module Tests.Tetrahedron
where
+import Test.Framework (Test, testGroup)
+import Test.Framework.Providers.HUnit (testCase)
import Test.HUnit
-import Test.QuickCheck
+import Test.QuickCheck (Property, (==>))
-import Cube
-import Point
-import Tests.Cube()
+import Cardinal
+import Comparisons
+import FunctionValues
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 ]
+-- | 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.
+-- | 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)
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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