Add haddocks
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-1
@@ -761,7 +761,7 @@ logistic x0 l k x = l / (1 + exp (k*(x0 - x)))
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wallLOS :: [Point2] -> Point2 -> Point2 -> Bool
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{-# INLINE wallLOS #-}
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wallLOS !(x:y:_) !c !p = isRHS c x y || isLHS p x' y' || isLHS c p x || isRHS c p y
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where n = 10 *.* (normV . vNormal $ y -.- x)
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where n = 10 *.* (safeNormalizeV . vNormal $ y -.- x)
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x' = x +.+ n
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y' = y +.+ n
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@@ -117,12 +117,6 @@ 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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-- | 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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@@ -3,8 +3,15 @@ module Geometry.Bezier
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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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@@ -17,11 +24,16 @@ splitBezierquad (a,b,c) z
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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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@@ -4,7 +4,6 @@ module Geometry.Data
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, Point4 (..)
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)
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where
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type Point2 = (Float,Float)
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type Point3 = (Float,Float,Float)
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type Point4 = (Float,Float,Float,Float)
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+48
-13
@@ -2,7 +2,8 @@
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module Geometry.Vector
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where
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import Geometry.Data
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{- | Moves from to three dimensions, adding zero in z direction.
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-}
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zeroZ :: Point2 -> Point3
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{-# INLINE zeroZ #-}
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zeroZ (x,y) = (x,y,0)
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@@ -10,6 +11,8 @@ zeroZ (x,y) = (x,y,0)
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infixl 6 +.+, -.-
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infixl 7 *.*
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{- | 2D coordinate-wise addition.
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-}
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(+.+) :: Point2 -> Point2 -> Point2
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{-# INLINE (+.+) #-}
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(x1, y1) +.+ (x2, y2) =
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@@ -17,7 +20,8 @@ infixl 7 *.*
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!x = x1 + x2
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!y = y1 + y2
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in (x, y)
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{- | 2D coordinate-wise subtraction.
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-}
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(-.-) :: Point2 -> Point2 -> Point2
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{-# INLINE (-.-) #-}
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(x1, y1) -.- (x2, y2) =
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@@ -25,7 +29,8 @@ infixl 7 *.*
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!x = x1 - x2
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!y = y1 - y2
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in (x, y)
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{- | 2D scalar multiplication.
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-}
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(*.*) :: Float -> Point2 -> Point2
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{-# INLINE (*.*) #-}
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a *.* (x2, y2) =
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@@ -37,6 +42,9 @@ a *.* (x2, y2) =
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infixl 6 +.+.+, -.-.-
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infixl 7 *.*.*
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{- | 3D coordinate-wise addition.
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-}
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(+.+.+) :: Point3 -> Point3 -> Point3
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{-# INLINE (+.+.+) #-}
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(x1, y1, z1) +.+.+ (x2, y2, z2) =
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@@ -46,6 +54,8 @@ infixl 7 *.*.*
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!z = z1 + z2
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in (x, y, z)
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{- | 3D coordinate-wise subtraction.
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-}
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(-.-.-) :: Point3 -> Point3 -> Point3
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{-# INLINE (-.-.-) #-}
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(x1, y1, z1) -.-.- (x2, y2, z2) =
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@@ -55,6 +65,8 @@ infixl 7 *.*.*
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!z = z1 - z2
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in (x, y, z)
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{- | 3D scalar multiplication.
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-}
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(*.*.*) :: Point3 -> Point3 -> Point3
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{-# INLINE (*.*.*) #-}
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(x1, y1, z1) *.*.* (x2, y2, z2) =
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@@ -64,10 +76,15 @@ infixl 7 *.*.*
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!z = z1 * z2
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in (x, y, z)
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{- | Normalize a vector to length 1.
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-}
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normalizeV :: Point2 -> Point2
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{-# INLINE normalizeV #-}
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normalizeV p = (1 / magV p) *.* p
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{- | Angle between two vectors.
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Always positive.
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-}
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angleVV :: Point2 -> Point2 -> Float
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{-# INLINE angleVV #-}
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angleVV a b = let ma = magV a
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@@ -75,20 +92,28 @@ angleVV a b = let ma = magV a
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d = a `dotV` b
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in acos $ d / (ma * mb)
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{- | Dot product.
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-}
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dotV :: Point2 -> Point2 -> Float
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{-# INLINE dotV #-}
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dotV (x,y) (z,w) = x*z + y*w
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{- | Given vector, returns the angle, anticlockwise from +ve x-axis, in radians.
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-}
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argV :: Point2 -> Float
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{-# INLINE argV #-}
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argV (x,y) = normalizeAngle $ atan2 y x
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{- | Determinant of the matrix formed by two vectors.
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-}
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detV :: Point2 -> Point2 -> Float
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{-# INLINE detV #-}
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detV (x1, y1) (x2, y2)
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= x1 * y2 - y1 * x2
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-- | Angle in radians, anticlockwise from +ve x-axis.
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{- | Given an angle in radians, anticlockwise from +ve x-axis, returns the
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corresponding unit vector.
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-}
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unitVectorAtAngle :: Float -> Point2
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{-# INLINE unitVectorAtAngle #-}
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unitVectorAtAngle r
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@@ -106,36 +131,46 @@ degToRad :: Float -> Float
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degToRad d = d * pi / 180
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{-# INLINE degToRad #-}
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-- | Convert radians to degrees
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radToDeg :: Float -> Float
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radToDeg r = r * 180 / pi
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{-# INLINE radToDeg #-}
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-- | Normalize an angle to be between 0 and 2*pi radians
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normalizeAngle :: Float -> Float
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normalizeAngle f = f - 2 * pi * floor' (f / (2 * pi))
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where floor' :: Float -> Float
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floor' x = fromIntegral (floor x :: Int)
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{-# INLINE normalizeAngle #-}
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normalizeAngle f = f - 2 * pi * floor' (f / (2 * pi))
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where
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floor' :: Float -> Float
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floor' x = fromIntegral (floor x :: Int)
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{- | Rotate vector by pi/2 clockwise.
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-}
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vNormal :: Point2 -> Point2
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{-# INLINE vNormal #-}
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vNormal (x,y) = (y,-x)
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{- | Negate a vector.
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-}
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vInverse :: Point2 -> Point2
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vInverse (x,y) = (-x,-y)
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normV :: Point2 -> Point2
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{-# INLINE normV #-}
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normV (0,0) = (0,0)
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normV p = (1/magV p ) *.* p
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{- | Normalize a vector safely: on (0,0) return (0,0).
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-}
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safeNormalizeV :: Point2 -> Point2
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{-# INLINE safeNormalizeV #-}
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safeNormalizeV (0,0) = (0,0)
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safeNormalizeV p = (1/magV p ) *.* p
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{- | Magnitude of a vector.
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-}
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magV :: Point2 -> Float
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{-# INLINE magV #-}
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magV (x,y) = sqrt $ x^2 + y^2
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{- | Magnitude of the cross product of two vectors.
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Identical to detV.
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-}
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crossV :: Point2 -> Point2 -> Float
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crossV (ax,ay) (bx,by) = ax*by - ay*bx
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