import Test.QuickCheck
+import Comparisons
import Cube
-import FunctionValues (FunctionValues(FunctionValues))
-import Tests.FunctionValues
-import Tetrahedron (v0, volume)
+import FunctionValues (FunctionValues)
+import Tests.FunctionValues ()
+import Tetrahedron (b0, b1, b2, b3, c,
+ Tetrahedron(Tetrahedron),
+ v0, v1, v2, v3, volume)
instance Arbitrary Cube where
arbitrary = do
-- | Since the grid size is necessarily positive, all tetrahedrons
-- (which comprise cubes of positive volume) must have positive volume
-- as well.
-prop_all_volumes_positive :: Cube -> Property
+prop_all_volumes_positive :: Cube -> Bool
prop_all_volumes_positive c =
- (delta > 0) ==> (null nonpositive_volumes)
+ null nonpositive_volumes
where
- delta = h c
ts = tetrahedrons c
volumes = map volume ts
nonpositive_volumes = filter (<= 0) volumes
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron0_volumes_exact :: Cube -> Bool
+prop_tetrahedron0_volumes_exact c =
+ volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron1_volumes_exact :: Cube -> Bool
+prop_tetrahedron1_volumes_exact c =
+ volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron2_volumes_exact :: Cube -> Bool
+prop_tetrahedron2_volumes_exact c =
+ volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron3_volumes_exact :: Cube -> Bool
+prop_tetrahedron3_volumes_exact c =
+ volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron4_volumes_exact :: Cube -> Bool
+prop_tetrahedron4_volumes_exact c =
+ volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron5_volumes_exact :: Cube -> Bool
+prop_tetrahedron5_volumes_exact c =
+ volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron6_volumes_exact :: Cube -> Bool
+prop_tetrahedron6_volumes_exact c =
+ volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron7_volumes_exact :: Cube -> Bool
+prop_tetrahedron7_volumes_exact c =
+ volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
-- | All tetrahedron should have their v0 located at the center of the cube.
prop_v0_all_equal :: Cube -> Bool
prop_v0_all_equal c = (v0 t0) == (v0 t1)
-- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which face's vertices are disoriented.
-prop_front_face_volumes_positive :: Cube -> Property
-prop_front_face_volumes_positive c =
- (delta > 0) ==> (null nonpositive_volumes)
- where
- delta = h c
- ts = [tetrahedron0 c, tetrahedron1 c, tetrahedron2 c, tetrahedron3 c]
- volumes = map volume ts
- nonpositive_volumes = filter (<= 0) volumes
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron0_volumes_positive :: Cube -> Bool
+prop_tetrahedron0_volumes_positive c =
+ volume (tetrahedron0 c) > 0
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron1_volumes_positive :: Cube -> Bool
+prop_tetrahedron1_volumes_positive c =
+ volume (tetrahedron1 c) > 0
-- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which face's vertices are disoriented.
-prop_top_face_volumes_positive :: Cube -> Property
-prop_top_face_volumes_positive c =
- (delta > 0) ==> (null nonpositive_volumes)
- where
- delta = h c
- ts = [tetrahedron4 c, tetrahedron5 c, tetrahedron6 c, tetrahedron7 c]
- volumes = map volume ts
- nonpositive_volumes = filter (<= 0) volumes
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron2_volumes_positive :: Cube -> Bool
+prop_tetrahedron2_volumes_positive c =
+ volume (tetrahedron2 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron3_volumes_positive :: Cube -> Bool
+prop_tetrahedron3_volumes_positive c =
+ volume (tetrahedron3 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron4_volumes_positive :: Cube -> Bool
+prop_tetrahedron4_volumes_positive c =
+ volume (tetrahedron4 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron5_volumes_positive :: Cube -> Bool
+prop_tetrahedron5_volumes_positive c =
+ volume (tetrahedron5 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron6_volumes_positive :: Cube -> Bool
+prop_tetrahedron6_volumes_positive c =
+ volume (tetrahedron6 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron7_volumes_positive :: Cube -> Bool
+prop_tetrahedron7_volumes_positive c =
+ volume (tetrahedron7 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron8_volumes_positive :: Cube -> Bool
+prop_tetrahedron8_volumes_positive c =
+ volume (tetrahedron8 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron9_volumes_positive :: Cube -> Bool
+prop_tetrahedron9_volumes_positive c =
+ volume (tetrahedron9 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron10_volumes_positive :: Cube -> Bool
+prop_tetrahedron10_volumes_positive c =
+ volume (tetrahedron10 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron11_volumes_positive :: Cube -> Bool
+prop_tetrahedron11_volumes_positive c =
+ volume (tetrahedron11 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron12_volumes_positive :: Cube -> Bool
+prop_tetrahedron12_volumes_positive c =
+ volume (tetrahedron12 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron13_volumes_positive :: Cube -> Bool
+prop_tetrahedron13_volumes_positive c =
+ volume (tetrahedron13 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron14_volumes_positive :: Cube -> Bool
+prop_tetrahedron14_volumes_positive c =
+ volume (tetrahedron14 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron15_volumes_positive :: Cube -> Bool
+prop_tetrahedron15_volumes_positive c =
+ volume (tetrahedron15 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron16_volumes_positive :: Cube -> Bool
+prop_tetrahedron16_volumes_positive c =
+ volume (tetrahedron16 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron17_volumes_positive :: Cube -> Bool
+prop_tetrahedron17_volumes_positive c =
+ volume (tetrahedron17 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron18_volumes_positive :: Cube -> Bool
+prop_tetrahedron18_volumes_positive c =
+ volume (tetrahedron18 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron19_volumes_positive :: Cube -> Bool
+prop_tetrahedron19_volumes_positive c =
+ volume (tetrahedron19 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron20_volumes_positive :: Cube -> Bool
+prop_tetrahedron20_volumes_positive c =
+ volume (tetrahedron20 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron21_volumes_positive :: Cube -> Bool
+prop_tetrahedron21_volumes_positive c =
+ volume (tetrahedron21 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron22_volumes_positive :: Cube -> Bool
+prop_tetrahedron22_volumes_positive c =
+ volume (tetrahedron22 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron23_volumes_positive :: Cube -> Bool
+prop_tetrahedron23_volumes_positive c =
+ volume (tetrahedron23 c) > 0
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0120_identity1 :: Cube -> Bool
+prop_c0120_identity1 cube =
+ c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0210_identity1 :: Cube -> Bool
+prop_c0210_identity1 cube =
+ c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0300_identity1 :: Cube -> Bool
+prop_c0300_identity1 cube =
+ c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1110_identity :: Cube -> Bool
+prop_c1110_identity cube =
+ c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1200_identity1 :: Cube -> Bool
+prop_c1200_identity1 cube =
+ c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c2100_identity1 :: Cube -> Bool
+prop_c2100_identity1 cube =
+ c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t1 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0102_identity1 :: Cube -> Bool
+prop_c0102_identity1 cube =
+ c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t1 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0201_identity1 :: Cube -> Bool
+prop_c0201_identity1 cube =
+ c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t1 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0300_identity2 :: Cube -> Bool
+prop_c0300_identity2 cube =
+ c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t1 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1101_identity :: Cube -> Bool
+prop_c1101_identity cube =
+ c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t1 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1200_identity2 :: Cube -> Bool
+prop_c1200_identity2 cube =
+ c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t1 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c2100_identity2 :: Cube -> Bool
+prop_c2100_identity2 cube =
+ c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+
+-- | Given in Sorokina and Zeilfelder, p. 78.
+-- prop_cijk1_identity :: Cube -> Bool
+-- prop_cijk1_identity cube =
+-- and [ c t0 i j k 1 ~=
+-- (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
+-- (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
+-- (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
+-- (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
+-- j <- [0..2],
+-- k <- [0..2],
+-- i + j + k == 2]
+-- where
+-- t0 = tetrahedron0 cube
+-- t1 = tetrahedron1 cube
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