src/Tests/Grid.hs

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