Face.hs

   1 module Tests.Face
   2 where
   3
   4 import Control.Monad (unless)
   5 import Test.HUnit
   6 import Test.QuickCheck
   7
   8 import Comparisons
   9 import Face
  10 import Grid (Grid(h), make_grid)
  11 import Point
  12 import Tetrahedron
  13
  14
  15 -- HUnit tests.
  16
  17 -- | An HUnit assertion that wraps the almost_equals function. Stolen
  18 --   from the definition of assertEqual in Test/HUnit/Base.hs.
  19 assertAlmostEqual :: String -> Double -> Double -> Assertion
  20 assertAlmostEqual preface expected actual =
  21   unless (actual ~= expected) (assertFailure msg)
  22  where msg = (if null preface then "" else preface ++ "\n") ++
  23              "expected: " ++ show expected ++ "\n but got: " ++ show actual
  24
  25
  26 -- | An HUnit assertion that wraps the is_close function. Stolen
  27 --   from the definition of assertEqual in Test/HUnit/Base.hs.
  28 assertClose :: String -> Point -> Point -> Assertion
  29 assertClose preface expected actual =
  30   unless (actual `is_close` expected) (assertFailure msg)
  31  where msg = (if null preface then "" else preface ++ "\n") ++
  32              "expected: " ++ show expected ++ "\n but got: " ++ show actual
  33
  34
  35 -- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at nine
  36 --   points (hi, hj, jk) with h = 1. From example one in the paper.
  37 --   Used in the next bunch of tests.
  38 trilinear :: [[[Double]]]
  39 trilinear = [ [ [ 1, 2, 3 ],
  40                 [ 1, 3, 5 ],
  41                 [ 1, 4, 7 ] ],
  42               [ [ 1, 2, 3 ],
  43                 [ 1, 4, 7 ],
  44                 [ 1, 6, 11 ] ],
  45               [ [ 1, 2, 3 ],
  46                 [ 1, 5, 9 ],
  47                 [ 1, 8, 15 ]]]
  48
  49 -- | Check the value of c0030 for any tetrahedron belonging to the
  50 --   cube centered on (1,1,1) with a grid constructed from the
  51 --   trilinear values. See example one in the paper.
  52 -- test_trilinear_c0030 :: Test
  53 -- test_trilinear_c0030 =
  54 --     TestCase $ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  55 --       where
  56 --         g = make_grid 1 trilinear
  57 --         cube = cube_at g 1 1 1
  58 --         t = head (tetrahedrons cube) -- Any one will do.
  59
  60
  61 -- -- | Check the value of c0003 for any tetrahedron belonging to the
  62 -- --   cube centered on (1,1,1) with a grid constructed from the
  63 -- --   trilinear values. See example one in the paper.
  64 -- test_trilinear_c0003 :: Test
  65 -- test_trilinear_c0003 =
  66 --     TestCase $ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  67 --       where
  68 --         g = make_grid 1 trilinear
  69 --         cube = cube_at g 1 1 1
  70 --         t = head (tetrahedrons cube) -- Any one will do.
  71
  72
  73 -- -- | Check the value of c0021 for any tetrahedron belonging to the
  74 -- --   cube centered on (1,1,1) with a grid constructed from the
  75 -- --   trilinear values. See example one in the paper.
  76 -- test_trilinear_c0021 :: Test
  77 -- test_trilinear_c0021 =
  78 --     TestCase $ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  79 --       where
  80 --         g = make_grid 1 trilinear
  81 --         cube = cube_at g 1 1 1
  82 --         t = head (tetrahedrons cube) -- Any one will do.
  83
  84
  85 -- -- | Check the value of c0012 for any tetrahedron belonging to the
  86 -- --   cube centered on (1,1,1) with a grid constructed from the
  87 -- --   trilinear values. See example one in the paper.
  88 -- test_trilinear_c0012 :: Test
  89 -- test_trilinear_c0012 =
  90 --     TestCase $ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  91 --       where
  92 --         g = make_grid 1 trilinear
  93 --         cube = cube_at g 1 1 1
  94 --         t = head (tetrahedrons cube) -- Any one will do.
  95
  96
  97 -- -- | Check the value of c0120 for any tetrahedron belonging to the
  98 -- --   cube centered on (1,1,1) with a grid constructed from the
  99 -- --   trilinear values. See example one in the paper.
 100 -- test_trilinear_c0120 :: Test
 101 -- test_trilinear_c0120 =
 102 --     TestCase $ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
 103 --       where
 104 --         g = make_grid 1 trilinear
 105 --         cube = cube_at g 1 1 1
 106 --         t = head (tetrahedrons cube) -- Any one will do.
 107
 108
 109 -- -- | Check the value of c0102 for any tetrahedron belonging to the
 110 -- --   cube centered on (1,1,1) with a grid constructed from the
 111 -- --   trilinear values. See example one in the paper.
 112 -- test_trilinear_c0102 :: Test
 113 -- test_trilinear_c0102 =
 114 --     TestCase $ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
 115 --       where
 116 --         g = make_grid 1 trilinear
 117 --         cube = cube_at g 1 1 1
 118 --         t = head (tetrahedrons cube) -- Any one will do.
 119
 120
 121 -- -- | Check the value of c0111 for any tetrahedron belonging to the
 122 -- --   cube centered on (1,1,1) with a grid constructed from the
 123 -- --   trilinear values. See example one in the paper.
 124 -- test_trilinear_c0111 :: Test
 125 -- test_trilinear_c0111 =
 126 --     TestCase $ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
 127 --       where
 128 --         g = make_grid 1 trilinear
 129 --         cube = cube_at g 1 1 1
 130 --         t = head (tetrahedrons cube) -- Any one will do.
 131
 132
 133 -- -- | Check the value of c0210 for any tetrahedron belonging to the
 134 -- --   cube centered on (1,1,1) with a grid constructed from the
 135 -- --   trilinear values. See example one in the paper.
 136 -- test_trilinear_c0210 :: Test
 137 -- test_trilinear_c0210 =
 138 --     TestCase $ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
 139 --       where
 140 --         g = make_grid 1 trilinear
 141 --         cube = cube_at g 1 1 1
 142 --         t = head (tetrahedrons cube) -- Any one will do.
 143
 144
 145 -- -- | Check the value of c0201 for any tetrahedron belonging to the
 146 -- --   cube centered on (1,1,1) with a grid constructed from the
 147 -- --   trilinear values. See example one in the paper.
 148 -- test_trilinear_c0201 :: Test
 149 -- test_trilinear_c0201 =
 150 --     TestCase $ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
 151 --       where
 152 --         g = make_grid 1 trilinear
 153 --         cube = cube_at g 1 1 1
 154 --         t = head (tetrahedrons cube) -- Any one will do.
 155
 156
 157 -- -- | Check the value of c0300 for any tetrahedron belonging to the
 158 -- --   cube centered on (1,1,1) with a grid constructed from the
 159 -- --   trilinear values. See example one in the paper.
 160 -- test_trilinear_c0300 :: Test
 161 -- test_trilinear_c0300 =
 162 --     TestCase $ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
 163 --       where
 164 --         g = make_grid 1 trilinear
 165 --         cube = cube_at g 1 1 1
 166 --         t = head (tetrahedrons cube) -- Any one will do.
 167
 168
 169 -- -- | Check the value of c1020 for any tetrahedron belonging to the
 170 -- --   cube centered on (1,1,1) with a grid constructed from the
 171 -- --   trilinear values. See example one in the paper.
 172 -- test_trilinear_c1020 :: Test
 173 -- test_trilinear_c1020 =
 174 --     TestCase $ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
 175 --       where
 176 --         g = make_grid 1 trilinear
 177 --         cube = cube_at g 1 1 1
 178 --         t = head (tetrahedrons cube) -- Any one will do.
 179
 180
 181 -- -- | Check the value of c1002 for any tetrahedron belonging to the
 182 -- --   cube centered on (1,1,1) with a grid constructed from the
 183 -- --   trilinear values. See example one in the paper.
 184 -- test_trilinear_c1002 :: Test
 185 -- test_trilinear_c1002 =
 186 --     TestCase $ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
 187 --       where
 188 --         g = make_grid 1 trilinear
 189 --         cube = cube_at g 1 1 1
 190 --         t = head (tetrahedrons cube) -- Any one will do.
 191
 192
 193 -- -- | Check the value of c1011 for any tetrahedron belonging to the
 194 -- --   cube centered on (1,1,1) with a grid constructed from the
 195 -- --   trilinear values. See example one in the paper.
 196 -- test_trilinear_c1011 :: Test
 197 -- test_trilinear_c1011 =
 198 --     TestCase $ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
 199 --       where
 200 --         g = make_grid 1 trilinear
 201 --         cube = cube_at g 1 1 1
 202 --         t = head (tetrahedrons cube) -- Any one will do.
 203
 204
 205 -- -- | Check the value of c1110 for any tetrahedron belonging to the
 206 -- --   cube centered on (1,1,1) with a grid constructed from the
 207 -- --   trilinear values. See example one in the paper.
 208 -- test_trilinear_c1110 :: Test
 209 -- test_trilinear_c1110 =
 210 --     TestCase $ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
 211 --       where
 212 --         g = make_grid 1 trilinear
 213 --         cube = cube_at g 1 1 1
 214 --         t = head (tetrahedrons cube) -- Any one will do.
 215
 216
 217 -- -- | Check the value of c1101 for any tetrahedron belonging to the
 218 -- --   cube centered on (1,1,1) with a grid constructed from the
 219 -- --   trilinear values. See example one in the paper.
 220 -- test_trilinear_c1101 :: Test
 221 -- test_trilinear_c1101 =
 222 --     TestCase $ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
 223 --       where
 224 --         g = make_grid 1 trilinear
 225 --         cube = cube_at g 1 1 1
 226 --         t = head (tetrahedrons cube) -- Any one will do.
 227
 228
 229 -- -- | Check the value of c1200 for any tetrahedron belonging to the
 230 -- --   cube centered on (1,1,1) with a grid constructed from the
 231 -- --   trilinear values. See example one in the paper.
 232 -- test_trilinear_c1200 :: Test
 233 -- test_trilinear_c1200 =
 234 --     TestCase $ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
 235 --       where
 236 --         g = make_grid 1 trilinear
 237 --         cube = cube_at g 1 1 1
 238 --         t = head (tetrahedrons cube) -- Any one will do.
 239
 240
 241 -- -- | Check the value of c2010 for any tetrahedron belonging to the
 242 -- --   cube centered on (1,1,1) with a grid constructed from the
 243 -- --   trilinear values. See example one in the paper.
 244 -- test_trilinear_c2010 :: Test
 245 -- test_trilinear_c2010 =
 246 --     TestCase $ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
 247 --       where
 248 --         g = make_grid 1 trilinear
 249 --         cube = cube_at g 1 1 1
 250 --         t = head (tetrahedrons cube) -- Any one will do.
 251
 252
 253 -- -- | Check the value of c2001 for any tetrahedron belonging to the
 254 -- --   cube centered on (1,1,1) with a grid constructed from the
 255 -- --   trilinear values. See example one in the paper.
 256 -- test_trilinear_c2001 :: Test
 257 -- test_trilinear_c2001 =
 258 --     TestCase $ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
 259 --       where
 260 --         g = make_grid 1 trilinear
 261 --         cube = cube_at g 1 1 1
 262 --         t = head (tetrahedrons cube) -- Any one will do.
 263
 264
 265 -- -- | Check the value of c2100 for any tetrahedron belonging to the
 266 -- --   cube centered on (1,1,1) with a grid constructed from the
 267 -- --   trilinear values. See example one in the paper.
 268 -- test_trilinear_c2100 :: Test
 269 -- test_trilinear_c2100 =
 270 --     TestCase $ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
 271 --       where
 272 --         g = make_grid 1 trilinear
 273 --         cube = cube_at g 1 1 1
 274 --         t = head (tetrahedrons cube) -- Any one will do.
 275
 276
 277 -- -- | Check the value of c3000 for any tetrahedron belonging to the
 278 -- --   cube centered on (1,1,1) with a grid constructed from the
 279 -- --   trilinear values. See example one in the paper.
 280 -- -- test_trilinear_c3000 :: Test
 281 -- -- test_trilinear_c3000 =
 282 -- --     TestCase $ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 283 -- --       where
 284 -- --         g = make_grid 1 trilinear
 285 -- --         cube = cube_at g 1 1 1
 286 -- --         t = head (tetrahedrons cube) -- Any one will do.
 287
 288
 289
 290 -- -- test_trilinear_f0_t0_v0 :: Test
 291 -- -- test_trilinear_f0_t0_v0 =
 292 -- --     TestCase $ assertClose "v0 is correct" (v0 t) (0.5, 1.5, 1.5)
 293 -- --       where
 294 -- --         g = make_grid 1 trilinear
 295 -- --         cube = cube_at g 1 1 1
 296 -- --         t = tetrahedron0 (face0 cube) -- Any one will do.
 297
 298
 299 -- -- test_trilinear_f0_t0_v1 :: Test
 300 -- -- test_trilinear_f0_t0_v1 =
 301 -- --     TestCase $ assertClose "v1 is correct" (v1 t) (1.5, 1.5, 1.5)
 302 -- --       where
 303 -- --         g = make_grid 1 trilinear
 304 -- --         cube = cube_at g 1 1 1
 305 -- --         t = tetrahedron0 (face0 cube) -- Any one will do.
 306
 307
 308 -- -- test_trilinear_f0_t0_v2 :: Test
 309 -- -- test_trilinear_f0_t0_v2 =
 310 -- --     TestCase $ assertClose "v2 is correct" (v2 t) (1, 1, 1.5)
 311 -- --       where
 312 -- --         g = make_grid 1 trilinear
 313 -- --         cube = cube_at g 1 1 1
 314 -- --         t = tetrahedron0 (face0 cube) -- Any one will do.
 315
 316
 317
 318 -- -- test_trilinear_f0_t0_v3 :: Test
 319 -- -- test_trilinear_f0_t0_v3 =
 320 -- --     TestCase $ assertClose "v3 is correct" (v3 t) (1, 1, 1)
 321 -- --       where
 322 -- --         g = make_grid 1 trilinear
 323 -- --         cube = cube_at g 1 1 1
 324 -- --         t = tetrahedron0 (face0 cube) -- Any one will do.
 325
 326
 327
 328 -- face_tests :: [Test]
 329 face_tests = []
 330 -- face_tests = [test_trilinear_c0030,
 331 --               test_trilinear_c0003,
 332 --               test_trilinear_c0021,
 333 --               test_trilinear_c0012,
 334 --               test_trilinear_c0120,
 335 --               test_trilinear_c0102,
 336 --               test_trilinear_c0111,
 337 --               test_trilinear_c0210,
 338 --               test_trilinear_c0201,
 339 --               test_trilinear_c0300,
 340 --               test_trilinear_c1020,
 341 --               test_trilinear_c1002,
 342 --               test_trilinear_c1011,
 343 --               test_trilinear_c1110,
 344 --               test_trilinear_c1101,
 345 --               test_trilinear_c1200,
 346 --               test_trilinear_c2010,
 347 --               test_trilinear_c2001,
 348 --               test_trilinear_c2100,
 349 --               test_trilinear_c3000,
 350 --               test_trilinear_f0_t0_v0,
 351 --               test_trilinear_f0_t0_v1,
 352 --               test_trilinear_f0_t0_v2,
 353 --               test_trilinear_f0_t0_v3]
 354
 355
 356 -- -- QuickCheck Tests.
 357
 358
 359 -- -- | Given in Sorokina and Zeilfelder, p. 78.
 360 -- prop_cijk1_identity :: Cube -> Bool
 361 -- prop_cijk1_identity cube =
 362 --      and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
 363 --                             (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
 364 --                             (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
 365 --                             (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
 366 --                                                                     j <- [0..2],
 367 --                                                                     k <- [0..2],
 368 --                                                                     i + j + k == 2]
 369 --       where
 370 --         t0 = tetrahedron0 (face0 cube)
 371 --         t1 = tetrahedron1 (face0 cube)
 372 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 373 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 374
 375 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 376 -- prop_c0120_identity1 :: Cube -> Bool
 377 -- prop_c0120_identity1 cube =
 378 --     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
 379 --       where
 380 --         t0 = tetrahedron0 (face0 cube)
 381 --         t1 = tetrahedron1 (face0 cube)
 382 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 383 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 384
 385
 386 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 387 -- prop_c0210_identity1 :: Cube -> Bool
 388 -- prop_c0210_identity1 cube =
 389 --     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
 390 --       where
 391 --         t0 = tetrahedron0 (face0 cube)
 392 --         t1 = tetrahedron1 (face0 cube)
 393 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 394 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 395
 396
 397 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 398 -- prop_c0300_identity1 :: Cube -> Bool
 399 -- prop_c0300_identity1 cube =
 400 --     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
 401 --       where
 402 --         t0 = tetrahedron0 (face0 cube)
 403 --         t1 = tetrahedron1 (face0 cube)
 404 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 405 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 406
 407 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 408 -- prop_c1110_identity :: Cube -> Bool
 409 -- prop_c1110_identity cube =
 410 --     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 411 --       where
 412 --         t0 = tetrahedron0 (face0 cube)
 413 --         t1 = tetrahedron1 (face0 cube)
 414 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 415 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 416
 417
 418 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 419 -- prop_c1200_identity1 :: Cube -> Bool
 420 -- prop_c1200_identity1 cube =
 421 --     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
 422 --       where
 423 --         t0 = tetrahedron0 (face0 cube)
 424 --         t1 = tetrahedron1 (face0 cube)
 425 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 426 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 427
 428
 429 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 430 -- prop_c2100_identity1 :: Cube -> Bool
 431 -- prop_c2100_identity1 cube =
 432 --     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
 433 --       where
 434 --         t0 = tetrahedron0 (face0 cube)
 435 --         t1 = tetrahedron1 (face0 cube)
 436 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 437 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 438
 439
 440 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 441 -- prop_c0102_identity1 :: Cube -> Bool
 442 -- prop_c0102_identity1 cube =
 443 --     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
 444 --       where
 445 --         t0 = tetrahedron0 (face0 cube)
 446 --         t3 = tetrahedron3 (face0 cube)
 447 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 448 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 449
 450
 451 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 452 -- prop_c0201_identity1 :: Cube -> Bool
 453 -- prop_c0201_identity1 cube =
 454 --     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
 455 --       where
 456 --         t0 = tetrahedron0 (face0 cube)
 457 --         t3 = tetrahedron3 (face0 cube)
 458 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 459 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 460
 461
 462 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 463 -- prop_c0300_identity2 :: Cube -> Bool
 464 -- prop_c0300_identity2 cube =
 465 --     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
 466 --       where
 467 --         t0 = tetrahedron0 (face0 cube)
 468 --         t3 = tetrahedron3 (face0 cube)
 469 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 470 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 471
 472 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 473 -- prop_c1101_identity :: Cube -> Bool
 474 -- prop_c1101_identity cube =
 475 --     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
 476 --       where
 477 --         t0 = tetrahedron0 (face0 cube)
 478 --         t3 = tetrahedron3 (face0 cube)
 479 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 480 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 481
 482
 483 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 484 -- prop_c1200_identity2 :: Cube -> Bool
 485 -- prop_c1200_identity2 cube =
 486 --     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
 487 --       where
 488 --         t0 = tetrahedron0 (face0 cube)
 489 --         t3 = tetrahedron3 (face0 cube)
 490 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 491 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 492
 493
 494 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 495 -- prop_c2100_identity2 :: Cube -> Bool
 496 -- prop_c2100_identity2 cube =
 497 --     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
 498 --       where
 499 --         t0 = tetrahedron0 (face0 cube)
 500 --         t3 = tetrahedron3 (face0 cube)
 501 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 502 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 503
 504
 505 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 506 -- prop_c3000_identity :: Cube -> Bool
 507 -- prop_c3000_identity cube =
 508 --     c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
 509 --       where
 510 --         t0 = tetrahedron0 (face0 cube)
 511 --         t2 = tetrahedron2 (face5 cube)
 512 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 513 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 514
 515
 516 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 517 -- prop_c2010_identity :: Cube -> Bool
 518 -- prop_c2010_identity cube =
 519 --     c t0' 2 0 1 0 ~= c t0' 1 1 1 0 + c t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
 520 --       where
 521 --         t0 = tetrahedron0 (face0 cube)
 522 --         t2 = tetrahedron2 (face5 cube)
 523 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 524 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 525
 526
 527 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 528 -- prop_c2001_identity :: Cube -> Bool
 529 -- prop_c2001_identity cube =
 530 --     c t0' 2 0 0 1 ~= c t0' 1 1 0 1 + c t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
 531 --       where
 532 --         t0 = tetrahedron0 (face0 cube)
 533 --         t2 = tetrahedron2 (face5 cube)
 534 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 535 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 536
 537 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 538 -- prop_c1020_identity :: Cube -> Bool
 539 -- prop_c1020_identity cube =
 540 --     c t0' 1 0 2 0 ~= c t0' 0 1 2 0 + c t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
 541 --       where
 542 --         t0 = tetrahedron0 (face0 cube)
 543 --         t2 = tetrahedron2 (face5 cube)
 544 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 545 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 546
 547
 548 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 549 -- prop_c1002_identity :: Cube -> Bool
 550 -- prop_c1002_identity cube =
 551 --     c t0' 1 0 0 2 ~= c t0' 0 1 0 2 + c t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
 552 --       where
 553 --         t0 = tetrahedron0 (face0 cube)
 554 --         t2 = tetrahedron2 (face5 cube)
 555 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 556 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 557
 558
 559 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 560 -- prop_c1011_identity :: Cube -> Bool
 561 -- prop_c1011_identity cube =
 562 --     c t0' 1 0 1 1 ~= c t0' 0 1 1 1 + c t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
 563 --       where
 564 --         t0 = tetrahedron0 (face0 cube)
 565 --         t2 = tetrahedron2 (face5 cube)
 566 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 567 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 568
 569
 570 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 571 -- prop_c0120_identity2 :: Cube -> Bool
 572 -- prop_c0120_identity2 cube =
 573 --         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 574 --       where
 575 --         t0 = tetrahedron0 (face0 cube)
 576 --         t1 = tetrahedron0 (face2 (top cube))
 577 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 578 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 579
 580
 581 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 582 -- prop_c0102_identity2 :: Cube -> Bool
 583 -- prop_c0102_identity2 cube =
 584 --     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 585 --       where
 586 --         t0 = tetrahedron0 (face0 cube)
 587 --         t1 = tetrahedron0 (face2 (top cube))
 588 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 589 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 590
 591
 592 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 593 -- prop_c0111_identity :: Cube -> Bool
 594 -- prop_c0111_identity cube =
 595 --     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 596 --       where
 597 --         t0 = tetrahedron0 (face0 cube)
 598 --         t1 = tetrahedron0 (face2 (top cube))
 599 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 600 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 601
 602
 603 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 604 -- prop_c0210_identity2 :: Cube -> Bool
 605 -- prop_c0210_identity2 cube =
 606 --     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 607 --       where
 608 --         t0 = tetrahedron0 (face0 cube)
 609 --         t1 = tetrahedron0 (face2 (top cube))
 610 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 611 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 612
 613
 614 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 615 -- prop_c0201_identity2 :: Cube -> Bool
 616 -- prop_c0201_identity2 cube =
 617 --     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 618 --       where
 619 --         t0 = tetrahedron0 (face0 cube)
 620 --         t1 = tetrahedron0 (face2 (top cube))
 621 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 622 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 623
 624
 625 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 626 -- prop_c0300_identity3 :: Cube -> Bool
 627 -- prop_c0300_identity3 cube =
 628 --     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 629 --       where
 630 --         t0 = tetrahedron0 (face0 cube)
 631 --         t1 = tetrahedron0 (face2 (top cube))
 632 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 633 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)