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 Cardinal
import Comparisons
-import Point
import FunctionValues
-import Tests.FunctionValues()
import Tetrahedron
import ThreeDimensional
-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)
-
-- HUnit Tests
--- | Check the volume of a particular tetrahedron against the value
--- computed by hand. Its vertices are in clockwise order, so the
--- volume should be negative.
-test_volume1 :: Assertion
-test_volume1 =
- 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 { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
- vol = volume t
-
-
--- | Check the volume of a particular tetrahedron against the value
--- computed by hand. Its vertices are in counter-clockwise order, so
--- the volume should be positive.
-test_volume2 :: Assertion
-test_volume2 =
- 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 { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
- vol = volume t
-
-
--- | Ensure that a tetrahedron contains a particular point chosen to
--- be inside of it.
-test_contains_point1 :: Assertion
-test_contains_point1 =
- 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 { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
-
-
--- | Ensure that a tetrahedron does not contain a particular point chosen to
--- be outside of it (first test).
-test_doesnt_contain_point1 :: Assertion
-test_doesnt_contain_point1 =
- 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)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
-
-
--- | Ensure that a tetrahedron does not contain a particular point chosen to
--- be outside of it (second test).
-test_doesnt_contain_point2 :: Assertion
-test_doesnt_contain_point2 =
- 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)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
-
-
--- | Ensure that a tetrahedron does not contain a particular point chosen to
--- be outside of it (third test).
-test_doesnt_contain_point3 :: Assertion
-test_doesnt_contain_point3 =
- 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)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
-
-
--- | Ensure that a tetrahedron does not contain a particular point chosen to
--- be outside of it (fourth test).
-test_doesnt_contain_point4 :: Assertion
-test_doesnt_contain_point4 =
- 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)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
-
-
--- | Ensure that a tetrahedron does not contain a particular point chosen to
--- be outside of it (fifth test).
-test_doesnt_contain_point5 :: Assertion
-test_doesnt_contain_point5 =
- 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)
- t = Tetrahedron { v0 = p0,
- v1 = p1,
- v2 = p2,
- v3 = p3,
- fv = empty_values }
+-- | 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
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_x_rotation_doesnt_affect_front :: Tetrahedron -> Bool
-prop_x_rotation_doesnt_affect_front t =
- expr1 == expr2
- where
- fv0 = Tetrahedron.fv t
- fv1 = rotate (Tetrahedron.fv t) cwx
- expr1 = front $ fv0
- expr2 = front $ fv1
-
-prop_x_rotation_doesnt_affect_back :: Tetrahedron -> Bool
-prop_x_rotation_doesnt_affect_back t =
- expr1 == expr2
- where
- fv0 = Tetrahedron.fv t
- fv1 = rotate (Tetrahedron.fv t) cwx
- expr1 = back $ fv0
- expr2 = back $ fv1
-
-
-prop_y_rotation_doesnt_affect_left :: Tetrahedron -> Bool
-prop_y_rotation_doesnt_affect_left t =
- expr1 == expr2
- where
- fv0 = Tetrahedron.fv t
- fv1 = rotate (Tetrahedron.fv t) cwy
- expr1 = left $ fv0
- expr2 = left $ fv1
-
-prop_y_rotation_doesnt_affect_right :: Tetrahedron -> Bool
-prop_y_rotation_doesnt_affect_right t =
- expr1 == expr2
- where
- fv0 = Tetrahedron.fv t
- fv1 = rotate (Tetrahedron.fv t) cwy
- expr1 = right $ fv0
- expr2 = right $ fv1
-
-
-prop_z_rotation_doesnt_affect_down :: Tetrahedron -> Bool
-prop_z_rotation_doesnt_affect_down t =
- expr1 == expr2
- where
- fv0 = Tetrahedron.fv t
- fv1 = rotate (Tetrahedron.fv t) cwz
- expr1 = down $ fv0
- expr2 = down $ fv1
-
-
-prop_z_rotation_doesnt_affect_top :: Tetrahedron -> Bool
-prop_z_rotation_doesnt_affect_top t =
- expr1 == expr2
- where
- fv0 = Tetrahedron.fv t
- fv1 = rotate (Tetrahedron.fv t) cwz
- expr1 = top $ fv0
- expr2 = top $ fv1
prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
prop_swapping_vertices_doesnt_affect_coefficients1 t =
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