import FunctionValues (FunctionValues)
import Tests.FunctionValues ()
import Tetrahedron (b0, b1, b2, b3, c,
- Tetrahedron(Tetrahedron),
v0, v1, v2, v3, volume)
instance Arbitrary Cube where
-- (which comprise cubes of positive volume) must have positive volume
-- as well.
prop_all_volumes_positive :: Cube -> Bool
-prop_all_volumes_positive c =
+prop_all_volumes_positive cube =
null nonpositive_volumes
where
- ts = tetrahedrons c
+ ts = tetrahedrons cube
volumes = map volume ts
nonpositive_volumes = filter (<= 0) volumes
-- 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))
+prop_tetrahedron0_volumes_exact cube =
+ volume (tetrahedron0 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron1_volumes_exact cube =
+ volume (tetrahedron1 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron2_volumes_exact cube =
+ volume (tetrahedron2 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron3_volumes_exact cube =
+ volume (tetrahedron3 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron4_volumes_exact cube =
+ volume (tetrahedron4 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron5_volumes_exact cube =
+ volume (tetrahedron5 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron6_volumes_exact cube =
+ volume (tetrahedron6 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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))
+prop_tetrahedron7_volumes_exact cube =
+ volume (tetrahedron7 cube) ~= (1/24)*(delta^(3::Int))
where
- delta = h c
+ delta = h cube
-- | 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)
+prop_v0_all_equal cube = (v0 t0) == (v0 t1)
where
- t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
- t1 = head $ tail (tetrahedrons c)
+ t0 = head (tetrahedrons cube) -- Doesn't matter which two we choose.
+ t1 = head $ tail (tetrahedrons cube)
-- | This pretty much repeats the prop_all_volumes_positive property,
-- 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
+prop_tetrahedron0_volumes_positive cube =
+ volume (tetrahedron0 cube) > 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
+prop_tetrahedron1_volumes_positive cube =
+ volume (tetrahedron1 cube) > 0
-- | This pretty much repeats the prop_all_volumes_positive property,
-- 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
+prop_tetrahedron2_volumes_positive cube =
+ volume (tetrahedron2 cube) > 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
+prop_tetrahedron3_volumes_positive cube =
+ volume (tetrahedron3 cube) > 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
+prop_tetrahedron4_volumes_positive cube =
+ volume (tetrahedron4 cube) > 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
+prop_tetrahedron5_volumes_positive cube =
+ volume (tetrahedron5 cube) > 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
+prop_tetrahedron6_volumes_positive cube =
+ volume (tetrahedron6 cube) > 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
+prop_tetrahedron7_volumes_positive cube =
+ volume (tetrahedron7 cube) > 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
+prop_tetrahedron8_volumes_positive cube =
+ volume (tetrahedron8 cube) > 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
+prop_tetrahedron9_volumes_positive cube =
+ volume (tetrahedron9 cube) > 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
+prop_tetrahedron10_volumes_positive cube =
+ volume (tetrahedron10 cube) > 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
+prop_tetrahedron11_volumes_positive cube =
+ volume (tetrahedron11 cube) > 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
+prop_tetrahedron12_volumes_positive cube =
+ volume (tetrahedron12 cube) > 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
+prop_tetrahedron13_volumes_positive cube =
+ volume (tetrahedron13 cube) > 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
+prop_tetrahedron14_volumes_positive cube =
+ volume (tetrahedron14 cube) > 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
+prop_tetrahedron15_volumes_positive cube =
+ volume (tetrahedron15 cube) > 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
+prop_tetrahedron16_volumes_positive cube =
+ volume (tetrahedron16 cube) > 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
+prop_tetrahedron17_volumes_positive cube =
+ volume (tetrahedron17 cube) > 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
+prop_tetrahedron18_volumes_positive cube =
+ volume (tetrahedron18 cube) > 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
+prop_tetrahedron19_volumes_positive cube =
+ volume (tetrahedron19 cube) > 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
+prop_tetrahedron20_volumes_positive cube =
+ volume (tetrahedron20 cube) > 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
+prop_tetrahedron21_volumes_positive cube =
+ volume (tetrahedron21 cube) > 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
+prop_tetrahedron22_volumes_positive cube =
+ volume (tetrahedron22 cube) > 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
+prop_tetrahedron23_volumes_positive cube =
+ volume (tetrahedron23 cube) > 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
-- | 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
+-- 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 =
t1 = tetrahedron1 cube
+prop_t0_shares_edge_with_t6 :: Cube -> Bool
+prop_t0_shares_edge_with_t6 cube =
+ (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c3000_identity :: Cube -> Bool
+prop_c3000_identity cube =
+ c t0 3 0 0 0 ~= c t0 2 1 0 0 + c t6 2 1 0 0 - ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2010_identity :: Cube -> Bool
+prop_c2010_identity cube =
+ c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 1 0 - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2001_identity :: Cube -> Bool
+prop_c2001_identity cube =
+ c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 0 1 - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1020_identity :: Cube -> Bool
+prop_c1020_identity cube =
+ c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 2 0 - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1002_identity :: Cube -> Bool
+prop_c1002_identity cube =
+ c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 0 2 - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1011_identity :: Cube -> Bool
+prop_c1011_identity cube =
+ c t0 1 0 1 1 ~= c t0 0 1 1 1 + c t6 0 1 1 1 - ((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+
-- | Given in Sorokina and Zeilfelder, p. 78.
-- prop_cijk1_identity :: Cube -> Bool
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