+module Tests.Tetrahedron
+where
+
+import Test.HUnit
+import Test.QuickCheck
+
+import Cube
+import Point
+import Tests.Cube()
+import Tetrahedron
+import ThreeDimensional
+
+instance Arbitrary Tetrahedron where
+ arbitrary = do
+ rnd_c0 <- arbitrary :: Gen Cube
+ rnd_v0 <- arbitrary :: Gen Point
+ rnd_v1 <- arbitrary :: Gen Point
+ rnd_v2 <- arbitrary :: Gen Point
+ rnd_v3 <- arbitrary :: Gen Point
+ return (Tetrahedron rnd_c0 rnd_v0 rnd_v1 rnd_v2 rnd_v3)
+
+almost_equals :: Double -> Double -> Bool
+almost_equals x y = (abs (x - y)) < 0.0001
+
+(~=) :: Double -> Double -> Bool
+(~=) = almost_equals
+
+
+-- HUnit Tests
+
+-- Since p0, p1, p2 are in clockwise order, we expect the volume here
+-- to be negative.
+test_volume1 :: Test
+test_volume1 =
+ TestCase $ assertEqual "volume is correct" True (vol ~= (-1/3))
+ where
+ p0 = (0, -0.5, 0)
+ p1 = (0, 0.5, 0)
+ p2 = (2, 0, 0)
+ p3 = (1, 0, 1)
+ t = Tetrahedron { cube = empty_cube,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+ vol = volume t
+
+
+-- Now, p0, p1, and p2 are in counter-clockwise order. The volume
+-- should therefore be positive.
+test_volume2 :: Test
+test_volume2 =
+ TestCase $ assertEqual "volume is correct" True (vol ~= (1/3))
+ where
+ p0 = (0, -0.5, 0)
+ p1 = (2, 0, 0)
+ p2 = (0, 0.5, 0)
+ p3 = (1, 0, 1)
+ t = Tetrahedron { cube = empty_cube,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+ vol = volume t
+
+test_contains_point1 :: Test
+test_contains_point1 =
+ TestCase $ assertEqual "contains an inner point" True (contains_point t inner_point)
+ where
+ p0 = (0, -0.5, 0)
+ p1 = (0, 0.5, 0)
+ p2 = (2, 0, 0)
+ p3 = (1, 0, 1)
+ inner_point = (1, 0, 0.5)
+ t = Tetrahedron { cube = empty_cube,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+
+
+test_doesnt_contain_point1 :: Test
+test_doesnt_contain_point1 =
+ TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
+ where
+ p0 = (0, -0.5, 0)
+ p1 = (0, 0.5, 0)
+ p2 = (2, 0, 0)
+ p3 = (1, 0, 1)
+ exterior_point = (5, 2, -9.0212)
+ c_empty = empty_cube
+ t = Tetrahedron { cube = c_empty,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+
+
+test_doesnt_contain_point2 :: Test
+test_doesnt_contain_point2 =
+ TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
+ where
+ p0 = (0, 1, 1)
+ p1 = (1, 1, 1)
+ p2 = (0.5, 0.5, 1)
+ p3 = (0.5, 0.5, 0.5)
+ exterior_point = (0, 0, 0)
+ c_empty = empty_cube
+ t = Tetrahedron { cube = c_empty,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+
+test_doesnt_contain_point3 :: Test
+test_doesnt_contain_point3 =
+ TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
+ where
+ p0 = (1, 1, 1)
+ p1 = (1, 0, 1)
+ p2 = (0.5, 0.5, 1)
+ p3 = (0.5, 0.5, 0.5)
+ exterior_point = (0, 0, 0)
+ c_empty = empty_cube
+ t = Tetrahedron { cube = c_empty,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+
+test_doesnt_contain_point4 :: Test
+test_doesnt_contain_point4 =
+ TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
+ where
+ p0 = (1, 0, 1)
+ p1 = (0, 0, 1)
+ p2 = (0.5, 0.5, 1)
+ p3 = (0.5, 0.5, 0.5)
+ exterior_point = (0, 0, 0)
+ c_empty = empty_cube
+ t = Tetrahedron { cube = c_empty,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+
+test_doesnt_contain_point5 :: Test
+test_doesnt_contain_point5 =
+ TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
+ where
+ p0 = (0, 0, 1)
+ p1 = (0, 1, 1)
+ p2 = (0.5, 0.5, 1)
+ p3 = (0.5, 0.5, 0.5)
+ exterior_point = (0, 0, 0)
+ c_empty = empty_cube
+ t = Tetrahedron { cube = c_empty,
+ v0 = p0,
+ v1 = p1,
+ v2 = p2,
+ v3 = p3 }
+
+tetrahedron_tests :: [Test]
+tetrahedron_tests = [test_volume1,
+ test_volume2,
+ test_contains_point1,
+ test_doesnt_contain_point1,
+ test_doesnt_contain_point2,
+ test_doesnt_contain_point3,
+ test_doesnt_contain_point4,
+ test_doesnt_contain_point5 ]
+
+prop_b0_v0_always_unity :: Tetrahedron -> Property
+prop_b0_v0_always_unity t =
+ (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
+
+prop_b0_v1_always_zero :: Tetrahedron -> Property
+prop_b0_v1_always_zero t =
+ (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
+
+prop_b0_v2_always_zero :: Tetrahedron -> Property
+prop_b0_v2_always_zero t =
+ (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
+
+prop_b0_v3_always_zero :: Tetrahedron -> Property
+prop_b0_v3_always_zero t =
+ (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
+
+prop_b1_v1_always_unity :: Tetrahedron -> Property
+prop_b1_v1_always_unity t =
+ (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
+
+prop_b1_v0_always_zero :: Tetrahedron -> Property
+prop_b1_v0_always_zero t =
+ (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
+
+prop_b1_v2_always_zero :: Tetrahedron -> Property
+prop_b1_v2_always_zero t =
+ (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
+
+prop_b1_v3_always_zero :: Tetrahedron -> Property
+prop_b1_v3_always_zero t =
+ (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
+
+prop_b2_v2_always_unity :: Tetrahedron -> Property
+prop_b2_v2_always_unity t =
+ (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
+
+prop_b2_v0_always_zero :: Tetrahedron -> Property
+prop_b2_v0_always_zero t =
+ (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
+
+prop_b2_v1_always_zero :: Tetrahedron -> Property
+prop_b2_v1_always_zero t =
+ (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
+
+prop_b2_v3_always_zero :: Tetrahedron -> Property
+prop_b2_v3_always_zero t =
+ (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
+
+prop_b3_v3_always_unity :: Tetrahedron -> Property
+prop_b3_v3_always_unity t =
+ (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
+
+prop_b3_v0_always_zero :: Tetrahedron -> Property
+prop_b3_v0_always_zero t =
+ (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
+
+prop_b3_v1_always_zero :: Tetrahedron -> Property
+prop_b3_v1_always_zero t =
+ (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
+
+prop_b3_v2_always_zero :: Tetrahedron -> Property
+prop_b3_v2_always_zero t =
+ (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
+
+
+-- Used for convenience in the next few tests.
+p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
+p t i j k l = (polynomial t) (xi t i j k l)
+
+-- | Given in Sorokina and Zeilfelder, p. 78.
+prop_c3000_identity :: Tetrahedron -> Property
+prop_c3000_identity t =
+ (volume t) > 0 ==>
+ c t 3 0 0 0 ~= p t 3 0 0 0
+
+-- | Given in Sorokina and Zeilfelder, p. 78.
+prop_c2100_identity :: Tetrahedron -> Property
+prop_c2100_identity t =
+ (volume t) > 0 ==>
+ c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
+ where
+ term1 = (1/3)*(p t 0 3 0 0)
+ term2 = (5/6)*(p t 3 0 0 0)
+ term3 = 3*(p t 2 1 0 0)
+ term4 = (3/2)*(p t 1 2 0 0)
+
+-- | Given in Sorokina and Zeilfelder, p. 78.
+prop_c1110_identity :: Tetrahedron -> Property
+prop_c1110_identity t =
+ (volume t) > 0 ==>
+ c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
+ where
+ term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
+ term2 = (9/2)*(p t 1 1 1 0)
+ term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
+ term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))