POLYINT: first try of polygon intersection algorithm in O(n)

Algebra/Vector.hs

@@ -3,7 +3,10 @@
 module Algebra.Vector where
 
 import Algebra.VectorTypes
+import Control.Applicative
 import Diagrams.TwoD.Types
+import Graphics.Gloss.Geometry.Line
+import GHC.Float
 import MyPrelude
 
 
@@ -72,6 +75,27 @@ det a b c =
     (cx, cy) = unp2 c
 
 
+-- |Computes the determinant of 2 points.
+det' :: PT -> PT -> Double
+det' a b =
+  ax * by - ay * bx
+  where
+    (ax, ay) = unp2 a
+    (bx, by) = unp2 b
+
+
+-- |Get the point where two lines intesect, if any.
+intersectSeg' :: Segment -> Segment -> Maybe PT
+intersectSeg' (a, b) (c, d) =
+  glossToPt <$> intersectSegSeg (ptToGloss a)
+                                (ptToGloss b)
+                                (ptToGloss c)
+                                (ptToGloss d)
+  where
+    ptToGloss = (\(x, y) -> (double2Float x, double2Float y)) <$> unp2
+    glossToPt = p2 . (\(x, y) -> (float2Double x, float2Double y))
+
+
 -- |Get the orientation of 3 points which can either be
 -- * clock-wise
 -- * counter-clock-wise
@@ -95,3 +119,26 @@ notcw a b c = case getOrient a b c of
 -- |Sort X and Y coordinates lexicographically.
 sortedXY :: [PT] -> [PT]
 sortedXY = fmap p2 . sortLex . fmap unp2
+
+
+-- |Apply a function on the coordinates of a point.
+onPT :: ((Double, Double) -> (Double, Double)) -> PT -> PT
+onPT f = p2 . f . unp2
+
+
+-- |Compare the y-coordinate of two points.
+ptCmpY :: PT -> PT -> Ordering
+ptCmpY p1' p2' = compare ((snd . unp2) p1') ((snd . unp2) p2')
+
+
+-- |Compare the y-coordinate of two points.
+ptCmpX :: PT -> PT -> Ordering
+ptCmpX p1' p2' = compare ((fst . unp2) p1') ((fst . unp2) p2')
+
+
+posInfPT :: PT
+posInfPT = p2 (read "Infinity", read "Infinity")
+
+
+negInfPT :: PT
+negInfPT = p2 (negate . read $ "Infinity", negate . read $ "Infinity")