+++ /dev/null
-module Tests.Tetrahedron
-where
-
-import Test.Framework (Test, testGroup)
-import Test.Framework.Providers.HUnit (testCase)
-import Test.HUnit
-import Test.QuickCheck (Property, (==>))
-
-import Cardinal
-import Comparisons
-import FunctionValues
-import Tetrahedron
-import ThreeDimensional
-
--- HUnit Tests
-
-
--- | Check the volume of a particular tetrahedron (computed by hand)
--- and whether or not it contains a specific point chosen to be
--- outside of it. Its vertices are in clockwise order, so the volume
--- should be negative.
-tetrahedron1_geometry_tests :: Test.Framework.Test
-tetrahedron1_geometry_tests =
- testGroup "tetrahedron1 geometry"
- [ testCase "volume1" volume1,
- testCase "doesn't contain point1" doesnt_contain_point1]
- where
- p0 = (0, -0.5, 0)
- p1 = (0, 0.5, 0)
- p2 = (2, 0, 0)
- p3 = (1, 0, 1)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values,
- precomputed_volume = 0 }
-
- volume1 :: Assertion
- volume1 =
- assertEqual "volume is correct" True (vol ~= (-1/3))
- where
- vol = volume t
-
- doesnt_contain_point1 :: Assertion
- doesnt_contain_point1 =
- assertEqual "doesn't contain an exterior point" False contained
- where
- exterior_point = (5, 2, -9.0212)
- contained = contains_point t exterior_point
-
-
--- | Check the volume of a particular tetrahedron (computed by hand)
--- and whether or not it contains a specific point chosen to be
--- inside of it. Its vertices are in counter-clockwise order, so the
--- volume should be positive.
-tetrahedron2_geometry_tests :: Test.Framework.Test
-tetrahedron2_geometry_tests =
- testGroup "tetrahedron2 geometry"
- [ testCase "volume1" volume1,
- testCase "contains point1" contains_point1]
- where
- p0 = (0, -0.5, 0)
- p1 = (2, 0, 0)
- p2 = (0, 0.5, 0)
- p3 = (1, 0, 1)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values,
- precomputed_volume = 0 }
-
- volume1 :: Assertion
- volume1 = assertEqual "volume1 is correct" True (vol ~= (1/3))
- where
- vol = volume t
-
- contains_point1 :: Assertion
- contains_point1 = assertEqual "contains an inner point" True contained
- where
- inner_point = (1, 0, 0.5)
- contained = contains_point t inner_point
-
-
--- | Ensure that tetrahedra do not contain a particular point chosen to
--- be outside of them.
-containment_tests :: Test.Framework.Test
-containment_tests =
- testGroup "containment tests"
- [ testCase "doesn't contain point2" doesnt_contain_point2,
- testCase "doesn't contain point3" doesnt_contain_point3,
- testCase "doesn't contain point4" doesnt_contain_point4,
- testCase "doesn't contain point5" doesnt_contain_point5]
- where
- p2 = (0.5, 0.5, 1)
- p3 = (0.5, 0.5, 0.5)
- exterior_point = (0, 0, 0)
-
- doesnt_contain_point2 :: Assertion
- doesnt_contain_point2 =
- assertEqual "doesn't contain an exterior point" False contained
- where
- p0 = (0, 1, 1)
- p1 = (1, 1, 1)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values,
- precomputed_volume = 0 }
- contained = contains_point t exterior_point
-
-
- doesnt_contain_point3 :: Assertion
- doesnt_contain_point3 =
- assertEqual "doesn't contain an exterior point" False contained
- where
- p0 = (1, 1, 1)
- p1 = (1, 0, 1)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values,
- precomputed_volume = 0 }
- contained = contains_point t exterior_point
-
-
- doesnt_contain_point4 :: Assertion
- doesnt_contain_point4 =
- assertEqual "doesn't contain an exterior point" False contained
- where
- p0 = (1, 0, 1)
- p1 = (0, 0, 1)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values,
- precomputed_volume = 0 }
- contained = contains_point t exterior_point
-
-
- doesnt_contain_point5 :: Assertion
- doesnt_contain_point5 =
- assertEqual "doesn't contain an exterior point" False contained
- where
- p0 = (0, 0, 1)
- p1 = (0, 1, 1)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values,
- precomputed_volume = 0 }
- contained = contains_point t exterior_point
-
-
--- | The barycentric coordinate of v0 with respect to itself should
--- be one.
-prop_b0_v0_always_unity :: Tetrahedron -> Property
-prop_b0_v0_always_unity t =
- (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
-
--- | The barycentric coordinate of v1 with respect to v0 should
--- be zero.
-prop_b0_v1_always_zero :: Tetrahedron -> Property
-prop_b0_v1_always_zero t =
- (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
-
--- | The barycentric coordinate of v2 with respect to v0 should
--- be zero.
-prop_b0_v2_always_zero :: Tetrahedron -> Property
-prop_b0_v2_always_zero t =
- (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
-
--- | The barycentric coordinate of v3 with respect to v0 should
--- be zero.
-prop_b0_v3_always_zero :: Tetrahedron -> Property
-prop_b0_v3_always_zero t =
- (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
-
--- | The barycentric coordinate of v1 with respect to itself should
--- be one.
-prop_b1_v1_always_unity :: Tetrahedron -> Property
-prop_b1_v1_always_unity t =
- (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
-
--- | The barycentric coordinate of v0 with respect to v1 should
--- be zero.
-prop_b1_v0_always_zero :: Tetrahedron -> Property
-prop_b1_v0_always_zero t =
- (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
-
--- | The barycentric coordinate of v2 with respect to v1 should
--- be zero.
-prop_b1_v2_always_zero :: Tetrahedron -> Property
-prop_b1_v2_always_zero t =
- (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
-
--- | The barycentric coordinate of v3 with respect to v1 should
--- be zero.
-prop_b1_v3_always_zero :: Tetrahedron -> Property
-prop_b1_v3_always_zero t =
- (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
-
--- | The barycentric coordinate of v2 with respect to itself should
--- be one.
-prop_b2_v2_always_unity :: Tetrahedron -> Property
-prop_b2_v2_always_unity t =
- (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
-
--- | The barycentric coordinate of v0 with respect to v2 should
--- be zero.
-prop_b2_v0_always_zero :: Tetrahedron -> Property
-prop_b2_v0_always_zero t =
- (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
-
--- | The barycentric coordinate of v1 with respect to v2 should
--- be zero.
-prop_b2_v1_always_zero :: Tetrahedron -> Property
-prop_b2_v1_always_zero t =
- (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
-
--- | The barycentric coordinate of v3 with respect to v2 should
--- be zero.
-prop_b2_v3_always_zero :: Tetrahedron -> Property
-prop_b2_v3_always_zero t =
- (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
-
--- | The barycentric coordinate of v3 with respect to itself should
--- be one.
-prop_b3_v3_always_unity :: Tetrahedron -> Property
-prop_b3_v3_always_unity t =
- (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
-
--- | The barycentric coordinate of v0 with respect to v3 should
--- be zero.
-prop_b3_v0_always_zero :: Tetrahedron -> Property
-prop_b3_v0_always_zero t =
- (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
-
--- | The barycentric coordinate of v1 with respect to v3 should
--- be zero.
-prop_b3_v1_always_zero :: Tetrahedron -> Property
-prop_b3_v1_always_zero t =
- (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
-
--- | The barycentric coordinate of v2 with respect to v3 should
--- be zero.
-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; not a test itself.
-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))
-
-
-prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
-prop_swapping_vertices_doesnt_affect_coefficients1 t =
- c t 0 0 1 2 == c t' 0 0 1 2
- where
- t' = t { v0 = (v1 t), v1 = (v0 t) }
-
-prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool
-prop_swapping_vertices_doesnt_affect_coefficients2 t =
- c t 0 1 1 1 == c t' 0 1 1 1
- where
- t' = t { v2 = (v3 t), v3 = (v2 t) }
-
-prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool
-prop_swapping_vertices_doesnt_affect_coefficients3 t =
- c t 2 1 0 0 == c t' 2 1 0 0
- where
- t' = t { v2 = (v3 t), v3 = (v2 t) }
-
-prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool
-prop_swapping_vertices_doesnt_affect_coefficients4 t =
- c t 2 0 0 1 == c t' 2 0 0 1
- where
- t' = t { v0 = (v3 t), v3 = (v0 t) }
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