import Test.QuickCheck
import Comparisons
-import Cube
import Point
-import Tests.Cube()
+import FunctionValues
+import Tests.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)
+ rnd_fv <- arbitrary :: Gen FunctionValues
+ return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
-- HUnit Tests
--- Since p0, p1, p2 are in clockwise order, we expect the volume here
--- to be negative.
+
+-- | 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 :: Test
test_volume1 =
TestCase $ assertEqual "volume is correct" True (vol ~= (-1/3))
p1 = (0, 0.5, 0)
p2 = (2, 0, 0)
p3 = (1, 0, 1)
- t = Tetrahedron { cube = empty_cube,
- v0 = p0,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ v3 = p3,
+ fv = empty_values }
vol = volume t
--- Now, p0, p1, and p2 are in counter-clockwise order. The volume
--- should therefore be positive.
+-- | 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 :: Test
test_volume2 =
TestCase $ assertEqual "volume is correct" True (vol ~= (1/3))
p1 = (2, 0, 0)
p2 = (0, 0.5, 0)
p3 = (1, 0, 1)
- t = Tetrahedron { cube = empty_cube,
- v0 = p0,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ 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 :: Test
test_contains_point1 =
TestCase $ assertEqual "contains an inner point" True (contains_point t inner_point)
p2 = (2, 0, 0)
p3 = (1, 0, 1)
inner_point = (1, 0, 0.5)
- t = Tetrahedron { cube = empty_cube,
- v0 = p0,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ 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 :: Test
test_doesnt_contain_point1 =
TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
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,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ 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 :: Test
test_doesnt_contain_point2 =
TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
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,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ 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 :: Test
test_doesnt_contain_point3 =
TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
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,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ 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 :: Test
test_doesnt_contain_point4 =
TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
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,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ 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 :: Test
test_doesnt_contain_point5 =
TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
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,
+ t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
- v3 = p3 }
+ v3 = p3,
+ fv = empty_values }
+-- | A list of all HUnit tests defined in this module.
tetrahedron_tests :: [Test]
tetrahedron_tests = [test_volume1,
test_volume2,
test_doesnt_contain_point4,
test_doesnt_contain_point5 ]
+
+-- | 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)
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