hasufell
8300929fd7
Move sortedXY to Vector.hs, fix shadowing of scanH. Simplified grahamCHSteps by making use of a more generalized scanH function.
98 lines
2.1 KiB
Haskell
98 lines
2.1 KiB
Haskell
{-# OPTIONS_HADDOCK ignore-exports #-}
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module Algebra.Vector where
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import Algebra.VectorTypes
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import Diagrams.TwoD.Types
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import MyPrelude
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-- |Checks whether the Point is in a given dimension.
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inRange :: Coord -- ^ X dimension
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-> Coord -- ^ Y dimension
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-> PT -- ^ Coordinates
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-> Bool -- ^ result
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inRange (xlD, xuD) (ylD, yuD) p = x <= xuD && x >= xlD && y <= yuD && y >= ylD
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where
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(x, y) = unp2 p
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-- |Get the angle between two vectors.
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getAngle :: Vec -> Vec -> Double
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getAngle a b =
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acos .
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flip (/) (vecLength a * vecLength b) .
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scalarProd a $
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b
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-- |Get the length of a vector.
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vecLength :: Vec -> Double
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vecLength v = sqrt (x^(2 :: Int) + y^(2 :: Int))
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where
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(x, y) = unr2 v
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-- |Compute the scalar product of two vectors.
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scalarProd :: Vec -> Vec -> Double
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scalarProd v1 v2 = a1 * b1 + a2 * b2
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where
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(a1, a2) = unr2 v1
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(b1, b2) = unr2 v2
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-- |Construct a vector that points to a point from the origin.
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pt2Vec :: PT -> Vec
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pt2Vec = r2 . unp2
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-- |Give the point which is at the coordinates the vector
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-- points to from the origin.
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vec2Pt :: Vec -> PT
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vec2Pt = p2 . unr2
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-- |Construct a vector between two points.
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vp2 :: PT -- ^ vector origin
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-> PT -- ^ vector points here
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-> Vec
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vp2 a b = pt2Vec b - pt2Vec a
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-- |Computes the determinant of 3 points.
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det :: PT -> PT -> PT -> Double
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det a b c =
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(bx - ax) *
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(cy - ay) -
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(by - ay) *
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(cx - ax)
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where
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(ax, ay) = unp2 a
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(bx, by) = unp2 b
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(cx, cy) = unp2 c
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-- |Get the orientation of 3 points which can either be
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-- * clock-wise
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-- * counter-clock-wise
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-- * collinear
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getOrient :: PT -> PT -> PT -> Alignment
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getOrient a b c = case compare (det a b c) 0 of
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LT -> CW
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GT -> CCW
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EQ -> CL
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--- |Checks if 3 points a,b,c do not build a clockwise triangle by
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--- connecting a-b-c. This is done by computing the determinant and
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--- checking the algebraic sign.
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notcw :: PT -> PT -> PT -> Bool
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notcw a b c = case getOrient a b c of
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CW -> False
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_ -> True
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-- |Sort X and Y coordinates lexicographically.
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sortedXY :: [PT] -> [PT]
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sortedXY = fmap p2 . sortLex . fmap unp2
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