implement uniform triangle sampling

hgeometry/src/Algorithms/Geometry/UniformPolygonSampling.hs

@@ -0,0 +1,29 @@
+module Algorithms.Geometry.UniformPolygonSampling where
+
+import Control.Monad.Random
+import Data.Geometry.Point
+import Data.Geometry.Polygon.Core
+import Data.Geometry.Triangle
+import Control.Lens
+import Data.Ext
+import Linear.Affine hiding (Point)
+import Linear.Vector
+
+-- | O(n log n)
+samplePolygon :: (RandomGen g, Random r, Fractional r) => Polygon t p r -> Rand g (Point 2 r)
+samplePolygon = error "not implemented yet"
+
+-- | O(1)
+sampleTriangle :: (RandomGen g, Random r, Fractional r, Ord r) => Triangle 2 p r -> Rand g (Point 2 r)
+sampleTriangle (Triangle v1 v2 v3) = do
+  a' <- getRandomR (0, 1)
+  b' <- getRandomR (0, 1)
+  let (a, b) = if a' + b' > 1 then (1 - a', 1 - b') else (a', b') in
+    return $ v1^.core .+^ a*^u .+^ b*^v
+  where
+    u = v2^.core .-. v1^.core
+    v = v3^.core .-. v1^.core
+
+-- | O(n log n)
+toTriangles :: (Fractional r, Ord r) => Polygon t p r -> [Triangle 2 p r]
+toTriangles = error "not implemented yet"