X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=6c13f4bbb429f2a185cdd1eaae3a541f1b147cb8;hb=b9c6d5f4f9cf3e0e8c32499959c879e6300717f6;hp=9d90f713e9e214897d13151295ac4599fa983ea4;hpb=58cf11569acb270995d2de924dda03ef526647e2;p=spline3.git

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index 9d90f71..6c13f4b 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
@@ -18,6 +20,17 @@ data Tetrahedron = Tetrahedron { fv :: FunctionValues,
                                  v3 :: Point }
                    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
+      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
+
+
 instance Show Tetrahedron where
     show t = "Tetrahedron:\n" ++
              "  fv: " ++ (show (fv t)) ++ "\n" ++
@@ -30,7 +43,10 @@ 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 t p) `nearly_ge` 0 &&
+      (b1 t p) `nearly_ge` 0 &&
+      (b2 t p) `nearly_ge` 0 &&
+      (b3 t p) `nearly_ge` 0
 
 
 polynomial :: Tetrahedron -> (RealFunction Point)
@@ -76,6 +92,11 @@ beta t i j k l
     b3_term = (b3 t) `fexp` l
 
 
+-- | The coefficient function. c t i j k l returns the coefficient
+--   c_ijkl with respect to the tetrahedron t. The definition uses
+--   pattern matching to mimic the definitions given in Sorokina and
+--   Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
+--   function will simply error.
 c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 c t 0 0 3 0 = eval (fv t) $
               (1/8) * (I + F + L + T + LT + FL + FT + FLT)
@@ -197,6 +218,8 @@ c _ _ _ _ _ = error "coefficient index out of bounds"
 
 
 
+-- | The matrix used in the tetrahedron volume calculation as given in
+--   Lai & Schumaker, Definition 15.4, page 436.
 vol_matrix :: Tetrahedron -> Matrix Double
 vol_matrix t = (4><4)
                [1,  1,  1,  1,
@@ -204,18 +227,10 @@ 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.