src/Tests/Cube.hs

   1 module Tests.Cube
   2 where
   3
   4 import Prelude hiding (LT)
   5 import Test.QuickCheck
   6
   7 import Cardinal
   8 import Comparisons
   9 import Cube
  10 import FunctionValues
  11 import Tests.FunctionValues ()
  12 import Tetrahedron (b0, b1, b2, b3, c, fv,
  13                     v0, v1, v2, v3, volume)
  14
  15 instance Arbitrary Cube where
  16     arbitrary = do
  17       (Positive h') <- arbitrary :: Gen (Positive Double)
  18       i' <- choose (coordmin, coordmax)
  19       j' <- choose (coordmin, coordmax)
  20       k' <- choose (coordmin, coordmax)
  21       fv' <- arbitrary :: Gen FunctionValues
  22       return (Cube h' i' j' k' fv')
  23         where
  24           coordmin = -268435456 -- -(2^29 / 2)
  25           coordmax = 268435456  -- +(2^29 / 2)
  26
  27
  28 -- Quickcheck tests.
  29
  30 -- | Since the grid size is necessarily positive, all tetrahedrons
  31 --   (which comprise cubes of positive volume) must have positive volume
  32 --   as well.
  33 prop_all_volumes_positive :: Cube -> Bool
  34 prop_all_volumes_positive cube =
  35     null nonpositive_volumes
  36     where
  37       ts = tetrahedrons cube
  38       volumes = map volume ts
  39       nonpositive_volumes = filter (<= 0) volumes
  40
  41 -- | In fact, since all of the tetrahedra are identical, we should
  42 --   already know their volumes. There's 24 tetrahedra to a cube, so
  43 --   we'd expect the volume of each one to be (1/24)*h^3.
  44 prop_tetrahedron0_volumes_exact :: Cube -> Bool
  45 prop_tetrahedron0_volumes_exact cube =
  46     volume (tetrahedron0 cube) ~= (1/24)*(delta^(3::Int))
  47     where
  48       delta = h cube
  49
  50 -- | In fact, since all of the tetrahedra are identical, we should
  51 --   already know their volumes. There's 24 tetrahedra to a cube, so
  52 --   we'd expect the volume of each one to be (1/24)*h^3.
  53 prop_tetrahedron1_volumes_exact :: Cube -> Bool
  54 prop_tetrahedron1_volumes_exact cube =
  55     volume (tetrahedron1 cube) ~= (1/24)*(delta^(3::Int))
  56     where
  57       delta = h cube
  58
  59 -- | In fact, since all of the tetrahedra are identical, we should
  60 --   already know their volumes. There's 24 tetrahedra to a cube, so
  61 --   we'd expect the volume of each one to be (1/24)*h^3.
  62 prop_tetrahedron2_volumes_exact :: Cube -> Bool
  63 prop_tetrahedron2_volumes_exact cube =
  64     volume (tetrahedron2 cube) ~= (1/24)*(delta^(3::Int))
  65     where
  66       delta = h cube
  67
  68 -- | In fact, since all of the tetrahedra are identical, we should
  69 --   already know their volumes. There's 24 tetrahedra to a cube, so
  70 --   we'd expect the volume of each one to be (1/24)*h^3.
  71 prop_tetrahedron3_volumes_exact :: Cube -> Bool
  72 prop_tetrahedron3_volumes_exact cube =
  73     volume (tetrahedron3 cube) ~= (1/24)*(delta^(3::Int))
  74     where
  75       delta = h cube
  76
  77 -- | In fact, since all of the tetrahedra are identical, we should
  78 --   already know their volumes. There's 24 tetrahedra to a cube, so
  79 --   we'd expect the volume of each one to be (1/24)*h^3.
  80 prop_tetrahedron4_volumes_exact :: Cube -> Bool
  81 prop_tetrahedron4_volumes_exact cube =
  82     volume (tetrahedron4 cube) ~= (1/24)*(delta^(3::Int))
  83     where
  84       delta = h cube
  85
  86 -- | In fact, since all of the tetrahedra are identical, we should
  87 --   already know their volumes. There's 24 tetrahedra to a cube, so
  88 --   we'd expect the volume of each one to be (1/24)*h^3.
  89 prop_tetrahedron5_volumes_exact :: Cube -> Bool
  90 prop_tetrahedron5_volumes_exact cube =
  91     volume (tetrahedron5 cube) ~= (1/24)*(delta^(3::Int))
  92     where
  93       delta = h cube
  94
  95 -- | In fact, since all of the tetrahedra are identical, we should
  96 --   already know their volumes. There's 24 tetrahedra to a cube, so
  97 --   we'd expect the volume of each one to be (1/24)*h^3.
  98 prop_tetrahedron6_volumes_exact :: Cube -> Bool
  99 prop_tetrahedron6_volumes_exact cube =
 100     volume (tetrahedron6 cube) ~= (1/24)*(delta^(3::Int))
 101     where
 102       delta = h cube
 103
 104 -- | In fact, since all of the tetrahedra are identical, we should
 105 --   already know their volumes. There's 24 tetrahedra to a cube, so
 106 --   we'd expect the volume of each one to be (1/24)*h^3.
 107 prop_tetrahedron7_volumes_exact :: Cube -> Bool
 108 prop_tetrahedron7_volumes_exact cube =
 109     volume (tetrahedron7 cube) ~= (1/24)*(delta^(3::Int))
 110     where
 111       delta = h cube
 112
 113 -- | All tetrahedron should have their v0 located at the center of the cube.
 114 prop_v0_all_equal :: Cube -> Bool
 115 prop_v0_all_equal cube = (v0 t0) == (v0 t1)
 116     where
 117       t0 = head (tetrahedrons cube) -- Doesn't matter which two we choose.
 118       t1 = head $ tail (tetrahedrons cube)
 119
 120
 121 -- | This pretty much repeats the prop_all_volumes_positive property,
 122 --   but will let me know which tetrahedrons's vertices are disoriented.
 123 prop_tetrahedron0_volumes_positive :: Cube -> Bool
 124 prop_tetrahedron0_volumes_positive cube =
 125     volume (tetrahedron0 cube) > 0
 126
 127 -- | This pretty much repeats the prop_all_volumes_positive property,
 128 --   but will let me know which tetrahedrons's vertices are disoriented.
 129 prop_tetrahedron1_volumes_positive :: Cube -> Bool
 130 prop_tetrahedron1_volumes_positive cube =
 131     volume (tetrahedron1 cube) > 0
 132
 133 -- | This pretty much repeats the prop_all_volumes_positive property,
 134 --   but will let me know which tetrahedrons's vertices are disoriented.
 135 prop_tetrahedron2_volumes_positive :: Cube -> Bool
 136 prop_tetrahedron2_volumes_positive cube =
 137     volume (tetrahedron2 cube) > 0
 138
 139 -- | This pretty much repeats the prop_all_volumes_positive property,
 140 --   but will let me know which tetrahedrons's vertices are disoriented.
 141 prop_tetrahedron3_volumes_positive :: Cube -> Bool
 142 prop_tetrahedron3_volumes_positive cube =
 143     volume (tetrahedron3 cube) > 0
 144
 145 -- | This pretty much repeats the prop_all_volumes_positive property,
 146 --   but will let me know which tetrahedrons's vertices are disoriented.
 147 prop_tetrahedron4_volumes_positive :: Cube -> Bool
 148 prop_tetrahedron4_volumes_positive cube =
 149     volume (tetrahedron4 cube) > 0
 150
 151 -- | This pretty much repeats the prop_all_volumes_positive property,
 152 --   but will let me know which tetrahedrons's vertices are disoriented.
 153 prop_tetrahedron5_volumes_positive :: Cube -> Bool
 154 prop_tetrahedron5_volumes_positive cube =
 155     volume (tetrahedron5 cube) > 0
 156
 157 -- | This pretty much repeats the prop_all_volumes_positive property,
 158 --   but will let me know which tetrahedrons's vertices are disoriented.
 159 prop_tetrahedron6_volumes_positive :: Cube -> Bool
 160 prop_tetrahedron6_volumes_positive cube =
 161     volume (tetrahedron6 cube) > 0
 162
 163 -- | This pretty much repeats the prop_all_volumes_positive property,
 164 --   but will let me know which tetrahedrons's vertices are disoriented.
 165 prop_tetrahedron7_volumes_positive :: Cube -> Bool
 166 prop_tetrahedron7_volumes_positive cube =
 167     volume (tetrahedron7 cube) > 0
 168
 169 -- | This pretty much repeats the prop_all_volumes_positive property,
 170 --   but will let me know which tetrahedrons's vertices are disoriented.
 171 prop_tetrahedron8_volumes_positive :: Cube -> Bool
 172 prop_tetrahedron8_volumes_positive cube =
 173     volume (tetrahedron8 cube) > 0
 174
 175 -- | This pretty much repeats the prop_all_volumes_positive property,
 176 --   but will let me know which tetrahedrons's vertices are disoriented.
 177 prop_tetrahedron9_volumes_positive :: Cube -> Bool
 178 prop_tetrahedron9_volumes_positive cube =
 179     volume (tetrahedron9 cube) > 0
 180
 181 -- | This pretty much repeats the prop_all_volumes_positive property,
 182 --   but will let me know which tetrahedrons's vertices are disoriented.
 183 prop_tetrahedron10_volumes_positive :: Cube -> Bool
 184 prop_tetrahedron10_volumes_positive cube =
 185     volume (tetrahedron10 cube) > 0
 186
 187 -- | This pretty much repeats the prop_all_volumes_positive property,
 188 --   but will let me know which tetrahedrons's vertices are disoriented.
 189 prop_tetrahedron11_volumes_positive :: Cube -> Bool
 190 prop_tetrahedron11_volumes_positive cube =
 191     volume (tetrahedron11 cube) > 0
 192
 193 -- | This pretty much repeats the prop_all_volumes_positive property,
 194 --   but will let me know which tetrahedrons's vertices are disoriented.
 195 prop_tetrahedron12_volumes_positive :: Cube -> Bool
 196 prop_tetrahedron12_volumes_positive cube =
 197     volume (tetrahedron12 cube) > 0
 198
 199 -- | This pretty much repeats the prop_all_volumes_positive property,
 200 --   but will let me know which tetrahedrons's vertices are disoriented.
 201 prop_tetrahedron13_volumes_positive :: Cube -> Bool
 202 prop_tetrahedron13_volumes_positive cube =
 203     volume (tetrahedron13 cube) > 0
 204
 205 -- | This pretty much repeats the prop_all_volumes_positive property,
 206 --   but will let me know which tetrahedrons's vertices are disoriented.
 207 prop_tetrahedron14_volumes_positive :: Cube -> Bool
 208 prop_tetrahedron14_volumes_positive cube =
 209     volume (tetrahedron14 cube) > 0
 210
 211 -- | This pretty much repeats the prop_all_volumes_positive property,
 212 --   but will let me know which tetrahedrons's vertices are disoriented.
 213 prop_tetrahedron15_volumes_positive :: Cube -> Bool
 214 prop_tetrahedron15_volumes_positive cube =
 215     volume (tetrahedron15 cube) > 0
 216
 217 -- | This pretty much repeats the prop_all_volumes_positive property,
 218 --   but will let me know which tetrahedrons's vertices are disoriented.
 219 prop_tetrahedron16_volumes_positive :: Cube -> Bool
 220 prop_tetrahedron16_volumes_positive cube =
 221     volume (tetrahedron16 cube) > 0
 222
 223 -- | This pretty much repeats the prop_all_volumes_positive property,
 224 --   but will let me know which tetrahedrons's vertices are disoriented.
 225 prop_tetrahedron17_volumes_positive :: Cube -> Bool
 226 prop_tetrahedron17_volumes_positive cube =
 227     volume (tetrahedron17 cube) > 0
 228
 229 -- | This pretty much repeats the prop_all_volumes_positive property,
 230 --   but will let me know which tetrahedrons's vertices are disoriented.
 231 prop_tetrahedron18_volumes_positive :: Cube -> Bool
 232 prop_tetrahedron18_volumes_positive cube =
 233     volume (tetrahedron18 cube) > 0
 234
 235 -- | This pretty much repeats the prop_all_volumes_positive property,
 236 --   but will let me know which tetrahedrons's vertices are disoriented.
 237 prop_tetrahedron19_volumes_positive :: Cube -> Bool
 238 prop_tetrahedron19_volumes_positive cube =
 239     volume (tetrahedron19 cube) > 0
 240
 241 -- | This pretty much repeats the prop_all_volumes_positive property,
 242 --   but will let me know which tetrahedrons's vertices are disoriented.
 243 prop_tetrahedron20_volumes_positive :: Cube -> Bool
 244 prop_tetrahedron20_volumes_positive cube =
 245     volume (tetrahedron20 cube) > 0
 246
 247 -- | This pretty much repeats the prop_all_volumes_positive property,
 248 --   but will let me know which tetrahedrons's vertices are disoriented.
 249 prop_tetrahedron21_volumes_positive :: Cube -> Bool
 250 prop_tetrahedron21_volumes_positive cube =
 251     volume (tetrahedron21 cube) > 0
 252
 253 -- | This pretty much repeats the prop_all_volumes_positive property,
 254 --   but will let me know which tetrahedrons's vertices are disoriented.
 255 prop_tetrahedron22_volumes_positive :: Cube -> Bool
 256 prop_tetrahedron22_volumes_positive cube =
 257     volume (tetrahedron22 cube) > 0
 258
 259 -- | This pretty much repeats the prop_all_volumes_positive property,
 260 --   but will let me know which tetrahedrons's vertices are disoriented.
 261 prop_tetrahedron23_volumes_positive :: Cube -> Bool
 262 prop_tetrahedron23_volumes_positive cube =
 263     volume (tetrahedron23 cube) > 0
 264
 265
 266 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 267 --   fourth indices of c-t3 have been switched. This is because we
 268 --   store the triangles oriented such that their volume is
 269 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
 270 --   in opposite directions, one of them has to have negative volume!
 271 prop_c0120_identity1 :: Cube -> Bool
 272 prop_c0120_identity1 cube =
 273    c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
 274      where
 275        t0 = tetrahedron0 cube
 276        t3 = tetrahedron3 cube
 277
 278
 279 -- | Given in Sorokina and Zeilfelder, p. 79. Repeats
 280 --   prop_c0120_identity2 with tetrahedrons 3 and 2.
 281 prop_c0120_identity2 :: Cube -> Bool
 282 prop_c0120_identity2 cube =
 283    c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
 284      where
 285        t3 = tetrahedron3 cube
 286        t2 = tetrahedron2 cube
 287
 288 -- | Given in Sorokina and Zeilfelder, p. 79. Repeats
 289 --   prop_c0120_identity1 with tetrahedrons 2 and 1.
 290 prop_c0120_identity3 :: Cube -> Bool
 291 prop_c0120_identity3 cube =
 292    c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
 293      where
 294        t2 = tetrahedron2 cube
 295        t1 = tetrahedron1 cube
 296
 297
 298 -- | Given in Sorokina and Zeilfelder, p. 79. Repeats
 299 --   prop_c0120_identity1 with tetrahedrons 4 and 7.
 300 prop_c0120_identity4 :: Cube -> Bool
 301 prop_c0120_identity4 cube =
 302    c t4 0 1 2 0 ~= (c t4 0 0 2 1 + c t7 0 0 1 2) / 2
 303      where
 304        t4 = tetrahedron4 cube
 305        t7 = tetrahedron7 cube
 306
 307
 308 -- | Given in Sorokina and Zeilfelder, p. 79. Repeats
 309 --   prop_c0120_identity1 with tetrahedrons 7 and 6.
 310 prop_c0120_identity5 :: Cube -> Bool
 311 prop_c0120_identity5 cube =
 312    c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
 313      where
 314        t7 = tetrahedron7 cube
 315        t6 = tetrahedron6 cube
 316
 317
 318 -- | Given in Sorokina and Zeilfelder, p. 79. Repeats
 319 --   prop_c0120_identity1 with tetrahedrons 6 and 5.
 320 prop_c0120_identity6 :: Cube -> Bool
 321 prop_c0120_identity6 cube =
 322    c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
 323      where
 324        t6 = tetrahedron6 cube
 325        t5 = tetrahedron5 cube
 326
 327
 328 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 329 --   fourth indices of c-t3 have been switched. This is because we
 330 --   store the triangles oriented such that their volume is
 331 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
 332 --   in opposite directions, one of them has to have negative volume!
 333 prop_c0210_identity1 :: Cube -> Bool
 334 prop_c0210_identity1 cube =
 335     c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
 336       where
 337         t0 = tetrahedron0 cube
 338         t3 = tetrahedron3 cube
 339
 340
 341 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 342 --   fourth indices of c-t3 have been switched. This is because we
 343 --   store the triangles oriented such that their volume is
 344 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
 345 --   in opposite directions, one of them has to have negative volume!
 346 prop_c0300_identity1 :: Cube -> Bool
 347 prop_c0300_identity1 cube =
 348     c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
 349       where
 350         t0 = tetrahedron0 cube
 351         t3 = tetrahedron3 cube
 352
 353
 354 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 355 --   fourth indices of c-t3 have been switched. This is because we
 356 --   store the triangles oriented such that their volume is
 357 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
 358 --   in opposite directions, one of them has to have negative volume!
 359 prop_c1110_identity :: Cube -> Bool
 360 prop_c1110_identity cube =
 361     c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
 362       where
 363         t0 = tetrahedron0 cube
 364         t3 = tetrahedron3 cube
 365
 366
 367 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 368 --   fourth indices of c-t3 have been switched. This is because we
 369 --   store the triangles oriented such that their volume is
 370 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
 371 --   in opposite directions, one of them has to have negative volume!
 372 prop_c1200_identity1 :: Cube -> Bool
 373 prop_c1200_identity1 cube =
 374     c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
 375       where
 376         t0 = tetrahedron0 cube
 377         t3 = tetrahedron3 cube
 378
 379
 380 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 381 --   fourth indices of c-t3 have been switched. This is because we
 382 --   store the triangles oriented such that their volume is
 383 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
 384 --   in opposite directions, one of them has to have negative volume!
 385 prop_c2100_identity1 :: Cube -> Bool
 386 prop_c2100_identity1 cube =
 387     c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
 388       where
 389         t0 = tetrahedron0 cube
 390         t3 = tetrahedron3 cube
 391
 392
 393
 394 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 395 --   fourth indices of c-t1 have been switched. This is because we
 396 --   store the triangles oriented such that their volume is
 397 --   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 398 --   in opposite directions, one of them has to have negative volume!
 399 prop_c0102_identity1 :: Cube -> Bool
 400 prop_c0102_identity1 cube =
 401     c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
 402       where
 403         t0 = tetrahedron0 cube
 404         t1 = tetrahedron1 cube
 405
 406
 407 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 408 --   fourth indices of c-t1 have been switched. This is because we
 409 --   store the triangles oriented such that their volume is
 410 --   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 411 --   in opposite directions, one of them has to have negative volume!
 412 prop_c0201_identity1 :: Cube -> Bool
 413 prop_c0201_identity1 cube =
 414     c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
 415       where
 416         t0 = tetrahedron0 cube
 417         t1 = tetrahedron1 cube
 418
 419
 420 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 421 --   fourth indices of c-t1 have been switched. This is because we
 422 --   store the triangles oriented such that their volume is
 423 --   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 424 --   in opposite directions, one of them has to have negative volume!
 425 prop_c0300_identity2 :: Cube -> Bool
 426 prop_c0300_identity2 cube =
 427     c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
 428       where
 429         t0 = tetrahedron0 cube
 430         t1 = tetrahedron1 cube
 431
 432
 433 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 434 --   fourth indices of c-t1 have been switched. This is because we
 435 --   store the triangles oriented such that their volume is
 436 --   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 437 --   in opposite directions, one of them has to have negative volume!
 438 prop_c1101_identity :: Cube -> Bool
 439 prop_c1101_identity cube =
 440     c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
 441       where
 442         t0 = tetrahedron0 cube
 443         t1 = tetrahedron1 cube
 444
 445
 446 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 447 --   fourth indices of c-t1 have been switched. This is because we
 448 --   store the triangles oriented such that their volume is
 449 --   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 450 --   in opposite directions, one of them has to have negative volume!
 451 prop_c1200_identity2 :: Cube -> Bool
 452 prop_c1200_identity2 cube =
 453     c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
 454       where
 455         t0 = tetrahedron0 cube
 456         t1 = tetrahedron1 cube
 457
 458
 459 -- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
 460 --   fourth indices of c-t1 have been switched. This is because we
 461 --   store the triangles oriented such that their volume is
 462 --   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 463 --   in opposite directions, one of them has to have negative volume!
 464 prop_c2100_identity2 :: Cube -> Bool
 465 prop_c2100_identity2 cube =
 466     c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
 467       where
 468         t0 = tetrahedron0 cube
 469         t1 = tetrahedron1 cube
 470
 471
 472 -- | Given in Sorokina and Zeilfelder, p. 79.
 473 prop_c3000_identity :: Cube -> Bool
 474 prop_c3000_identity cube =
 475     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)
 476       where
 477         t0 = tetrahedron0 cube
 478         t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
 479
 480
 481 -- | Given in Sorokina and Zeilfelder, p. 79.
 482 prop_c2010_identity :: Cube -> Bool
 483 prop_c2010_identity cube =
 484     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)
 485       where
 486         t0 = tetrahedron0 cube
 487         t6 = tetrahedron6 cube
 488
 489
 490 -- | Given in Sorokina and Zeilfelder, p. 79.
 491 prop_c2001_identity :: Cube -> Bool
 492 prop_c2001_identity cube =
 493     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)
 494       where
 495         t0 = tetrahedron0 cube
 496         t6 = tetrahedron6 cube
 497
 498 -- | Given in Sorokina and Zeilfelder, p. 79.
 499 prop_c1020_identity :: Cube -> Bool
 500 prop_c1020_identity cube =
 501     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)
 502       where
 503         t0 = tetrahedron0 cube
 504         t6 = tetrahedron6 cube
 505
 506
 507 -- | Given in Sorokina and Zeilfelder, p. 79.
 508 prop_c1002_identity :: Cube -> Bool
 509 prop_c1002_identity cube =
 510     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)
 511       where
 512         t0 = tetrahedron0 cube
 513         t6 = tetrahedron6 cube
 514
 515
 516 -- | Given in Sorokina and Zeilfelder, p. 79.
 517 prop_c1011_identity :: Cube -> Bool
 518 prop_c1011_identity cube =
 519     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)
 520       where
 521         t0 = tetrahedron0 cube
 522         t6 = tetrahedron6 cube
 523
 524
 525
 526 -- | Given in Sorokina and Zeilfelder, p. 78.
 527 -- prop_cijk1_identity :: Cube -> Bool
 528 -- prop_cijk1_identity cube =
 529 --      and [ c t0 i j k 1 ~=
 530 --                  (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
 531 --                  (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
 532 --                  (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
 533 --                  (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
 534 --                                                       j <- [0..2],
 535 --                                                       k <- [0..2],
 536 --                                                       i + j + k == 2]
 537 --       where
 538 --         t0 = tetrahedron0 cube
 539 --         t1 = tetrahedron1 cube
 540
 541
 542
 543 -- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
 544 --   This test checks the rotation works as expected.
 545 prop_c_tilde_2100_rotation_correct :: Cube -> Bool
 546 prop_c_tilde_2100_rotation_correct cube =
 547     expr1 == expr2
 548     where
 549       t0 = tetrahedron0 cube
 550       t6 = tetrahedron6 cube
 551
 552       -- What gets computed for c2100 of t6.
 553       expr1 = eval (Tetrahedron.fv t6) $
 554           (3/8)*I +
 555           (1/12)*(T + R + L + D) +
 556           (1/64)*(FT + FR + FL + FD) +
 557           (7/48)*F +
 558           (1/48)*B +
 559           (1/96)*(RT + LD + LT + RD) +
 560           (1/192)*(BT + BR + BL + BD)
 561
 562       -- What should be computed for c2100 of t6.
 563       expr2 = eval (Tetrahedron.fv t0) $
 564               (3/8)*I +
 565               (1/12)*(F + R + L + B) +
 566               (1/64)*(FT + RT + LT + BT) +
 567               (7/48)*T +
 568               (1/48)*D +
 569               (1/96)*(FR + FL + BR + BL) +
 570               (1/192)*(FD + RD + LD + BD)
 571
 572
 573 -- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
 574 --   This test checks the actual value based on the FunctionValues of the cube.
 575 prop_c_tilde_2100_correct :: Cube -> Bool
 576 prop_c_tilde_2100_correct cube =
 577     c t6 2 1 0 0 == (3/8)*int + (1/12)*(f + r + l + b) + (1/64)*(ft + rt + lt + bt)
 578                               + (7/48)*t + (1/48)*d + (1/96)*(fr + fl + br + bl)
 579                               + (1/192)*(fd + rd + ld + bd)
 580     where
 581       t0 = tetrahedron0 cube
 582       t6 = tetrahedron6 cube
 583       fvs = Tetrahedron.fv t0
 584       int = interior fvs
 585       f = front fvs
 586       r = right fvs
 587       l = left fvs
 588       b = back fvs
 589       ft = front_top fvs
 590       rt = right_top fvs
 591       lt = left_top fvs
 592       bt = back_top fvs
 593       t = top fvs
 594       d = down fvs
 595       fr = front_right fvs
 596       fl = front_left fvs
 597       br = back_right fvs
 598       bl = back_left fvs
 599       fd = front_down fvs
 600       rd = right_down fvs
 601       ld = left_down fvs
 602       bd = back_down fvs
 603
 604 -- Tests to check that the correct edges are incidental.
 605 prop_t0_shares_edge_with_t1 :: Cube -> Bool
 606 prop_t0_shares_edge_with_t1 cube =
 607     (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
 608       where
 609         t0 = tetrahedron0 cube
 610         t1 = tetrahedron1 cube
 611
 612 prop_t0_shares_edge_with_t3 :: Cube -> Bool
 613 prop_t0_shares_edge_with_t3 cube =
 614     (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
 615       where
 616         t0 = tetrahedron0 cube
 617         t3 = tetrahedron3 cube
 618
 619 prop_t0_shares_edge_with_t6 :: Cube -> Bool
 620 prop_t0_shares_edge_with_t6 cube =
 621     (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
 622       where
 623         t0 = tetrahedron0 cube
 624         t6 = tetrahedron6 cube
 625
 626 prop_t1_shares_edge_with_t2 :: Cube -> Bool
 627 prop_t1_shares_edge_with_t2 cube =
 628     (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
 629       where
 630         t1 = tetrahedron1 cube
 631         t2 = tetrahedron2 cube
 632
 633 prop_t1_shares_edge_with_t19 :: Cube -> Bool
 634 prop_t1_shares_edge_with_t19 cube =
 635     (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
 636       where
 637         t1 = tetrahedron1 cube
 638         t19 = tetrahedron19 cube
 639
 640 prop_t2_shares_edge_with_t3 :: Cube -> Bool
 641 prop_t2_shares_edge_with_t3 cube =
 642     (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
 643       where
 644         t1 = tetrahedron1 cube
 645         t2 = tetrahedron2 cube
 646
 647 prop_t2_shares_edge_with_t12 :: Cube -> Bool
 648 prop_t2_shares_edge_with_t12 cube =
 649     (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
 650       where
 651         t2 = tetrahedron2 cube
 652         t12 = tetrahedron12 cube
 653
 654 prop_t3_shares_edge_with_t21 :: Cube -> Bool
 655 prop_t3_shares_edge_with_t21 cube =
 656     (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
 657       where
 658         t3 = tetrahedron3 cube
 659         t21 = tetrahedron21 cube
 660
 661 prop_t4_shares_edge_with_t5 :: Cube -> Bool
 662 prop_t4_shares_edge_with_t5 cube =
 663     (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
 664       where
 665         t4 = tetrahedron4 cube
 666         t5 = tetrahedron5 cube
 667
 668 prop_t4_shares_edge_with_t7 :: Cube -> Bool
 669 prop_t4_shares_edge_with_t7 cube =
 670     (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
 671       where
 672         t4 = tetrahedron4 cube
 673         t7 = tetrahedron7 cube
 674
 675 prop_t4_shares_edge_with_t10 :: Cube -> Bool
 676 prop_t4_shares_edge_with_t10 cube =
 677     (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
 678       where
 679         t4 = tetrahedron4 cube
 680         t10 = tetrahedron10 cube
 681
 682 prop_t5_shares_edge_with_t6 :: Cube -> Bool
 683 prop_t5_shares_edge_with_t6 cube =
 684     (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
 685       where
 686         t5 = tetrahedron5 cube
 687         t6 = tetrahedron6 cube
 688
 689 prop_t5_shares_edge_with_t16 :: Cube -> Bool
 690 prop_t5_shares_edge_with_t16 cube =
 691     (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
 692       where
 693         t5 = tetrahedron5 cube
 694         t16 = tetrahedron16 cube
 695
 696 prop_t6_shares_edge_with_t7 :: Cube -> Bool
 697 prop_t6_shares_edge_with_t7 cube =
 698     (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
 699       where
 700         t6 = tetrahedron6 cube
 701         t7 = tetrahedron7 cube
 702
 703 prop_t7_shares_edge_with_t20 :: Cube -> Bool
 704 prop_t7_shares_edge_with_t20 cube =
 705     (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
 706       where
 707         t7 = tetrahedron7 cube
 708         t20 = tetrahedron20 cube