X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;fp=src%2FTests%2FCube.hs;h=0000000000000000000000000000000000000000;hb=3a954903101eca7594a65824868517b9758e188d;hp=2fd8cb67187c601fb63b3811bb3e7ad5cb6341fe;hpb=3f0b6b7faecc561af0b7312a11c73a44a1b416f6;p=spline3.git diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs deleted file mode 100644 index 2fd8cb6..0000000 --- a/src/Tests/Cube.hs +++ /dev/null @@ -1,506 +0,0 @@ -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 \ 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 \ 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 \ 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