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
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" ++
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)
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)
+-- | 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,
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.