src/Tests/Cube.hs

   1 module Tests.Cube
   2 where
   3
   4 import Test.QuickCheck
   5
   6 import Comparisons
   7 import Cube
   8 import FunctionValues (FunctionValues)
   9 import Tests.FunctionValues ()
  10 import Tetrahedron (b0, b1, b2, b3, c,
  11                     Tetrahedron(Tetrahedron),
  12                     v0, v1, v2, v3, volume)
  13
  14 instance Arbitrary Cube where
  15     arbitrary = do
  16       (Positive h') <- arbitrary :: Gen (Positive Double)
  17       i' <- choose (coordmin, coordmax)
  18       j' <- choose (coordmin, coordmax)
  19       k' <- choose (coordmin, coordmax)
  20       fv' <- arbitrary :: Gen FunctionValues
  21       return (Cube h' i' j' k' fv')
  22         where
  23           coordmin = -268435456 -- -(2^29 / 2)
  24           coordmax = 268435456  -- +(2^29 / 2)
  25
  26
  27 -- Quickcheck tests.
  28
  29 -- | Since the grid size is necessarily positive, all tetrahedrons
  30 --   (which comprise cubes of positive volume) must have positive volume
  31 --   as well.
  32 prop_all_volumes_positive :: Cube -> Bool
  33 prop_all_volumes_positive c =
  34     null nonpositive_volumes
  35     where
  36       ts = tetrahedrons c
  37       volumes = map volume ts
  38       nonpositive_volumes = filter (<= 0) volumes
  39
  40 -- | In fact, since all of the tetrahedra are identical, we should
  41 --   already know their volumes. There's 24 tetrahedra to a cube, so
  42 --   we'd expect the volume of each one to be (1/24)*h^3.
  43 prop_tetrahedron0_volumes_exact :: Cube -> Bool
  44 prop_tetrahedron0_volumes_exact c =
  45     volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
  46     where
  47       delta = h c
  48
  49 -- | In fact, since all of the tetrahedra are identical, we should
  50 --   already know their volumes. There's 24 tetrahedra to a cube, so
  51 --   we'd expect the volume of each one to be (1/24)*h^3.
  52 prop_tetrahedron1_volumes_exact :: Cube -> Bool
  53 prop_tetrahedron1_volumes_exact c =
  54     volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
  55     where
  56       delta = h c
  57
  58 -- | In fact, since all of the tetrahedra are identical, we should
  59 --   already know their volumes. There's 24 tetrahedra to a cube, so
  60 --   we'd expect the volume of each one to be (1/24)*h^3.
  61 prop_tetrahedron2_volumes_exact :: Cube -> Bool
  62 prop_tetrahedron2_volumes_exact c =
  63     volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
  64     where
  65       delta = h c
  66
  67 -- | In fact, since all of the tetrahedra are identical, we should
  68 --   already know their volumes. There's 24 tetrahedra to a cube, so
  69 --   we'd expect the volume of each one to be (1/24)*h^3.
  70 prop_tetrahedron3_volumes_exact :: Cube -> Bool
  71 prop_tetrahedron3_volumes_exact c =
  72     volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
  73     where
  74       delta = h c
  75
  76 -- | In fact, since all of the tetrahedra are identical, we should
  77 --   already know their volumes. There's 24 tetrahedra to a cube, so
  78 --   we'd expect the volume of each one to be (1/24)*h^3.
  79 prop_tetrahedron4_volumes_exact :: Cube -> Bool
  80 prop_tetrahedron4_volumes_exact c =
  81     volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
  82     where
  83       delta = h c
  84
  85 -- | In fact, since all of the tetrahedra are identical, we should
  86 --   already know their volumes. There's 24 tetrahedra to a cube, so
  87 --   we'd expect the volume of each one to be (1/24)*h^3.
  88 prop_tetrahedron5_volumes_exact :: Cube -> Bool
  89 prop_tetrahedron5_volumes_exact c =
  90     volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
  91     where
  92       delta = h c
  93
  94 -- | In fact, since all of the tetrahedra are identical, we should
  95 --   already know their volumes. There's 24 tetrahedra to a cube, so
  96 --   we'd expect the volume of each one to be (1/24)*h^3.
  97 prop_tetrahedron6_volumes_exact :: Cube -> Bool
  98 prop_tetrahedron6_volumes_exact c =
  99     volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
 100     where
 101       delta = h c
 102
 103 -- | In fact, since all of the tetrahedra are identical, we should
 104 --   already know their volumes. There's 24 tetrahedra to a cube, so
 105 --   we'd expect the volume of each one to be (1/24)*h^3.
 106 prop_tetrahedron7_volumes_exact :: Cube -> Bool
 107 prop_tetrahedron7_volumes_exact c =
 108     volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
 109     where
 110       delta = h c
 111
 112 -- | All tetrahedron should have their v0 located at the center of the cube.
 113 prop_v0_all_equal :: Cube -> Bool
 114 prop_v0_all_equal c = (v0 t0) == (v0 t1)
 115     where
 116       t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
 117       t1 = head $ tail (tetrahedrons c)
 118
 119
 120 -- | This pretty much repeats the prop_all_volumes_positive property,
 121 --   but will let me know which tetrahedrons's vertices are disoriented.
 122 prop_tetrahedron0_volumes_positive :: Cube -> Bool
 123 prop_tetrahedron0_volumes_positive c =
 124     volume (tetrahedron0 c) > 0
 125
 126 -- | This pretty much repeats the prop_all_volumes_positive property,
 127 --   but will let me know which tetrahedrons's vertices are disoriented.
 128 prop_tetrahedron1_volumes_positive :: Cube -> Bool
 129 prop_tetrahedron1_volumes_positive c =
 130     volume (tetrahedron1 c) > 0
 131
 132 -- | This pretty much repeats the prop_all_volumes_positive property,
 133 --   but will let me know which tetrahedrons's vertices are disoriented.
 134 prop_tetrahedron2_volumes_positive :: Cube -> Bool
 135 prop_tetrahedron2_volumes_positive c =
 136     volume (tetrahedron2 c) > 0
 137
 138 -- | This pretty much repeats the prop_all_volumes_positive property,
 139 --   but will let me know which tetrahedrons's vertices are disoriented.
 140 prop_tetrahedron3_volumes_positive :: Cube -> Bool
 141 prop_tetrahedron3_volumes_positive c =
 142     volume (tetrahedron3 c) > 0
 143
 144 -- | This pretty much repeats the prop_all_volumes_positive property,
 145 --   but will let me know which tetrahedrons's vertices are disoriented.
 146 prop_tetrahedron4_volumes_positive :: Cube -> Bool
 147 prop_tetrahedron4_volumes_positive c =
 148     volume (tetrahedron4 c) > 0
 149
 150 -- | This pretty much repeats the prop_all_volumes_positive property,
 151 --   but will let me know which tetrahedrons's vertices are disoriented.
 152 prop_tetrahedron5_volumes_positive :: Cube -> Bool
 153 prop_tetrahedron5_volumes_positive c =
 154     volume (tetrahedron5 c) > 0
 155
 156 -- | This pretty much repeats the prop_all_volumes_positive property,
 157 --   but will let me know which tetrahedrons's vertices are disoriented.
 158 prop_tetrahedron6_volumes_positive :: Cube -> Bool
 159 prop_tetrahedron6_volumes_positive c =
 160     volume (tetrahedron6 c) > 0
 161
 162 -- | This pretty much repeats the prop_all_volumes_positive property,
 163 --   but will let me know which tetrahedrons's vertices are disoriented.
 164 prop_tetrahedron7_volumes_positive :: Cube -> Bool
 165 prop_tetrahedron7_volumes_positive c =
 166     volume (tetrahedron7 c) > 0
 167
 168 -- | This pretty much repeats the prop_all_volumes_positive property,
 169 --   but will let me know which tetrahedrons's vertices are disoriented.
 170 prop_tetrahedron8_volumes_positive :: Cube -> Bool
 171 prop_tetrahedron8_volumes_positive c =
 172     volume (tetrahedron8 c) > 0
 173
 174 -- | This pretty much repeats the prop_all_volumes_positive property,
 175 --   but will let me know which tetrahedrons's vertices are disoriented.
 176 prop_tetrahedron9_volumes_positive :: Cube -> Bool
 177 prop_tetrahedron9_volumes_positive c =
 178     volume (tetrahedron9 c) > 0
 179
 180 -- | This pretty much repeats the prop_all_volumes_positive property,
 181 --   but will let me know which tetrahedrons's vertices are disoriented.
 182 prop_tetrahedron10_volumes_positive :: Cube -> Bool
 183 prop_tetrahedron10_volumes_positive c =
 184     volume (tetrahedron10 c) > 0
 185
 186 -- | This pretty much repeats the prop_all_volumes_positive property,
 187 --   but will let me know which tetrahedrons's vertices are disoriented.
 188 prop_tetrahedron11_volumes_positive :: Cube -> Bool
 189 prop_tetrahedron11_volumes_positive c =
 190     volume (tetrahedron11 c) > 0
 191
 192 -- | This pretty much repeats the prop_all_volumes_positive property,
 193 --   but will let me know which tetrahedrons's vertices are disoriented.
 194 prop_tetrahedron12_volumes_positive :: Cube -> Bool
 195 prop_tetrahedron12_volumes_positive c =
 196     volume (tetrahedron12 c) > 0
 197
 198 -- | This pretty much repeats the prop_all_volumes_positive property,
 199 --   but will let me know which tetrahedrons's vertices are disoriented.
 200 prop_tetrahedron13_volumes_positive :: Cube -> Bool
 201 prop_tetrahedron13_volumes_positive c =
 202     volume (tetrahedron13 c) > 0
 203
 204 -- | This pretty much repeats the prop_all_volumes_positive property,
 205 --   but will let me know which tetrahedrons's vertices are disoriented.
 206 prop_tetrahedron14_volumes_positive :: Cube -> Bool
 207 prop_tetrahedron14_volumes_positive c =
 208     volume (tetrahedron14 c) > 0
 209
 210 -- | This pretty much repeats the prop_all_volumes_positive property,
 211 --   but will let me know which tetrahedrons's vertices are disoriented.
 212 prop_tetrahedron15_volumes_positive :: Cube -> Bool
 213 prop_tetrahedron15_volumes_positive c =
 214     volume (tetrahedron15 c) > 0
 215
 216 -- | This pretty much repeats the prop_all_volumes_positive property,
 217 --   but will let me know which tetrahedrons's vertices are disoriented.
 218 prop_tetrahedron16_volumes_positive :: Cube -> Bool
 219 prop_tetrahedron16_volumes_positive c =
 220     volume (tetrahedron16 c) > 0
 221
 222 -- | This pretty much repeats the prop_all_volumes_positive property,
 223 --   but will let me know which tetrahedrons's vertices are disoriented.
 224 prop_tetrahedron17_volumes_positive :: Cube -> Bool
 225 prop_tetrahedron17_volumes_positive c =
 226     volume (tetrahedron17 c) > 0
 227
 228 -- | This pretty much repeats the prop_all_volumes_positive property,
 229 --   but will let me know which tetrahedrons's vertices are disoriented.
 230 prop_tetrahedron18_volumes_positive :: Cube -> Bool
 231 prop_tetrahedron18_volumes_positive c =
 232     volume (tetrahedron18 c) > 0
 233
 234 -- | This pretty much repeats the prop_all_volumes_positive property,
 235 --   but will let me know which tetrahedrons's vertices are disoriented.
 236 prop_tetrahedron19_volumes_positive :: Cube -> Bool
 237 prop_tetrahedron19_volumes_positive c =
 238     volume (tetrahedron19 c) > 0
 239
 240 -- | This pretty much repeats the prop_all_volumes_positive property,
 241 --   but will let me know which tetrahedrons's vertices are disoriented.
 242 prop_tetrahedron20_volumes_positive :: Cube -> Bool
 243 prop_tetrahedron20_volumes_positive c =
 244     volume (tetrahedron20 c) > 0
 245
 246 -- | This pretty much repeats the prop_all_volumes_positive property,
 247 --   but will let me know which tetrahedrons's vertices are disoriented.
 248 prop_tetrahedron21_volumes_positive :: Cube -> Bool
 249 prop_tetrahedron21_volumes_positive c =
 250     volume (tetrahedron21 c) > 0
 251
 252 -- | This pretty much repeats the prop_all_volumes_positive property,
 253 --   but will let me know which tetrahedrons's vertices are disoriented.
 254 prop_tetrahedron22_volumes_positive :: Cube -> Bool
 255 prop_tetrahedron22_volumes_positive c =
 256     volume (tetrahedron22 c) > 0
 257
 258 -- | This pretty much repeats the prop_all_volumes_positive property,
 259 --   but will let me know which tetrahedrons's vertices are disoriented.
 260 prop_tetrahedron23_volumes_positive :: Cube -> Bool
 261 prop_tetrahedron23_volumes_positive c =
 262     volume (tetrahedron23 c) > 0
 263
 264
 265 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 266 --   fourth indices of c-t3 have been switched. This is because we
 267 --   store the triangles oriented such that their volume is
 268 --   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
 269 --   in opposite directions, one of them has to have negative volume!
 270 prop_c0120_identity1 :: Cube -> Bool
 271 prop_c0120_identity1 cube =
 272    c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
 273      where
 274        t0 = tetrahedron0 cube
 275        t3 = tetrahedron3 cube
 276
 277
 278 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 279 --   fourth indices of c-t3 have been switched. This is because we
 280 --   store the triangles oriented such that their volume is
 281 --   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
 282 --   in opposite directions, one of them has to have negative volume!
 283 prop_c0210_identity1 :: Cube -> Bool
 284 prop_c0210_identity1 cube =
 285     c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
 286       where
 287         t0 = tetrahedron0 cube
 288         t3 = tetrahedron3 cube
 289
 290
 291 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 292 --   fourth indices of c-t3 have been switched. This is because we
 293 --   store the triangles oriented such that their volume is
 294 --   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
 295 --   in opposite directions, one of them has to have negative volume!
 296 prop_c0300_identity1 :: Cube -> Bool
 297 prop_c0300_identity1 cube =
 298     c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
 299       where
 300         t0 = tetrahedron0 cube
 301         t3 = tetrahedron3 cube
 302
 303
 304 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 305 --   fourth indices of c-t3 have been switched. This is because we
 306 --   store the triangles oriented such that their volume is
 307 --   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
 308 --   in opposite directions, one of them has to have negative volume!
 309 prop_c1110_identity :: Cube -> Bool
 310 prop_c1110_identity cube =
 311     c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
 312       where
 313         t0 = tetrahedron0 cube
 314         t3 = tetrahedron3 cube
 315
 316
 317 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 318 --   fourth indices of c-t3 have been switched. This is because we
 319 --   store the triangles oriented such that their volume is
 320 --   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
 321 --   in opposite directions, one of them has to have negative volume!
 322 prop_c1200_identity1 :: Cube -> Bool
 323 prop_c1200_identity1 cube =
 324     c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
 325       where
 326         t0 = tetrahedron0 cube
 327         t3 = tetrahedron3 cube
 328
 329
 330 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 331 --   fourth indices of c-t3 have been switched. This is because we
 332 --   store the triangles oriented such that their volume is
 333 --   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
 334 --   in opposite directions, one of them has to have negative volume!
 335 prop_c2100_identity1 :: Cube -> Bool
 336 prop_c2100_identity1 cube =
 337     c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
 338       where
 339         t0 = tetrahedron0 cube
 340         t3 = tetrahedron3 cube
 341
 342
 343
 344 -- | Given in Sorokina and Zeilfelder, p. 78.
 345 -- prop_cijk1_identity :: Cube -> Bool
 346 -- prop_cijk1_identity cube =
 347 --      and [ c t0 i j k 1 ~=
 348 --                  (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
 349 --                  (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
 350 --                  (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
 351 --                  (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
 352 --                                                       j <- [0..2],
 353 --                                                       k <- [0..2],
 354 --                                                       i + j + k == 2]
 355 --       where
 356 --         t0 = tetrahedron0 cube
 357 --         t1 = tetrahedron1 cube