X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=1f7c22b355c0392f26988a1d9c315e63fee2d68e;hb=b2e1c440b9b1bb99ae564d6600230bbd1f7d204c;hp=bcf9a0b599b9fe36098663b71966445ac602bbb6;hpb=60ff027e52faf66c111b3dc2779c3bf5c7dfb6b9;p=spline3.git

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index bcf9a0b..1f7c22b 100644
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -3,8 +3,10 @@ where
 
 import Numeric.LinearAlgebra hiding (i, scale)
 import Prelude hiding (LT)
+import Test.QuickCheck (Arbitrary(..), Gen)
 
 import Cardinal
+import Comparisons (nearly_ge)
 import FunctionValues
 import Misc (factorial)
 import Point
@@ -15,9 +17,25 @@ data Tetrahedron = Tetrahedron { fv :: FunctionValues,
                                  v0 :: Point,
                                  v1 :: Point,
                                  v2 :: Point,
-                                 v3 :: Point }
+                                 v3 :: Point,
+                                 precomputed_volume :: Double }
                    deriving (Eq)
 
+
+instance Arbitrary Tetrahedron where
+    arbitrary = do
+      rnd_v0 <- arbitrary :: Gen Point
+      rnd_v1 <- arbitrary :: Gen Point
+      rnd_v2 <- arbitrary :: Gen Point
+      rnd_v3 <- arbitrary :: Gen Point
+      rnd_fv <- arbitrary :: Gen FunctionValues
+      -- We can't assign an incorrect precomputed volume,
+      -- so we have to calculate the correct one here.
+      let t' = Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 0
+      let vol = volume t'
+      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 vol)
+
+
 instance Show Tetrahedron where
     show t = "Tetrahedron:\n" ++
              "  fv: " ++ (show (fv t)) ++ "\n" ++
@@ -30,7 +48,28 @@ instance Show Tetrahedron where
 instance ThreeDimensional Tetrahedron where
     center t = ((v0 t) + (v1 t) + (v2 t) + (v3 t)) `scale` (1/4)
     contains_point t p =
-        (b0 t p) >= 0 && (b1 t p) >= 0 && (b2 t p) >= 0 && (b3 t p) >= 0
+      b0_unscaled `nearly_ge` 0 &&
+      b1_unscaled `nearly_ge` 0 &&
+      b2_unscaled `nearly_ge` 0 &&
+      b3_unscaled `nearly_ge` 0
+      where
+        -- Drop the useless division and volume calculation that we
+        -- would do if we used the regular b0,..b3 functions.
+        b0_unscaled :: Double
+        b0_unscaled = volume inner_tetrahedron
+          where inner_tetrahedron = t { v0 = p }
+
+        b1_unscaled :: Double
+        b1_unscaled = volume inner_tetrahedron
+          where inner_tetrahedron = t { v1 = p }
+
+        b2_unscaled :: Double
+        b2_unscaled = volume inner_tetrahedron
+          where inner_tetrahedron = t { v2 = p }
+
+        b3_unscaled :: Double
+        b3_unscaled = volume inner_tetrahedron
+          where inner_tetrahedron = t { v3 = p }
 
 
 polynomial :: Tetrahedron -> (RealFunction Point)
@@ -211,18 +250,10 @@ vol_matrix t = (4><4)
                 y1, y2, y3, y4,
                 z1, z2, z3, z4 ]
     where
-      x1 = x_coord (v0 t)
-      x2 = x_coord (v1 t)
-      x3 = x_coord (v2 t)
-      x4 = x_coord (v3 t)
-      y1 = y_coord (v0 t)
-      y2 = y_coord (v1 t)
-      y3 = y_coord (v2 t)
-      y4 = y_coord (v3 t)
-      z1 = z_coord (v0 t)
-      z2 = z_coord (v1 t)
-      z3 = z_coord (v2 t)
-      z4 = z_coord (v3 t)
+      (x1, y1, z1) = v0 t
+      (x2, y2, z2) = v1 t
+      (x3, y3, z3) = v2 t
+      (x4, y4, z4) = v3 t
 
 -- | Computed using the formula from Lai & Schumaker, Definition 15.4,
 --   page 436.
@@ -239,27 +270,27 @@ volume t
 
 -- | The barycentric coordinates of a point with respect to v0.
 b0 :: Tetrahedron -> (RealFunction Point)
-b0 t point = (volume inner_tetrahedron) / (volume t)
+b0 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v0 = point }
 
 
 -- | The barycentric coordinates of a point with respect to v1.
 b1 :: Tetrahedron -> (RealFunction Point)
-b1 t point = (volume inner_tetrahedron) / (volume t)
+b1 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v1 = point }
 
 
 -- | The barycentric coordinates of a point with respect to v2.
 b2 :: Tetrahedron -> (RealFunction Point)
-b2 t point = (volume inner_tetrahedron) / (volume t)
+b2 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v2 = point }
 
 
 -- | The barycentric coordinates of a point with respect to v3.
 b3 :: Tetrahedron -> (RealFunction Point)
-b3 t point = (volume inner_tetrahedron) / (volume t)
+b3 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v3 = point }