src/Tests/Grid.hs

   1 module Tests.Grid
   2 where
   3
   4 import Data.Maybe (fromJust)
   5 import Test.HUnit
   6
   7 import Assertions
   8 import Comparisons
   9 import Cube hiding (i, j, k)
  10 import Examples
  11 import FunctionValues (value_at)
  12 import Grid
  13 import Tetrahedron
  14
  15
  16 -- | Check the value of c0030 for tetrahedron0 belonging to the
  17 --   cube centered on (1,1,1) with a grid constructed from the
  18 --   trilinear values. See example one in the paper.
  19 test_trilinear_c0030 :: Assertion
  20 test_trilinear_c0030 =
  21     assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  22       where
  23         g = make_grid 1 trilinear
  24         cube = fromJust $ cube_at g 1 1 1
  25         t = tetrahedron0 cube
  26
  27
  28 -- | Check the value of c0003 for tetrahedron0 belonging to the
  29 --   cube centered on (1,1,1) with a grid constructed from the
  30 --   trilinear values. See example one in the paper.
  31 test_trilinear_c0003 :: Assertion
  32 test_trilinear_c0003 =
  33     assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  34       where
  35         g = make_grid 1 trilinear
  36         cube = fromJust $ cube_at g 1 1 1
  37         t = tetrahedron0 cube
  38
  39
  40 -- | Check the value of c0021 for tetrahedron0 belonging to the
  41 --   cube centered on (1,1,1) with a grid constructed from the
  42 --   trilinear values. See example one in the paper.
  43 test_trilinear_c0021 :: Assertion
  44 test_trilinear_c0021 =
  45     assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  46       where
  47         g = make_grid 1 trilinear
  48         cube = fromJust $ cube_at g 1 1 1
  49         t = tetrahedron0 cube
  50
  51
  52 -- | Check the value of c0012 for tetrahedron0 belonging to the
  53 --   cube centered on (1,1,1) with a grid constructed from the
  54 --   trilinear values. See example one in the paper.
  55 test_trilinear_c0012 :: Assertion
  56 test_trilinear_c0012 =
  57     assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  58       where
  59         g = make_grid 1 trilinear
  60         cube = fromJust $ cube_at g 1 1 1
  61         t = tetrahedron0 cube
  62
  63
  64 -- | Check the value of c0120 for tetrahedron0 belonging to the
  65 --   cube centered on (1,1,1) with a grid constructed from the
  66 --   trilinear values. See example one in the paper.
  67 test_trilinear_c0120 :: Assertion
  68 test_trilinear_c0120 =
  69     assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
  70       where
  71         g = make_grid 1 trilinear
  72         cube = fromJust $ cube_at g 1 1 1
  73         t = tetrahedron0 cube
  74
  75
  76 -- | Check the value of c0102 for tetrahedron0 belonging to the
  77 --   cube centered on (1,1,1) with a grid constructed from the
  78 --   trilinear values. See example one in the paper.
  79 test_trilinear_c0102 :: Assertion
  80 test_trilinear_c0102 =
  81     assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
  82       where
  83         g = make_grid 1 trilinear
  84         cube = fromJust $ cube_at g 1 1 1
  85         t = tetrahedron0 cube
  86
  87
  88 -- | Check the value of c0111 for tetrahedron0 belonging to the
  89 --   cube centered on (1,1,1) with a grid constructed from the
  90 --   trilinear values. See example one in the paper.
  91 test_trilinear_c0111 :: Assertion
  92 test_trilinear_c0111 =
  93     assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
  94       where
  95         g = make_grid 1 trilinear
  96         cube = fromJust $ cube_at g 1 1 1
  97         t = tetrahedron0 cube
  98
  99
 100 -- | Check the value of c0210 for tetrahedron0 belonging to the
 101 --   cube centered on (1,1,1) with a grid constructed from the
 102 --   trilinear values. See example one in the paper.
 103 test_trilinear_c0210 :: Assertion
 104 test_trilinear_c0210 =
 105     assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
 106       where
 107         g = make_grid 1 trilinear
 108         cube = fromJust $ cube_at g 1 1 1
 109         t = tetrahedron0 cube
 110
 111
 112 -- | Check the value of c0201 for tetrahedron0 belonging to the
 113 --   cube centered on (1,1,1) with a grid constructed from the
 114 --   trilinear values. See example one in the paper.
 115 test_trilinear_c0201 :: Assertion
 116 test_trilinear_c0201 =
 117     assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
 118       where
 119         g = make_grid 1 trilinear
 120         cube = fromJust $ cube_at g 1 1 1
 121         t = tetrahedron0 cube
 122
 123
 124 -- | Check the value of c0300 for tetrahedron0 belonging to the
 125 --   cube centered on (1,1,1) with a grid constructed from the
 126 --   trilinear values. See example one in the paper.
 127 test_trilinear_c0300 :: Assertion
 128 test_trilinear_c0300 =
 129     assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
 130       where
 131         g = make_grid 1 trilinear
 132         cube = fromJust $ cube_at g 1 1 1
 133         t = tetrahedron0 cube
 134
 135
 136 -- | Check the value of c1020 for tetrahedron0 belonging to the
 137 --   cube centered on (1,1,1) with a grid constructed from the
 138 --   trilinear values. See example one in the paper.
 139 test_trilinear_c1020 :: Assertion
 140 test_trilinear_c1020 =
 141     assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
 142       where
 143         g = make_grid 1 trilinear
 144         cube = fromJust $ cube_at g 1 1 1
 145         t = tetrahedron0 cube
 146
 147
 148 -- | Check the value of c1002 for tetrahedron0 belonging to the
 149 --   cube centered on (1,1,1) with a grid constructed from the
 150 --   trilinear values. See example one in the paper.
 151 test_trilinear_c1002 :: Assertion
 152 test_trilinear_c1002 =
 153     assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
 154       where
 155         g = make_grid 1 trilinear
 156         cube = fromJust $ cube_at g 1 1 1
 157         t = tetrahedron0 cube
 158
 159
 160 -- | Check the value of c1011 for tetrahedron0 belonging to the
 161 --   cube centered on (1,1,1) with a grid constructed from the
 162 --   trilinear values. See example one in the paper.
 163 test_trilinear_c1011 :: Assertion
 164 test_trilinear_c1011 =
 165     assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
 166       where
 167         g = make_grid 1 trilinear
 168         cube = fromJust $ cube_at g 1 1 1
 169         t = tetrahedron0 cube
 170
 171
 172 -- | Check the value of c1110 for tetrahedron0 belonging to the
 173 --   cube centered on (1,1,1) with a grid constructed from the
 174 --   trilinear values. See example one in the paper.
 175 test_trilinear_c1110 :: Assertion
 176 test_trilinear_c1110 =
 177     assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
 178       where
 179         g = make_grid 1 trilinear
 180         cube = fromJust $ cube_at g 1 1 1
 181         t = tetrahedron0 cube
 182
 183
 184 -- | Check the value of c1101 for tetrahedron0 belonging to the
 185 --   cube centered on (1,1,1) with a grid constructed from the
 186 --   trilinear values. See example one in the paper.
 187 test_trilinear_c1101 :: Assertion
 188 test_trilinear_c1101 =
 189     assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
 190       where
 191         g = make_grid 1 trilinear
 192         cube = fromJust $ cube_at g 1 1 1
 193         t = tetrahedron0 cube
 194
 195
 196 -- | Check the value of c1200 for tetrahedron0 belonging to the
 197 --   cube centered on (1,1,1) with a grid constructed from the
 198 --   trilinear values. See example one in the paper.
 199 test_trilinear_c1200 :: Assertion
 200 test_trilinear_c1200 =
 201     assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
 202       where
 203         g = make_grid 1 trilinear
 204         cube = fromJust $ cube_at g 1 1 1
 205         t = tetrahedron0 cube
 206
 207
 208 -- | Check the value of c2010 for tetrahedron0 belonging to the
 209 --   cube centered on (1,1,1) with a grid constructed from the
 210 --   trilinear values. See example one in the paper.
 211 test_trilinear_c2010 :: Assertion
 212 test_trilinear_c2010 =
 213     assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
 214       where
 215         g = make_grid 1 trilinear
 216         cube = fromJust $ cube_at g 1 1 1
 217         t = tetrahedron0 cube
 218
 219
 220 -- | Check the value of c2001 for tetrahedron0 belonging to the
 221 --   cube centered on (1,1,1) with a grid constructed from the
 222 --   trilinear values. See example one in the paper.
 223 test_trilinear_c2001 :: Assertion
 224 test_trilinear_c2001 =
 225     assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
 226       where
 227         g = make_grid 1 trilinear
 228         cube = fromJust $ cube_at g 1 1 1
 229         t = tetrahedron0 cube
 230
 231
 232 -- | Check the value of c2100 for tetrahedron0 belonging to the
 233 --   cube centered on (1,1,1) with a grid constructed from the
 234 --   trilinear values. See example one in the paper.
 235 test_trilinear_c2100 :: Assertion
 236 test_trilinear_c2100 =
 237     assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
 238       where
 239         g = make_grid 1 trilinear
 240         cube = fromJust $ cube_at g 1 1 1
 241         t = tetrahedron0 cube
 242
 243
 244 -- | Check the value of c3000 for tetrahedron0 belonging to the
 245 --   cube centered on (1,1,1) with a grid constructed from the
 246 --   trilinear values. See example one in the paper.
 247 test_trilinear_c3000 :: Assertion
 248 test_trilinear_c3000 =
 249     assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 250       where
 251         g = make_grid 1 trilinear
 252         cube = fromJust $ cube_at g 1 1 1
 253         t = tetrahedron0 cube
 254
 255
 256 -- | Make sure that v0 of tetrahedron0 belonging to the cube centered
 257 --   on (1,1,1) with a grid constructed from the trilinear values
 258 --   winds up in the right place. See example one in the paper.
 259 test_trilinear_f0_t0_v0 :: Assertion
 260 test_trilinear_f0_t0_v0 =
 261     assertEqual "v0 is correct" (v0 t) (1, 1, 1)
 262       where
 263         g = make_grid 1 trilinear
 264         cube = fromJust $ cube_at g 1 1 1
 265         t = tetrahedron0 cube
 266
 267
 268 -- | Make sure that v1 of tetrahedron0 belonging to the cube centered
 269 --   on (1,1,1) with a grid constructed from the trilinear values
 270 --   winds up in the right place. See example one in the paper.
 271 test_trilinear_f0_t0_v1 :: Assertion
 272 test_trilinear_f0_t0_v1 =
 273     assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
 274       where
 275         g = make_grid 1 trilinear
 276         cube = fromJust $ cube_at g 1 1 1
 277         t = tetrahedron0 cube
 278
 279
 280 -- | Make sure that v2 of tetrahedron0 belonging to the cube centered
 281 --   on (1,1,1) with a grid constructed from the trilinear values
 282 --   winds up in the right place. See example one in the paper.
 283 test_trilinear_f0_t0_v2 :: Assertion
 284 test_trilinear_f0_t0_v2 =
 285     assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
 286       where
 287         g = make_grid 1 trilinear
 288         cube = fromJust $ cube_at g 1 1 1
 289         t = tetrahedron0 cube
 290
 291
 292 -- | Make sure that v3 of tetrahedron0 belonging to the cube centered
 293 --   on (1,1,1) with a grid constructed from the trilinear values
 294 --   winds up in the right place. See example one in the paper.
 295 test_trilinear_f0_t0_v3 :: Assertion
 296 test_trilinear_f0_t0_v3 =
 297     assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
 298       where
 299         g = make_grid 1 trilinear
 300         cube = fromJust $ cube_at g 1 1 1
 301         t = tetrahedron0 cube
 302
 303
 304 test_trilinear_reproduced_t0 :: Assertion
 305 test_trilinear_reproduced_t0 =
 306     assertTrue "trilinears are reproduced correctly" $
 307              and [p (i', j', k') ~= value_at trilinear i j k
 308                     | i <- [0..2],
 309                       j <- [0..2],
 310                       k <- [0..2],
 311                       let i' = fromIntegral i,
 312                       let j' = fromIntegral j,
 313                       let k' = fromIntegral k]
 314     where
 315       g = make_grid 1 trilinear
 316       c0 = fromJust $ cube_at g 1 1 1
 317       t0 = tetrahedron0 c0
 318       p = polynomial t0
 319
 320 test_trilinear_reproduced_t1 :: Assertion
 321 test_trilinear_reproduced_t1 =
 322     assertTrue "trilinears are reproduced correctly" $
 323              and [p (i', j', k') ~= value_at trilinear i j k
 324                     | i <- [0..2],
 325                       j <- [0..2],
 326                       k <- [0..2],
 327                       let i' = fromIntegral i,
 328                       let j' = fromIntegral j,
 329                       let k' = fromIntegral k]
 330     where
 331       g = make_grid 1 trilinear
 332       c0 = fromJust $ cube_at g 1 1 1
 333       t1 = tetrahedron1 c0
 334       p = polynomial t1
 335
 336 test_trilinear_reproduced_t2 :: Assertion
 337 test_trilinear_reproduced_t2 =
 338     assertTrue "trilinears are reproduced correctly" $
 339              and [p (i', j', k') ~= value_at trilinear i j k
 340                     | i <- [0..2],
 341                       j <- [0..2],
 342                       k <- [0..2],
 343                       let i' = fromIntegral i,
 344                       let j' = fromIntegral j,
 345                       let k' = fromIntegral k]
 346     where
 347       g = make_grid 1 trilinear
 348       c0 = fromJust $ cube_at g 1 1 1
 349       t2 = tetrahedron2 c0
 350       p = polynomial t2
 351
 352 test_trilinear_reproduced_t3 :: Assertion
 353 test_trilinear_reproduced_t3 =
 354     assertTrue "trilinears are reproduced correctly" $
 355              and [p (i', j', k') ~= value_at trilinear i j k
 356                     | i <- [0..2],
 357                       j <- [0..2],
 358                       k <- [0..2],
 359                       let i' = fromIntegral i,
 360                       let j' = fromIntegral j,
 361                       let k' = fromIntegral k]
 362     where
 363       g = make_grid 1 trilinear
 364       c0 = fromJust $ cube_at g 1 1 1
 365       t3 = tetrahedron3 c0
 366       p = polynomial t3
 367
 368 test_trilinear_reproduced_t4 :: Assertion
 369 test_trilinear_reproduced_t4 =
 370     assertTrue "trilinears are reproduced correctly" $
 371              and [p (i', j', k') ~= value_at trilinear i j k
 372                     | i <- [0..2],
 373                       j <- [0..2],
 374                       k <- [0..2],
 375                       let i' = fromIntegral i,
 376                       let j' = fromIntegral j,
 377                       let k' = fromIntegral k]
 378     where
 379       g = make_grid 1 trilinear
 380       c0 = fromJust $ cube_at g 1 1 1
 381       t4 = tetrahedron4 c0
 382       p = polynomial t4
 383
 384 test_trilinear_reproduced_t5 :: Assertion
 385 test_trilinear_reproduced_t5 =
 386     assertTrue "trilinears are reproduced correctly" $
 387              and [p (i', j', k') ~= value_at trilinear i j k
 388                     | i <- [0..2],
 389                       j <- [0..2],
 390                       k <- [0..2],
 391                       let i' = fromIntegral i,
 392                       let j' = fromIntegral j,
 393                       let k' = fromIntegral k]
 394     where
 395       g = make_grid 1 trilinear
 396       c0 = fromJust $ cube_at g 1 1 1
 397       t5 = tetrahedron5 c0
 398       p = polynomial t5
 399
 400 test_trilinear_reproduced_t6 :: Assertion
 401 test_trilinear_reproduced_t6 =
 402     assertTrue "trilinears are reproduced correctly" $
 403              and [p (i', j', k') ~= value_at trilinear i j k
 404                     | i <- [0..2],
 405                       j <- [0..2],
 406                       k <- [0..2],
 407                       let i' = fromIntegral i,
 408                       let j' = fromIntegral j,
 409                       let k' = fromIntegral k]
 410     where
 411       g = make_grid 1 trilinear
 412       c0 = fromJust $ cube_at g 1 1 1
 413       t6 = tetrahedron6 c0
 414       p = polynomial t6
 415
 416 test_trilinear_reproduced_t7 :: Assertion
 417 test_trilinear_reproduced_t7 =
 418     assertTrue "trilinears are reproduced correctly" $
 419              and [p (i', j', k') ~= value_at trilinear i j k
 420                     | i <- [0..2],
 421                       j <- [0..2],
 422                       k <- [0..2],
 423                       let i' = fromIntegral i,
 424                       let j' = fromIntegral j,
 425                       let k' = fromIntegral k]
 426     where
 427       g = make_grid 1 trilinear
 428       c0 = fromJust $ cube_at g 1 1 1
 429       t7 = tetrahedron7 c0
 430       p = polynomial t7
 431
 432 test_trilinear_reproduced_t8 :: Assertion
 433 test_trilinear_reproduced_t8 =
 434     assertTrue "trilinears are reproduced correctly" $
 435              and [p (i', j', k') ~= value_at trilinear i j k
 436                     | i <- [0..2],
 437                       j <- [0..2],
 438                       k <- [0..2],
 439                       let i' = fromIntegral i,
 440                       let j' = fromIntegral j,
 441                       let k' = fromIntegral k]
 442     where
 443       g = make_grid 1 trilinear
 444       c0 = fromJust $ cube_at g 1 1 1
 445       t8 = tetrahedron8 c0
 446       p = polynomial t8
 447
 448 test_trilinear_reproduced_t9 :: Assertion
 449 test_trilinear_reproduced_t9 =
 450     assertTrue "trilinears are reproduced correctly" $
 451              and [p (i', j', k') ~= value_at trilinear i j k
 452                     | i <- [0..2],
 453                       j <- [0..2],
 454                       k <- [0..2],
 455                       let i' = fromIntegral i,
 456                       let j' = fromIntegral j,
 457                       let k' = fromIntegral k]
 458     where
 459       g = make_grid 1 trilinear
 460       c0 = fromJust $ cube_at g 1 1 1
 461       t9 = tetrahedron9 c0
 462       p = polynomial t9
 463
 464 test_trilinear_reproduced_t10 :: Assertion
 465 test_trilinear_reproduced_t10 =
 466     assertTrue "trilinears are reproduced correctly" $
 467              and [p (i', j', k') ~= value_at trilinear i j k
 468                     | i <- [0..2],
 469                       j <- [0..2],
 470                       k <- [0..2],
 471                       let i' = fromIntegral i,
 472                       let j' = fromIntegral j,
 473                       let k' = fromIntegral k]
 474     where
 475       g = make_grid 1 trilinear
 476       c0 = fromJust $ cube_at g 1 1 1
 477       t10 = tetrahedron10 c0
 478       p = polynomial t10
 479
 480 test_trilinear_reproduced_t11 :: Assertion
 481 test_trilinear_reproduced_t11 =
 482     assertTrue "trilinears are reproduced correctly" $
 483              and [p (i', j', k') ~= value_at trilinear i j k
 484                     | i <- [0..2],
 485                       j <- [0..2],
 486                       k <- [0..2],
 487                       let i' = fromIntegral i,
 488                       let j' = fromIntegral j,
 489                       let k' = fromIntegral k]
 490     where
 491       g = make_grid 1 trilinear
 492       c0 = fromJust $ cube_at g 1 1 1
 493       t11 = tetrahedron11 c0
 494       p = polynomial t11
 495
 496 test_trilinear_reproduced_t12 :: Assertion
 497 test_trilinear_reproduced_t12 =
 498     assertTrue "trilinears are reproduced correctly" $
 499              and [p (i', j', k') ~= value_at trilinear i j k
 500                     | i <- [0..2],
 501                       j <- [0..2],
 502                       k <- [0..2],
 503                       let i' = fromIntegral i,
 504                       let j' = fromIntegral j,
 505                       let k' = fromIntegral k]
 506     where
 507       g = make_grid 1 trilinear
 508       c0 = fromJust $ cube_at g 1 1 1
 509       t12 = tetrahedron12 c0
 510       p = polynomial t12
 511
 512 test_trilinear_reproduced_t13 :: Assertion
 513 test_trilinear_reproduced_t13 =
 514     assertTrue "trilinears are reproduced correctly" $
 515              and [p (i', j', k') ~= value_at trilinear i j k
 516                     | i <- [0..2],
 517                       j <- [0..2],
 518                       k <- [0..2],
 519                       let i' = fromIntegral i,
 520                       let j' = fromIntegral j,
 521                       let k' = fromIntegral k]
 522     where
 523       g = make_grid 1 trilinear
 524       c0 = fromJust $ cube_at g 1 1 1
 525       t13 = tetrahedron13 c0
 526       p = polynomial t13
 527
 528
 529 test_trilinear_reproduced_t14 :: Assertion
 530 test_trilinear_reproduced_t14 =
 531     assertTrue "trilinears are reproduced correctly" $
 532              and [p (i', j', k') ~= value_at trilinear i j k
 533                     | i <- [0..2],
 534                       j <- [0..2],
 535                       k <- [0..2],
 536                       let i' = fromIntegral i,
 537                       let j' = fromIntegral j,
 538                       let k' = fromIntegral k]
 539     where
 540       g = make_grid 1 trilinear
 541       c0 = fromJust $ cube_at g 1 1 1
 542       t14 = tetrahedron14 c0
 543       p = polynomial t14
 544
 545 test_trilinear_reproduced_t15 :: Assertion
 546 test_trilinear_reproduced_t15 =
 547     assertTrue "trilinears are reproduced correctly" $
 548              and [p (i', j', k') ~= value_at trilinear i j k
 549                     | i <- [0..2],
 550                       j <- [0..2],
 551                       k <- [0..2],
 552                       let i' = fromIntegral i,
 553                       let j' = fromIntegral j,
 554                       let k' = fromIntegral k]
 555     where
 556       g = make_grid 1 trilinear
 557       c0 = fromJust $ cube_at g 1 1 1
 558       t15 = tetrahedron15 c0
 559       p = polynomial t15
 560
 561 test_trilinear_reproduced_t16 :: Assertion
 562 test_trilinear_reproduced_t16 =
 563     assertTrue "trilinears are reproduced correctly" $
 564              and [p (i', j', k') ~= value_at trilinear i j k
 565                     | i <- [0..2],
 566                       j <- [0..2],
 567                       k <- [0..2],
 568                       let i' = fromIntegral i,
 569                       let j' = fromIntegral j,
 570                       let k' = fromIntegral k]
 571     where
 572       g = make_grid 1 trilinear
 573       c0 = fromJust $ cube_at g 1 1 1
 574       t16 = tetrahedron16 c0
 575       p = polynomial t16
 576
 577 test_trilinear_reproduced_t17 :: Assertion
 578 test_trilinear_reproduced_t17 =
 579     assertTrue "trilinears are reproduced correctly" $
 580              and [p (i', j', k') ~= value_at trilinear i j k
 581                     | i <- [0..2],
 582                       j <- [0..2],
 583                       k <- [0..2],
 584                       let i' = fromIntegral i,
 585                       let j' = fromIntegral j,
 586                       let k' = fromIntegral k]
 587     where
 588       g = make_grid 1 trilinear
 589       c0 = fromJust $ cube_at g 1 1 1
 590       t17 = tetrahedron17 c0
 591       p = polynomial t17
 592
 593 test_trilinear_reproduced_t18 :: Assertion
 594 test_trilinear_reproduced_t18 =
 595     assertTrue "trilinears are reproduced correctly" $
 596              and [p (i', j', k') ~= value_at trilinear i j k
 597                     | i <- [0..2],
 598                       j <- [0..2],
 599                       k <- [0..2],
 600                       let i' = fromIntegral i,
 601                       let j' = fromIntegral j,
 602                       let k' = fromIntegral k]
 603     where
 604       g = make_grid 1 trilinear
 605       c0 = fromJust $ cube_at g 1 1 1
 606       t18 = tetrahedron18 c0
 607       p = polynomial t18
 608
 609 test_trilinear_reproduced_t19 :: Assertion
 610 test_trilinear_reproduced_t19 =
 611     assertTrue "trilinears are reproduced correctly" $
 612              and [p (i', j', k') ~= value_at trilinear i j k
 613                     | i <- [0..2],
 614                       j <- [0..2],
 615                       k <- [0..2],
 616                       let i' = fromIntegral i,
 617                       let j' = fromIntegral j,
 618                       let k' = fromIntegral k]
 619     where
 620       g = make_grid 1 trilinear
 621       c0 = fromJust $ cube_at g 1 1 1
 622       t19 = tetrahedron19 c0
 623       p = polynomial t19
 624
 625 test_trilinear_reproduced_t20 :: Assertion
 626 test_trilinear_reproduced_t20 =
 627     assertTrue "trilinears are reproduced correctly" $
 628              and [p (i', j', k') ~= value_at trilinear i j k
 629                     | i <- [0..2],
 630                       j <- [0..2],
 631                       k <- [0..2],
 632                       let i' = fromIntegral i,
 633                       let j' = fromIntegral j,
 634                       let k' = fromIntegral k]
 635     where
 636       g = make_grid 1 trilinear
 637       c0 = fromJust $ cube_at g 1 1 1
 638       t20 = tetrahedron20 c0
 639       p = polynomial t20
 640
 641
 642 test_trilinear_reproduced_t21 :: Assertion
 643 test_trilinear_reproduced_t21 =
 644     assertTrue "trilinears are reproduced correctly" $
 645              and [p (i', j', k') ~= value_at trilinear i j k
 646                     | i <- [0..2],
 647                       j <- [0..2],
 648                       k <- [0..2],
 649                       let i' = fromIntegral i,
 650                       let j' = fromIntegral j,
 651                       let k' = fromIntegral k]
 652     where
 653       g = make_grid 1 trilinear
 654       c0 = fromJust $ cube_at g 1 1 1
 655       t21 = tetrahedron21 c0
 656       p = polynomial t21
 657
 658 test_trilinear_reproduced_t22 :: Assertion
 659 test_trilinear_reproduced_t22 =
 660     assertTrue "trilinears are reproduced correctly" $
 661              and [p (i', j', k') ~= value_at trilinear i j k
 662                     | i <- [0..2],
 663                       j <- [0..2],
 664                       k <- [0..2],
 665                       let i' = fromIntegral i,
 666                       let j' = fromIntegral j,
 667                       let k' = fromIntegral k]
 668     where
 669       g = make_grid 1 trilinear
 670       c0 = fromJust $ cube_at g 1 1 1
 671       t22 = tetrahedron22 c0
 672       p = polynomial t22
 673
 674
 675 test_trilinear_reproduced_t23 :: Assertion
 676 test_trilinear_reproduced_t23 =
 677     assertTrue "trilinears are reproduced correctly" $
 678              and [p (i', j', k') ~= value_at trilinear i j k
 679                     | i <- [0..2],
 680                       j <- [0..2],
 681                       k <- [0..2],
 682                       let i' = fromIntegral i,
 683                       let j' = fromIntegral j,
 684                       let k' = fromIntegral k]
 685     where
 686       g = make_grid 1 trilinear
 687       c0 = fromJust $ cube_at g 1 1 1
 688       t19 = tetrahedron19 c0
 689       p = polynomial t19
 690
 691
 692 test_zeros_reproduced :: Assertion
 693 test_zeros_reproduced =
 694     assertTrue "the zero function is reproduced correctly" $
 695              and [p (i', j', k') ~= value_at zeros i j k
 696                     | i <- [0..2],
 697                       j <- [0..2],
 698                       k <- [0..2],
 699                       let i' = fromIntegral i,
 700                       let j' = fromIntegral j,
 701                       let k' = fromIntegral k]
 702     where
 703       g = make_grid 1 zeros
 704       c0 = fromJust $ cube_at g 1 1 1
 705       t0 = tetrahedron0 c0
 706       p = polynomial t0
 707
 708
 709 -- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
 710 test_trilinearx2_reproduced_t0 :: Assertion
 711 test_trilinearx2_reproduced_t0 =
 712     assertTrue "trilinearx2 is reproduced correctly" $
 713       and [p (i', j', k') ~= value_at trilinearx2 i j k
 714             | i <- [0..8],
 715               j <- [0..8],
 716               k <- [0..8],
 717               let i' = (fromIntegral i) * 0.5,
 718               let j' = (fromIntegral j) * 0.5,
 719               let k' = (fromIntegral k) * 0.5]
 720     where
 721       g = make_grid 1 trilinear
 722       c0 = fromJust $ cube_at g 1 1 1
 723       t0 = tetrahedron0 c0
 724       p = polynomial t0