+++ /dev/null
-module Tests.Cube
-where
-
-import Prelude hiding (LT)
-
-import Cardinal
-import Comparisons
-import Cube hiding (i, j, k)
-import FunctionValues
-import Misc (all_equal, disjoint)
-import Tetrahedron (b0, b1, b2, b3, c, fv,
- v0, v1, v2, v3, volume)
-
-
--- Quickcheck tests.
-
-prop_opposite_octant_tetrahedra_disjoint1 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint1 c =
- disjoint (front_left_top_tetrahedra c) (front_right_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint2 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint2 c =
- disjoint (back_left_top_tetrahedra c) (back_right_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint3 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint3 c =
- disjoint (front_left_top_tetrahedra c) (back_right_top_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint4 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint4 c =
- disjoint (front_left_down_tetrahedra c) (back_right_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint5 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint5 c =
- disjoint (front_left_top_tetrahedra c) (back_left_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint6 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint6 c =
- disjoint (front_right_top_tetrahedra c) (back_right_down_tetrahedra c)
-
-
--- | Since the grid size is necessarily positive, all tetrahedra
--- (which comprise cubes of positive volume) must have positive volume
--- as well.
-prop_all_volumes_positive :: Cube -> Bool
-prop_all_volumes_positive cube =
- null nonpositive_volumes
- where
- ts = tetrahedra cube
- 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_all_volumes_exact :: Cube -> Bool
-prop_all_volumes_exact cube =
- and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
- where
- 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 cube = (v0 t0) == (v0 t1)
- where
- t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
- t1 = head $ tail (tetrahedra cube)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). 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,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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
-prop_c0120_identity2 :: Cube -> Bool
-prop_c0120_identity2 cube =
- c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
-prop_c0120_identity3 :: Cube -> Bool
-prop_c0120_identity3 cube =
- c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
- where
- t1 = tetrahedron cube 1
- t2 = tetrahedron cube 2
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 2 and 3.
-prop_c0120_identity4 :: Cube -> Bool
-prop_c0120_identity4 cube =
- c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
- where
- t2 = tetrahedron cube 2
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 4 and 5.
-prop_c0120_identity5 :: Cube -> Bool
-prop_c0120_identity5 cube =
- c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
- where
- t4 = tetrahedron cube 4
- t5 = tetrahedron cube 5
-
--- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- -- 'prop_c0120_identity1' with tetrahedrons 5 and 6.
-prop_c0120_identity6 :: Cube -> Bool
-prop_c0120_identity6 cube =
- c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
- where
- t5 = tetrahedron cube 5
- t6 = tetrahedron cube 6
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- -- 'prop_c0120_identity1' with tetrahedrons 6 and 7.
-prop_c0120_identity7 :: Cube -> Bool
-prop_c0120_identity7 cube =
- c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
- where
- t6 = tetrahedron cube 6
- t7 = tetrahedron cube 7
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). 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_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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
--- fourth indices of c-t6 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_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 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-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 0 1
- - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-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 1 0
- - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-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 0 2
- - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-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 2 0
- - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-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 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
-
--- | 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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | The function values at the interior should be the same for all
--- tetrahedra.
-prop_interior_values_all_identical :: Cube -> Bool
-prop_interior_values_all_identical cube =
- all_equal [ eval (Tetrahedron.fv tet) I | tet <- tetrahedra cube ]
-
-
--- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
--- This test checks the rotation works as expected.
-prop_c_tilde_2100_rotation_correct :: Cube -> Bool
-prop_c_tilde_2100_rotation_correct cube =
- expr1 == expr2
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
- -- What gets computed for c2100 of t6.
- expr1 = eval (Tetrahedron.fv t6) $
- (3/8)*I +
- (1/12)*(T + R + L + D) +
- (1/64)*(FT + FR + FL + FD) +
- (7/48)*F +
- (1/48)*B +
- (1/96)*(RT + LD + LT + RD) +
- (1/192)*(BT + BR + BL + BD)
-
- -- What should be computed for c2100 of t6.
- expr2 = eval (Tetrahedron.fv t0) $
- (3/8)*I +
- (1/12)*(F + R + L + B) +
- (1/64)*(FT + RT + LT + BT) +
- (7/48)*T +
- (1/48)*D +
- (1/96)*(FR + FL + BR + BL) +
- (1/192)*(FD + RD + LD + BD)
-
-
--- | We know what (c t6 2 1 0 0) should be from Sorokina and
--- Zeilfelder, p. 87. This test checks the actual value based on
--- the FunctionValues of the cube.
---
--- If 'prop_c_tilde_2100_rotation_correct' passes, then this test is
--- even meaningful!
-prop_c_tilde_2100_correct :: Cube -> Bool
-prop_c_tilde_2100_correct cube =
- c t6 2 1 0 0 == expected
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
- fvs = Tetrahedron.fv t0
- expected = eval fvs $
- (3/8)*I +
- (1/12)*(F + R + L + B) +
- (1/64)*(FT + RT + LT + BT) +
- (7/48)*T +
- (1/48)*D +
- (1/96)*(FR + FL + BR + BL) +
- (1/192)*(FD + RD + LD + BD)
-
-
--- Tests to check that the correct edges are incidental.
-prop_t0_shares_edge_with_t1 :: Cube -> Bool
-prop_t0_shares_edge_with_t1 cube =
- (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-prop_t0_shares_edge_with_t3 :: Cube -> Bool
-prop_t0_shares_edge_with_t3 cube =
- (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-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 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-prop_t1_shares_edge_with_t2 :: Cube -> Bool
-prop_t1_shares_edge_with_t2 cube =
- (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
- where
- t1 = tetrahedron cube 1
- t2 = tetrahedron cube 2
-
-prop_t1_shares_edge_with_t19 :: Cube -> Bool
-prop_t1_shares_edge_with_t19 cube =
- (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
- where
- t1 = tetrahedron cube 1
- t19 = tetrahedron cube 19
-
-prop_t2_shares_edge_with_t3 :: Cube -> Bool
-prop_t2_shares_edge_with_t3 cube =
- (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
- where
- t1 = tetrahedron cube 1
- t2 = tetrahedron cube 2
-
-prop_t2_shares_edge_with_t12 :: Cube -> Bool
-prop_t2_shares_edge_with_t12 cube =
- (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
- where
- t2 = tetrahedron cube 2
- t12 = tetrahedron cube 12
-
-prop_t3_shares_edge_with_t21 :: Cube -> Bool
-prop_t3_shares_edge_with_t21 cube =
- (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
- where
- t3 = tetrahedron cube 3
- t21 = tetrahedron cube 21
-
-prop_t4_shares_edge_with_t5 :: Cube -> Bool
-prop_t4_shares_edge_with_t5 cube =
- (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
- where
- t4 = tetrahedron cube 4
- t5 = tetrahedron cube 5
-
-prop_t4_shares_edge_with_t7 :: Cube -> Bool
-prop_t4_shares_edge_with_t7 cube =
- (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
- where
- t4 = tetrahedron cube 4
- t7 = tetrahedron cube 7
-
-prop_t4_shares_edge_with_t10 :: Cube -> Bool
-prop_t4_shares_edge_with_t10 cube =
- (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
- where
- t4 = tetrahedron cube 4
- t10 = tetrahedron cube 10
-
-prop_t5_shares_edge_with_t6 :: Cube -> Bool
-prop_t5_shares_edge_with_t6 cube =
- (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
- where
- t5 = tetrahedron cube 5
- t6 = tetrahedron cube 6
-
-prop_t5_shares_edge_with_t16 :: Cube -> Bool
-prop_t5_shares_edge_with_t16 cube =
- (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
- where
- t5 = tetrahedron cube 5
- t16 = tetrahedron cube 16
-
-prop_t6_shares_edge_with_t7 :: Cube -> Bool
-prop_t6_shares_edge_with_t7 cube =
- (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
- where
- t6 = tetrahedron cube 6
- t7 = tetrahedron cube 7
-
-prop_t7_shares_edge_with_t20 :: Cube -> Bool
-prop_t7_shares_edge_with_t20 cube =
- (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
- where
- t7 = tetrahedron cube 7
- t20 = tetrahedron cube 20