X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;ds=sidebyside;f=src%2FTests%2FCube.hs;h=666fde8899c168f85b061430ce06f5ee3ca93e1f;hb=5109e41113a39024ef3fe799abb08de4a2ac74b0;hp=eee54449beaba02a3881f5fe06be2b633abd2cdb;hpb=89b8b6e94fcc944a1f4611811265f3c6217af850;p=spline3.git diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs index eee5444..666fde8 100644 --- a/src/Tests/Cube.hs +++ b/src/Tests/Cube.hs @@ -3,18 +3,355 @@ where import Test.QuickCheck +import Comparisons import Cube -import Grid (Grid) -import Tests.Grid () +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 - g' <- arbitrary :: Gen Grid + (Positive h') <- arbitrary :: Gen (Positive Double) i' <- choose (coordmin, coordmax) j' <- choose (coordmin, coordmax) k' <- choose (coordmin, coordmax) - d' <- arbitrary :: Gen Double - return (Cube g' i' j' k' d') + fv' <- arbitrary :: Gen FunctionValues + return (Cube h' i' j' k' fv') where coordmin = -268435456 -- -(2^29 / 2) coordmax = 268435456 -- +(2^29 / 2) + + +-- Quickcheck tests. + +-- | 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 -> Bool +prop_all_volumes_positive c = + null nonpositive_volumes + where + 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) + where + t0 = head (tetrahedrons c) -- Doesn't matter which two we choose. + t1 = head $ tail (tetrahedrons c) + + +-- | 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 + +-- | 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 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 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 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 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 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 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 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. 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