)
|
|
|
|
|
maySwitch = if steep then (\(x,y) -> (y,x)) else id
|
|
|
|
|
[(x1,y1),(x2,y2)] = sort [maySwitch pa, maySwitch pb]
|
|
|
|
|
deltax = x2 - x1
|
|
|
|
|
deltay = abs (y2 - y1)
|
|
|
|
|
ystep = if y1 < y2 then 1 else -1
|
|
|
|
|
go (xTemp, yTemp, error)
|
|
|
|
|
| xTemp > x2 = Nothing
|
|
|
|
|
| otherwise = Just ((xTemp, yTemp), (xTemp + 1, newY, newError))
|
|
|
|
|
where
|
|
|
|
|
tempError = error + deltay
|
|
|
|
|
(newY, newError) =
|
|
|
|
|
if (2*tempError) >= deltax
|
|
|
|
|
then (yTemp+ystep,tempError-deltax)
|
|
|
|
|
else (yTemp,tempError)
|
|
|
|
|
|
|
|
|
|
-- | Given two pairs of Ints, returns a list of pairs of Ints that form
|
|
|
|
|
-- a digital line between them.
|
|
|
|
|
digitalLine :: (Int,Int) -> (Int,Int) -> [(Int,Int)]
|
|
|
|
|
digitalLine (x1,y1) (x2,y2)
|
|
|
|
|
| abs (x1-x2) > abs (y1-y2) = [ (x,( (y1-y2) * x + x1*y2 - x2*y1) `rdiv` (x1-x2) )
|
|
|
|
@@ -371,34 +419,44 @@ digitalLine (x1,y1) (x2,y2)
|
|
|
|
|
where
|
|
|
|
|
rdiv a b = round $ fromIntegral a / fromIntegral b
|
|
|
|
|
|
|
|
|
|
-- | Given two Ints, creates the list of Ints between these.
|
|
|
|
|
intervalList :: Int -> Int -> [Int]
|
|
|
|
|
intervalList x y
|
|
|
|
|
| y >= x = [x .. y]
|
|
|
|
|
| otherwise = reverse [y..x]
|
|
|
|
|
|
|
|
|
|
-- | Create points on the circumference of a circle with maximal distance
|
|
|
|
|
-- between them.
|
|
|
|
|
divideCircle :: Float -> Point2 -> Float -> [Point2]
|
|
|
|
|
divideCircle x cen rad = map (cen +.+) $ nPointsOnCirc n rad
|
|
|
|
|
divideCircle x cen rad = map (cen +.+) $ nRaysRad n rad
|
|
|
|
|
where
|
|
|
|
|
n = ceiling $ rad * 2 * pi / x
|
|
|
|
|
|
|
|
|
|
nPointsOnCirc :: Int -> Float -> [Point2]
|
|
|
|
|
nPointsOnCirc n rad = take n $ iterate (rotateV (2*pi/fromIntegral n)) (rad,0)
|
|
|
|
|
--nPointsOnCirc :: Int -> Float -> [Point2]
|
|
|
|
|
--nPointsOnCirc n rad = take n $ iterate (rotateV (2*pi/fromIntegral n)) (rad,0)
|
|
|
|
|
|
|
|
|
|
lineInPolygon :: Point2 -> Point2 -> [Point2] -> Bool
|
|
|
|
|
lineInPolygon a b ps =
|
|
|
|
|
pointInPolygon a ps
|
|
|
|
|
|| pointInPolygon b ps
|
|
|
|
|
|| any (isJust . uncurry (intersectSegSeg' a b)) pss
|
|
|
|
|
where
|
|
|
|
|
pss = zip ps (tail ps ++ [head ps])
|
|
|
|
|
--lineInPolygon :: Point2 -> Point2 -> [Point2] -> Bool
|
|
|
|
|
--lineInPolygon a b ps =
|
|
|
|
|
-- pointInPolygon a ps
|
|
|
|
|
-- || pointInPolygon b ps
|
|
|
|
|
-- || any (isJust . uncurry (intersectSegSeg' a b)) pss
|
|
|
|
|
-- where
|
|
|
|
|
-- pss = zip ps (tail ps ++ [head ps])
|
|
|
|
|
|
|
|
|
|
-- | Given a list of points, returns pairs of points linking the points into a
|
|
|
|
|
-- loop.
|
|
|
|
|
makeLoopPairs :: [Point2] -> [(Point2,Point2)]
|
|
|
|
|
makeLoopPairs [] = error "tried to make loop with empty list of points"
|
|
|
|
|
makeLoopPairs [x] = error "tried to make loop with singleton list of points"
|
|
|
|
|
makeLoopPairs (x:xs) = zip (x:xs) (xs ++ [x])
|
|
|
|
|
|
|
|
|
|
-- note the pair is ordered
|
|
|
|
|
-- doesn't work for obtuse angles
|
|
|
|
|
pointIsInCone :: Point2 -> (Point2,Point2) -> Point2 -> Bool
|
|
|
|
|
-- | Test whether a point is in a cone.
|
|
|
|
|
-- Note the pair is ordered.
|
|
|
|
|
-- Doesn't work for obtuse angles.
|
|
|
|
|
pointIsInCone
|
|
|
|
|
:: Point2 -- ^ Cone point.
|
|
|
|
|
-> (Point2,Point2) -- ^ Points delimiting the left and right boundaries of the cone.
|
|
|
|
|
-> Point2 -- ^ Point to test.
|
|
|
|
|
-> Bool
|
|
|
|
|
pointIsInCone c (rightp,leftp) p = isLHS c rightp p && isLHS leftp c p
|
|
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|
|
|
|
|
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|
