import Numeric.LinearAlgebra hiding (i, scale)
import Prelude hiding (LT)
+import Test.QuickCheck (Arbitrary(..), Gen)
import Cardinal
import 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" ++
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,
z3 = z_coord (v2 t)
z4 = z_coord (v3 t)
--- Computed using the formula from Lai & Schumaker, Definition 15.4,
--- page 436.
+-- | Computed using the formula from Lai & Schumaker, Definition 15.4,
+-- page 436.
volume :: Tetrahedron -> Double
volume t
| (v0 t) == (v1 t) = 0
| otherwise = (1/6)*(det (vol_matrix t))
+-- | The barycentric coordinates of a point with respect to v0.
b0 :: Tetrahedron -> (RealFunction Point)
b0 t point = (volume inner_tetrahedron) / (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)
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)
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)
where