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 :: Assertion
 305 test_trilinear_reproduced =
 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                       t <- tetrahedra c0,
 312                       let p = polynomial t,
 313                       let i' = fromIntegral i,
 314                       let j' = fromIntegral j,
 315                       let k' = fromIntegral k]
 316     where
 317       g = make_grid 1 trilinear
 318       c0 = fromJust $ cube_at g 1 1 1
 319
 320
 321 test_zeros_reproduced :: Assertion
 322 test_zeros_reproduced =
 323     assertTrue "the zero function is reproduced correctly" $
 324              and [p (i', j', k') ~= value_at zeros i j k
 325                     | i <- [0..2],
 326                       j <- [0..2],
 327                       k <- [0..2],
 328                       let i' = fromIntegral i,
 329                       let j' = fromIntegral j,
 330                       let k' = fromIntegral k]
 331     where
 332       g = make_grid 1 zeros
 333       c0 = fromJust $ cube_at g 1 1 1
 334       t0 = tetrahedron0 c0
 335       p = polynomial t0
 336
 337
 338 -- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
 339 test_trilinear9x9x9_reproduced :: Assertion
 340 test_trilinear9x9x9_reproduced =
 341     assertTrue "trilinear 9x9x9 is reproduced correctly" $
 342       and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
 343             | i <- [0..8],
 344               j <- [0..8],
 345               k <- [0..8],
 346               t <- tetrahedra c0,
 347               let p = polynomial t,
 348               let i' = (fromIntegral i) * 0.5,
 349               let j' = (fromIntegral j) * 0.5,
 350               let k' = (fromIntegral k) * 0.5]
 351     where
 352       g = make_grid 1 trilinear
 353       c0 = fromJust $ cube_at g 1 1 1
 354       t0 = tetrahedron0 c0
 355       p = polynomial t0