X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=5b459fea2870de5c2fed88ee9f9e5b57c7e5cfc9;hb=8c9954ffb0d636ee383e00242a1c8214d28f8461;hp=73ed58863595cab2da3bd8a4a0e98cd2f5f69ad4;hpb=603d9155a29bfbc353b42a6c880edce224626a16;p=spline3.git

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index 73ed588..5b459fe 100644
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -3,21 +3,30 @@ where
 
 import Numeric.LinearAlgebra hiding (i, scale)
 import Prelude hiding (LT)
-import Test.QuickCheck (Arbitrary(..), Gen)
+import Test.QuickCheck (Arbitrary(..), Gen, choose)
 
 import Cardinal
+import Comparisons (nearly_ge)
 import FunctionValues
 import Misc (factorial)
 import Point
 import RealFunction
 import ThreeDimensional
 
-data Tetrahedron = Tetrahedron { fv :: FunctionValues,
-                                 v0 :: Point,
-                                 v1 :: Point,
-                                 v2 :: Point,
-                                 v3 :: Point }
-                   deriving (Eq)
+data Tetrahedron =
+  Tetrahedron { fv :: FunctionValues,
+                v0 :: Point,
+                v1 :: Point,
+                v2 :: Point,
+                v3 :: Point,
+                precomputed_volume :: Double,
+
+                -- | Between 0 and 23; used to quickly determine which
+                --   tetrahedron I am in the parent 'Cube' without
+                --   having to compare them all.
+                number :: Int
+              }
+    deriving (Eq)
 
 
 instance Arbitrary Tetrahedron where
@@ -27,11 +36,18 @@ instance Arbitrary Tetrahedron where
       rnd_v2 <- arbitrary :: Gen Point
       rnd_v3 <- arbitrary :: Gen Point
       rnd_fv <- arbitrary :: Gen FunctionValues
-      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
+      rnd_no <- choose (0,23)
+
+      -- 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 rnd_no
+      let vol = volume t'
+      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 vol rnd_no)
 
 
 instance Show Tetrahedron where
     show t = "Tetrahedron:\n" ++
+             "  no: " ++ (show (number t)) ++ "\n" ++
              "  fv: " ++ (show (fv t)) ++ "\n" ++
              "  v0: " ++ (show (v0 t)) ++ "\n" ++
              "  v1: " ++ (show (v1 t)) ++ "\n" ++
@@ -40,9 +56,32 @@ instance Show Tetrahedron where
 
 
 instance ThreeDimensional Tetrahedron where
-    center t = ((v0 t) + (v1 t) + (v2 t) + (v3 t)) `scale` (1/4)
+    center (Tetrahedron _ v0' v1' v2' v3' _ _) =
+        (v0' + v1' + v2' + v3') `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)
@@ -243,27 +282,27 @@ 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 }