src/Tests/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 Cube (Cube(grid), cube_at, top)
  10 import Face (face0,
  11              face2,
  12              face5,
  13              tetrahedron0,
  14              tetrahedron1,
  15              tetrahedron2,
  16              tetrahedron3,
  17              tetrahedrons)
  18 import Grid (Grid(h), make_grid)
  19 import Tetrahedron
  20
  21
  22 -- HUnit tests.
  23
  24 -- | An HUnit assertion that wraps the almost_equals function. Stolen
  25 --   from the definition of assertEqual in Test/HUnit/Base.hs.
  26 assertAlmostEqual :: String -> Double -> Double -> Assertion
  27 assertAlmostEqual preface expected actual =
  28   unless (actual ~= expected) (assertFailure msg)
  29  where msg = (if null preface then "" else preface ++ "\n") ++
  30              "expected: " ++ show expected ++ "\n but got: " ++ show actual
  31
  32
  33 -- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at nine
  34 --   points (hi, hj, jk) with h = 1. From example one in the paper.
  35 --   Used in the next bunch of tests.
  36 trilinear :: [[[Double]]]
  37 trilinear = [ [ [ 1, 2, 3 ],
  38                 [ 1, 3, 5 ],
  39                 [ 1, 4, 7 ] ],
  40               [ [ 1, 2, 3 ],
  41                 [ 1, 4, 7 ],
  42                 [ 1, 6, 11 ] ],
  43               [ [ 1, 2, 3 ],
  44                 [ 1, 5, 9 ],
  45                 [ 1, 8, 15 ]]]
  46
  47 -- | Check the value of c0030 for any tetrahedron belonging to the
  48 --   cube centered on (1,1,1) with a grid constructed from the
  49 --   trilinear values. See example one in the paper.
  50 test_trilinear_c0030 :: Test
  51 test_trilinear_c0030 =
  52     TestCase $ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  53       where
  54         g = make_grid 1 trilinear
  55         cube = cube_at g 1 1 1
  56         t = head (tetrahedrons cube) -- Any one will do.
  57
  58
  59 -- | Check the value of c0003 for any tetrahedron belonging to the
  60 --   cube centered on (1,1,1) with a grid constructed from the
  61 --   trilinear values. See example one in the paper.
  62 test_trilinear_c0003 :: Test
  63 test_trilinear_c0003 =
  64     TestCase $ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  65       where
  66         g = make_grid 1 trilinear
  67         cube = cube_at g 1 1 1
  68         t = head (tetrahedrons cube) -- Any one will do.
  69
  70
  71 -- | Check the value of c0021 for any tetrahedron belonging to the
  72 --   cube centered on (1,1,1) with a grid constructed from the
  73 --   trilinear values. See example one in the paper.
  74 test_trilinear_c0021 :: Test
  75 test_trilinear_c0021 =
  76     TestCase $ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  77       where
  78         g = make_grid 1 trilinear
  79         cube = cube_at g 1 1 1
  80         t = head (tetrahedrons cube) -- Any one will do.
  81
  82
  83 -- | Check the value of c0012 for any tetrahedron belonging to the
  84 --   cube centered on (1,1,1) with a grid constructed from the
  85 --   trilinear values. See example one in the paper.
  86 test_trilinear_c0012 :: Test
  87 test_trilinear_c0012 =
  88     TestCase $ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  89       where
  90         g = make_grid 1 trilinear
  91         cube = cube_at g 1 1 1
  92         t = head (tetrahedrons cube) -- Any one will do.
  93
  94
  95 -- | Check the value of c0120 for any tetrahedron belonging to the
  96 --   cube centered on (1,1,1) with a grid constructed from the
  97 --   trilinear values. See example one in the paper.
  98 test_trilinear_c0120 :: Test
  99 test_trilinear_c0120 =
 100     TestCase $ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
 101       where
 102         g = make_grid 1 trilinear
 103         cube = cube_at g 1 1 1
 104         t = head (tetrahedrons cube) -- Any one will do.
 105
 106
 107 face_tests :: [Test]
 108 face_tests = [test_trilinear_c0030,
 109               test_trilinear_c0003,
 110               test_trilinear_c0021,
 111               test_trilinear_c0012,
 112               test_trilinear_c0120]
 113
 114
 115 -- QuickCheck Tests.
 116
 117 -- | Since the grid size is necessarily positive, all tetrahedrons
 118 --   (which comprise cubes of positive volume) must have positive volume
 119 --   as well.
 120 prop_all_volumes_positive :: Cube -> Property
 121 prop_all_volumes_positive c =
 122     (delta > 0) ==> (null nonpositive_volumes)
 123     where
 124       delta = h (grid c)
 125       ts = tetrahedrons c
 126       volumes = map volume ts
 127       nonpositive_volumes = filter (<= 0) volumes
 128
 129
 130 -- | Given in Sorokina and Zeilfelder, p. 78.
 131 prop_cijk1_identity :: Cube -> Bool
 132 prop_cijk1_identity cube =
 133      and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
 134                             (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
 135                             (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
 136                             (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
 137                                                                     j <- [0..2],
 138                                                                     k <- [0..2],
 139                                                                     i + j + k == 2]
 140       where
 141         t0 = tetrahedron0 (face0 cube)
 142         t1 = tetrahedron1 (face0 cube)
 143         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 144         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 145
 146 -- | Given in Sorokina and Zeilfelder, p. 79.
 147 prop_c0120_identity1 :: Cube -> Bool
 148 prop_c0120_identity1 cube =
 149     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
 150       where
 151         t0 = tetrahedron0 (face0 cube)
 152         t1 = tetrahedron1 (face0 cube)
 153         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 154         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 155
 156
 157 -- | Given in Sorokina and Zeilfelder, p. 79.
 158 prop_c0210_identity1 :: Cube -> Bool
 159 prop_c0210_identity1 cube =
 160     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
 161       where
 162         t0 = tetrahedron0 (face0 cube)
 163         t1 = tetrahedron1 (face0 cube)
 164         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 165         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 166
 167
 168 -- | Given in Sorokina and Zeilfelder, p. 79.
 169 prop_c0300_identity1 :: Cube -> Bool
 170 prop_c0300_identity1 cube =
 171     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
 172       where
 173         t0 = tetrahedron0 (face0 cube)
 174         t1 = tetrahedron1 (face0 cube)
 175         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 176         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 177
 178 -- | Given in Sorokina and Zeilfelder, p. 79.
 179 prop_c1110_identity :: Cube -> Bool
 180 prop_c1110_identity cube =
 181     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 182       where
 183         t0 = tetrahedron0 (face0 cube)
 184         t1 = tetrahedron1 (face0 cube)
 185         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 186         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 187
 188
 189 -- | Given in Sorokina and Zeilfelder, p. 79.
 190 prop_c1200_identity1 :: Cube -> Bool
 191 prop_c1200_identity1 cube =
 192     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
 193       where
 194         t0 = tetrahedron0 (face0 cube)
 195         t1 = tetrahedron1 (face0 cube)
 196         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 197         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 198
 199
 200 -- | Given in Sorokina and Zeilfelder, p. 79.
 201 prop_c2100_identity1 :: Cube -> Bool
 202 prop_c2100_identity1 cube =
 203     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
 204       where
 205         t0 = tetrahedron0 (face0 cube)
 206         t1 = tetrahedron1 (face0 cube)
 207         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 208         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 209
 210
 211 -- | Given in Sorokina and Zeilfelder, p. 79.
 212 prop_c0102_identity1 :: Cube -> Bool
 213 prop_c0102_identity1 cube =
 214     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
 215       where
 216         t0 = tetrahedron0 (face0 cube)
 217         t3 = tetrahedron3 (face0 cube)
 218         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 219         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 220
 221
 222 -- | Given in Sorokina and Zeilfelder, p. 79.
 223 prop_c0201_identity1 :: Cube -> Bool
 224 prop_c0201_identity1 cube =
 225     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
 226       where
 227         t0 = tetrahedron0 (face0 cube)
 228         t3 = tetrahedron3 (face0 cube)
 229         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 230         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 231
 232
 233 -- | Given in Sorokina and Zeilfelder, p. 79.
 234 prop_c0300_identity2 :: Cube -> Bool
 235 prop_c0300_identity2 cube =
 236     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
 237       where
 238         t0 = tetrahedron0 (face0 cube)
 239         t3 = tetrahedron3 (face0 cube)
 240         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 241         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 242
 243 -- | Given in Sorokina and Zeilfelder, p. 79.
 244 prop_c1101_identity :: Cube -> Bool
 245 prop_c1101_identity cube =
 246     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
 247       where
 248         t0 = tetrahedron0 (face0 cube)
 249         t3 = tetrahedron3 (face0 cube)
 250         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 251         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 252
 253
 254 -- | Given in Sorokina and Zeilfelder, p. 79.
 255 prop_c1200_identity2 :: Cube -> Bool
 256 prop_c1200_identity2 cube =
 257     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
 258       where
 259         t0 = tetrahedron0 (face0 cube)
 260         t3 = tetrahedron3 (face0 cube)
 261         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 262         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 263
 264
 265 -- | Given in Sorokina and Zeilfelder, p. 79.
 266 prop_c2100_identity2 :: Cube -> Bool
 267 prop_c2100_identity2 cube =
 268     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
 269       where
 270         t0 = tetrahedron0 (face0 cube)
 271         t3 = tetrahedron3 (face0 cube)
 272         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 273         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 274
 275
 276 -- | Given in Sorokina and Zeilfelder, p. 79.
 277 prop_c3000_identity :: Cube -> Bool
 278 prop_c3000_identity cube =
 279     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)
 280       where
 281         t0 = tetrahedron0 (face0 cube)
 282         t2 = tetrahedron2 (face5 cube)
 283         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 284         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 285
 286
 287 -- | Given in Sorokina and Zeilfelder, p. 79.
 288 prop_c2010_identity :: Cube -> Bool
 289 prop_c2010_identity cube =
 290     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)
 291       where
 292         t0 = tetrahedron0 (face0 cube)
 293         t2 = tetrahedron2 (face5 cube)
 294         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 295         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 296
 297
 298 -- | Given in Sorokina and Zeilfelder, p. 79.
 299 prop_c2001_identity :: Cube -> Bool
 300 prop_c2001_identity cube =
 301     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)
 302       where
 303         t0 = tetrahedron0 (face0 cube)
 304         t2 = tetrahedron2 (face5 cube)
 305         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 306         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 307
 308 -- | Given in Sorokina and Zeilfelder, p. 79.
 309 prop_c1020_identity :: Cube -> Bool
 310 prop_c1020_identity cube =
 311     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)
 312       where
 313         t0 = tetrahedron0 (face0 cube)
 314         t2 = tetrahedron2 (face5 cube)
 315         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 316         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 317
 318
 319 -- | Given in Sorokina and Zeilfelder, p. 79.
 320 prop_c1002_identity :: Cube -> Bool
 321 prop_c1002_identity cube =
 322     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)
 323       where
 324         t0 = tetrahedron0 (face0 cube)
 325         t2 = tetrahedron2 (face5 cube)
 326         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 327         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 328
 329
 330 -- | Given in Sorokina and Zeilfelder, p. 79.
 331 prop_c1011_identity :: Cube -> Bool
 332 prop_c1011_identity cube =
 333     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)
 334       where
 335         t0 = tetrahedron0 (face0 cube)
 336         t2 = tetrahedron2 (face5 cube)
 337         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 338         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 339
 340
 341 -- | Given in Sorokina and Zeilfelder, p. 80.
 342 prop_c0120_identity2 :: Cube -> Bool
 343 prop_c0120_identity2 cube =
 344         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 345       where
 346         t0 = tetrahedron0 (face0 cube)
 347         t1 = tetrahedron0 (face2 (top cube))
 348         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 349         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 350
 351
 352 -- | Given in Sorokina and Zeilfelder, p. 80.
 353 prop_c0102_identity2 :: Cube -> Bool
 354 prop_c0102_identity2 cube =
 355     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 356       where
 357         t0 = tetrahedron0 (face0 cube)
 358         t1 = tetrahedron0 (face2 (top cube))
 359         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 360         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 361
 362
 363 -- | Given in Sorokina and Zeilfelder, p. 80.
 364 prop_c0111_identity :: Cube -> Bool
 365 prop_c0111_identity cube =
 366     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 367       where
 368         t0 = tetrahedron0 (face0 cube)
 369         t1 = tetrahedron0 (face2 (top cube))
 370         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 371         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 372
 373
 374 -- | Given in Sorokina and Zeilfelder, p. 80.
 375 prop_c0210_identity2 :: Cube -> Bool
 376 prop_c0210_identity2 cube =
 377     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 378       where
 379         t0 = tetrahedron0 (face0 cube)
 380         t1 = tetrahedron0 (face2 (top cube))
 381         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 382         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 383
 384
 385 -- | Given in Sorokina and Zeilfelder, p. 80.
 386 prop_c0201_identity2 :: Cube -> Bool
 387 prop_c0201_identity2 cube =
 388     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 389       where
 390         t0 = tetrahedron0 (face0 cube)
 391         t1 = tetrahedron0 (face2 (top cube))
 392         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 393         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 394
 395
 396 -- | Given in Sorokina and Zeilfelder, p. 80.
 397 prop_c0300_identity3 :: Cube -> Bool
 398 prop_c0300_identity3 cube =
 399     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 400       where
 401         t0 = tetrahedron0 (face0 cube)
 402         t1 = tetrahedron0 (face2 (top cube))
 403         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 404         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)