src/Tests/Grid.hs

   1 module Tests.Grid
   2 where
   3
   4 import Test.HUnit
   5
   6 import Assertions
   7 import Comparisons
   8 import Cube hiding (i, j, k)
   9 import Examples
  10 import FunctionValues (value_at)
  11 import Grid
  12 import Point (Point)
  13 import Tetrahedron
  14 import ThreeDimensional
  15
  16
  17 -- | Check the value of c0030 for tetrahedron0 belonging to the
  18 --   cube centered on (1,1,1) with a grid constructed from the
  19 --   trilinear values. See example one in the paper.
  20 test_trilinear_c0030 :: Assertion
  21 test_trilinear_c0030 =
  22     assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  23       where
  24         g = make_grid 1 trilinear
  25         cube = cube_at g 1 1 1
  26         t = tetrahedron0 cube
  27
  28
  29 -- | Check the value of c0003 for tetrahedron0 belonging to the
  30 --   cube centered on (1,1,1) with a grid constructed from the
  31 --   trilinear values. See example one in the paper.
  32 test_trilinear_c0003 :: Assertion
  33 test_trilinear_c0003 =
  34     assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  35       where
  36         g = make_grid 1 trilinear
  37         cube = cube_at g 1 1 1
  38         t = tetrahedron0 cube
  39
  40
  41 -- | Check the value of c0021 for tetrahedron0 belonging to the
  42 --   cube centered on (1,1,1) with a grid constructed from the
  43 --   trilinear values. See example one in the paper.
  44 test_trilinear_c0021 :: Assertion
  45 test_trilinear_c0021 =
  46     assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  47       where
  48         g = make_grid 1 trilinear
  49         cube = cube_at g 1 1 1
  50         t = tetrahedron0 cube
  51
  52
  53 -- | Check the value of c0012 for tetrahedron0 belonging to the
  54 --   cube centered on (1,1,1) with a grid constructed from the
  55 --   trilinear values. See example one in the paper.
  56 test_trilinear_c0012 :: Assertion
  57 test_trilinear_c0012 =
  58     assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  59       where
  60         g = make_grid 1 trilinear
  61         cube = cube_at g 1 1 1
  62         t = tetrahedron0 cube
  63
  64
  65 -- | Check the value of c0120 for tetrahedron0 belonging to the
  66 --   cube centered on (1,1,1) with a grid constructed from the
  67 --   trilinear values. See example one in the paper.
  68 test_trilinear_c0120 :: Assertion
  69 test_trilinear_c0120 =
  70     assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
  71       where
  72         g = make_grid 1 trilinear
  73         cube = cube_at g 1 1 1
  74         t = tetrahedron0 cube
  75
  76
  77 -- | Check the value of c0102 for tetrahedron0 belonging to the
  78 --   cube centered on (1,1,1) with a grid constructed from the
  79 --   trilinear values. See example one in the paper.
  80 test_trilinear_c0102 :: Assertion
  81 test_trilinear_c0102 =
  82     assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
  83       where
  84         g = make_grid 1 trilinear
  85         cube = cube_at g 1 1 1
  86         t = tetrahedron0 cube
  87
  88
  89 -- | Check the value of c0111 for tetrahedron0 belonging to the
  90 --   cube centered on (1,1,1) with a grid constructed from the
  91 --   trilinear values. See example one in the paper.
  92 test_trilinear_c0111 :: Assertion
  93 test_trilinear_c0111 =
  94     assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
  95       where
  96         g = make_grid 1 trilinear
  97         cube = cube_at g 1 1 1
  98         t = tetrahedron0 cube
  99
 100
 101 -- | Check the value of c0210 for tetrahedron0 belonging to the
 102 --   cube centered on (1,1,1) with a grid constructed from the
 103 --   trilinear values. See example one in the paper.
 104 test_trilinear_c0210 :: Assertion
 105 test_trilinear_c0210 =
 106     assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
 107       where
 108         g = make_grid 1 trilinear
 109         cube = cube_at g 1 1 1
 110         t = tetrahedron0 cube
 111
 112
 113 -- | Check the value of c0201 for tetrahedron0 belonging to the
 114 --   cube centered on (1,1,1) with a grid constructed from the
 115 --   trilinear values. See example one in the paper.
 116 test_trilinear_c0201 :: Assertion
 117 test_trilinear_c0201 =
 118     assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
 119       where
 120         g = make_grid 1 trilinear
 121         cube = cube_at g 1 1 1
 122         t = tetrahedron0 cube
 123
 124
 125 -- | Check the value of c0300 for tetrahedron0 belonging to the
 126 --   cube centered on (1,1,1) with a grid constructed from the
 127 --   trilinear values. See example one in the paper.
 128 test_trilinear_c0300 :: Assertion
 129 test_trilinear_c0300 =
 130     assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
 131       where
 132         g = make_grid 1 trilinear
 133         cube = cube_at g 1 1 1
 134         t = tetrahedron0 cube
 135
 136
 137 -- | Check the value of c1020 for tetrahedron0 belonging to the
 138 --   cube centered on (1,1,1) with a grid constructed from the
 139 --   trilinear values. See example one in the paper.
 140 test_trilinear_c1020 :: Assertion
 141 test_trilinear_c1020 =
 142     assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
 143       where
 144         g = make_grid 1 trilinear
 145         cube = cube_at g 1 1 1
 146         t = tetrahedron0 cube
 147
 148
 149 -- | Check the value of c1002 for tetrahedron0 belonging to the
 150 --   cube centered on (1,1,1) with a grid constructed from the
 151 --   trilinear values. See example one in the paper.
 152 test_trilinear_c1002 :: Assertion
 153 test_trilinear_c1002 =
 154     assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
 155       where
 156         g = make_grid 1 trilinear
 157         cube = cube_at g 1 1 1
 158         t = tetrahedron0 cube
 159
 160
 161 -- | Check the value of c1011 for tetrahedron0 belonging to the
 162 --   cube centered on (1,1,1) with a grid constructed from the
 163 --   trilinear values. See example one in the paper.
 164 test_trilinear_c1011 :: Assertion
 165 test_trilinear_c1011 =
 166     assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
 167       where
 168         g = make_grid 1 trilinear
 169         cube = cube_at g 1 1 1
 170         t = tetrahedron0 cube
 171
 172
 173 -- | Check the value of c1110 for tetrahedron0 belonging to the
 174 --   cube centered on (1,1,1) with a grid constructed from the
 175 --   trilinear values. See example one in the paper.
 176 test_trilinear_c1110 :: Assertion
 177 test_trilinear_c1110 =
 178     assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
 179       where
 180         g = make_grid 1 trilinear
 181         cube = cube_at g 1 1 1
 182         t = tetrahedron0 cube
 183
 184
 185 -- | Check the value of c1101 for tetrahedron0 belonging to the
 186 --   cube centered on (1,1,1) with a grid constructed from the
 187 --   trilinear values. See example one in the paper.
 188 test_trilinear_c1101 :: Assertion
 189 test_trilinear_c1101 =
 190     assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
 191       where
 192         g = make_grid 1 trilinear
 193         cube = cube_at g 1 1 1
 194         t = tetrahedron0 cube
 195
 196
 197 -- | Check the value of c1200 for tetrahedron0 belonging to the
 198 --   cube centered on (1,1,1) with a grid constructed from the
 199 --   trilinear values. See example one in the paper.
 200 test_trilinear_c1200 :: Assertion
 201 test_trilinear_c1200 =
 202     assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
 203       where
 204         g = make_grid 1 trilinear
 205         cube = cube_at g 1 1 1
 206         t = tetrahedron0 cube
 207
 208
 209 -- | Check the value of c2010 for tetrahedron0 belonging to the
 210 --   cube centered on (1,1,1) with a grid constructed from the
 211 --   trilinear values. See example one in the paper.
 212 test_trilinear_c2010 :: Assertion
 213 test_trilinear_c2010 =
 214     assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
 215       where
 216         g = make_grid 1 trilinear
 217         cube = cube_at g 1 1 1
 218         t = tetrahedron0 cube
 219
 220
 221 -- | Check the value of c2001 for tetrahedron0 belonging to the
 222 --   cube centered on (1,1,1) with a grid constructed from the
 223 --   trilinear values. See example one in the paper.
 224 test_trilinear_c2001 :: Assertion
 225 test_trilinear_c2001 =
 226     assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
 227       where
 228         g = make_grid 1 trilinear
 229         cube = cube_at g 1 1 1
 230         t = tetrahedron0 cube
 231
 232
 233 -- | Check the value of c2100 for tetrahedron0 belonging to the
 234 --   cube centered on (1,1,1) with a grid constructed from the
 235 --   trilinear values. See example one in the paper.
 236 test_trilinear_c2100 :: Assertion
 237 test_trilinear_c2100 =
 238     assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
 239       where
 240         g = make_grid 1 trilinear
 241         cube = cube_at g 1 1 1
 242         t = tetrahedron0 cube
 243
 244
 245 -- | Check the value of c3000 for tetrahedron0 belonging to the
 246 --   cube centered on (1,1,1) with a grid constructed from the
 247 --   trilinear values. See example one in the paper.
 248 test_trilinear_c3000 :: Assertion
 249 test_trilinear_c3000 =
 250     assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 251       where
 252         g = make_grid 1 trilinear
 253         cube = cube_at g 1 1 1
 254         t = tetrahedron0 cube
 255
 256
 257 -- | Make sure that v0 of tetrahedron0 belonging to the cube centered
 258 --   on (1,1,1) with a grid constructed from the trilinear values
 259 --   winds up in the right place. See example one in the paper.
 260 test_trilinear_f0_t0_v0 :: Assertion
 261 test_trilinear_f0_t0_v0 =
 262     assertEqual "v0 is correct" (v0 t) (1, 1, 1)
 263       where
 264         g = make_grid 1 trilinear
 265         cube = cube_at g 1 1 1
 266         t = tetrahedron0 cube
 267
 268
 269 -- | Make sure that v1 of tetrahedron0 belonging to the cube centered
 270 --   on (1,1,1) with a grid constructed from the trilinear values
 271 --   winds up in the right place. See example one in the paper.
 272 test_trilinear_f0_t0_v1 :: Assertion
 273 test_trilinear_f0_t0_v1 =
 274     assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
 275       where
 276         g = make_grid 1 trilinear
 277         cube = cube_at g 1 1 1
 278         t = tetrahedron0 cube
 279
 280
 281 -- | Make sure that v2 of tetrahedron0 belonging to the cube centered
 282 --   on (1,1,1) with a grid constructed from the trilinear values
 283 --   winds up in the right place. See example one in the paper.
 284 test_trilinear_f0_t0_v2 :: Assertion
 285 test_trilinear_f0_t0_v2 =
 286     assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
 287       where
 288         g = make_grid 1 trilinear
 289         cube = cube_at g 1 1 1
 290         t = tetrahedron0 cube
 291
 292
 293 -- | Make sure that v3 of tetrahedron0 belonging to the cube centered
 294 --   on (1,1,1) with a grid constructed from the trilinear values
 295 --   winds up in the right place. See example one in the paper.
 296 test_trilinear_f0_t0_v3 :: Assertion
 297 test_trilinear_f0_t0_v3 =
 298     assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
 299       where
 300         g = make_grid 1 trilinear
 301         cube = cube_at g 1 1 1
 302         t = tetrahedron0 cube
 303
 304
 305 test_trilinear_reproduced :: Assertion
 306 test_trilinear_reproduced =
 307     assertTrue "trilinears are reproduced correctly" $
 308              and [p (i', j', k') ~= value_at trilinear i j k
 309                     | i <- [0..2],
 310                       j <- [0..2],
 311                       k <- [0..2],
 312                       t <- tetrahedra c0,
 313                       let p = polynomial t,
 314                       let i' = fromIntegral i,
 315                       let j' = fromIntegral j,
 316                       let k' = fromIntegral k]
 317     where
 318       g = make_grid 1 trilinear
 319       c0 = cube_at g 1 1 1
 320
 321
 322 test_zeros_reproduced :: Assertion
 323 test_zeros_reproduced =
 324     assertTrue "the zero function is reproduced correctly" $
 325              and [p (i', j', k') ~= value_at zeros i j k
 326                     | i <- [0..2],
 327                       j <- [0..2],
 328                       k <- [0..2],
 329                       let i' = fromIntegral i,
 330                       let j' = fromIntegral j,
 331                       let k' = fromIntegral k]
 332     where
 333       g = make_grid 1 zeros
 334       c0 = cube_at g 1 1 1
 335       t0 = tetrahedron0 c0
 336       p = polynomial t0
 337
 338
 339 -- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
 340 test_trilinear9x9x9_reproduced :: Assertion
 341 test_trilinear9x9x9_reproduced =
 342     assertTrue "trilinear 9x9x9 is reproduced correctly" $
 343       and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
 344             | i <- [0..8],
 345               j <- [0..8],
 346               k <- [0..8],
 347               t <- tetrahedra c0,
 348               let p = polynomial t,
 349               let i' = (fromIntegral i) * 0.5,
 350               let j' = (fromIntegral j) * 0.5,
 351               let k' = (fromIntegral k) * 0.5]
 352     where
 353       g = make_grid 1 trilinear
 354       c0 = cube_at g 1 1 1
 355
 356
 357 -- | The point 'p' in this test lies on the boundary of tetrahedra 12 and 15.
 358 --   However, the 'contains_point' test fails due to some numerical innacuracy.
 359 --   This bug should have been fixed by setting a positive tolerance level.
 360 --
 361 --   Example from before the fix:
 362 --
 363 --   > b0 (tetrahedron15 c) p
 364 --   -3.4694469519536365e-18
 365 --
 366 test_tetrahedra_collision_sensitivity :: Assertion
 367 test_tetrahedra_collision_sensitivity =
 368   assertTrue "tetrahedron collision tests isn't too sensitive" $
 369              contains_point t15 p
 370   where
 371     g = make_grid 1 naturals_1d
 372     c = cube_at g 0 17 1
 373     p = (0, 16.75, 0.5) :: Point
 374     t15 = tetrahedron15 c