Grid.hs

   1 module Tests.Grid
   2 where
   3
   4 import Test.Framework (Test, testGroup)
   5 import Test.Framework.Providers.HUnit (testCase)
   6 import Test.HUnit
   7 import Test.QuickCheck
   8
   9
  10 import Assertions
  11 import Comparisons
  12 import Cube hiding (i, j, k)
  13 import Examples
  14 import FunctionValues (value_at)
  15 import Grid
  16 import Point (Point)
  17 import Tetrahedron
  18 import ThreeDimensional
  19 import Values (dims)
  20
  21
  22 -- | Check all coefficients of tetrahedron0 belonging to the cube
  23 --   centered on (1,1,1) with a grid constructed from the trilinear
  24 --   values. See example one in the paper.
  25 --
  26 --   We also verify that the four vertices on face0 of the cube are
  27 --   in the correct location.
  28 --
  29 trilinear_c0_t0_tests :: Test.Framework.Test
  30 trilinear_c0_t0_tests =
  31   testGroup "trilinear c0 t0"
  32     [testGroup "coefficients"
  33       [testCase "c0030 is correct" test_trilinear_c0030,
  34        testCase "c0003 is correct" test_trilinear_c0003,
  35        testCase "c0021 is correct" test_trilinear_c0021,
  36        testCase "c0012 is correct" test_trilinear_c0012,
  37        testCase "c0120 is correct" test_trilinear_c0120,
  38        testCase "c0102 is correct" test_trilinear_c0102,
  39        testCase "c0111 is correct" test_trilinear_c0111,
  40        testCase "c0210 is correct" test_trilinear_c0210,
  41        testCase "c0201 is correct" test_trilinear_c0201,
  42        testCase "c0300 is correct" test_trilinear_c0300,
  43        testCase "c1020 is correct" test_trilinear_c1020,
  44        testCase "c1002 is correct" test_trilinear_c1002,
  45        testCase "c1011 is correct" test_trilinear_c1011,
  46        testCase "c1110 is correct" test_trilinear_c1110,
  47        testCase "c1101 is correct" test_trilinear_c1101,
  48        testCase "c1200 is correct" test_trilinear_c1200,
  49        testCase "c2010 is correct" test_trilinear_c2010,
  50        testCase "c2001 is correct" test_trilinear_c2001,
  51        testCase "c2100 is correct" test_trilinear_c2100,
  52        testCase "c3000 is correct" test_trilinear_c3000],
  53
  54     testGroup "face0 vertices"
  55       [testCase "v0 is correct" test_trilinear_f0_t0_v0,
  56        testCase "v1 is correct" test_trilinear_f0_t0_v1,
  57        testCase "v2 is correct" test_trilinear_f0_t0_v2,
  58        testCase "v3 is correct" test_trilinear_f0_t0_v3]
  59     ]
  60   where
  61     g = make_grid 1 trilinear
  62     cube = cube_at g 1 1 1
  63     t = tetrahedron0 cube
  64
  65     test_trilinear_c0030 :: Assertion
  66     test_trilinear_c0030 =
  67       assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  68
  69     test_trilinear_c0003 :: Assertion
  70     test_trilinear_c0003 =
  71       assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  72
  73     test_trilinear_c0021 :: Assertion
  74     test_trilinear_c0021 =
  75       assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  76
  77     test_trilinear_c0012 :: Assertion
  78     test_trilinear_c0012 =
  79       assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  80
  81     test_trilinear_c0120 :: Assertion
  82     test_trilinear_c0120 =
  83       assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
  84
  85     test_trilinear_c0102 :: Assertion
  86     test_trilinear_c0102 =
  87       assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
  88
  89     test_trilinear_c0111 :: Assertion
  90     test_trilinear_c0111 =
  91       assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
  92
  93     test_trilinear_c0210 :: Assertion
  94     test_trilinear_c0210 =
  95       assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
  96
  97     test_trilinear_c0201 :: Assertion
  98     test_trilinear_c0201 =
  99       assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
 100
 101     test_trilinear_c0300 :: Assertion
 102     test_trilinear_c0300 =
 103       assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
 104
 105     test_trilinear_c1020 :: Assertion
 106     test_trilinear_c1020 =
 107       assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
 108
 109     test_trilinear_c1002 :: Assertion
 110     test_trilinear_c1002 =
 111       assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
 112
 113     test_trilinear_c1011 :: Assertion
 114     test_trilinear_c1011 =
 115       assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
 116
 117     test_trilinear_c1110 :: Assertion
 118     test_trilinear_c1110 =
 119       assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
 120
 121     test_trilinear_c1101 :: Assertion
 122     test_trilinear_c1101 =
 123       assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
 124
 125     test_trilinear_c1200 :: Assertion
 126     test_trilinear_c1200 =
 127       assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
 128
 129     test_trilinear_c2010 :: Assertion
 130     test_trilinear_c2010 =
 131       assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
 132
 133     test_trilinear_c2001 :: Assertion
 134     test_trilinear_c2001 =
 135       assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
 136
 137     test_trilinear_c2100 :: Assertion
 138     test_trilinear_c2100 =
 139       assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
 140
 141     test_trilinear_c3000 :: Assertion
 142     test_trilinear_c3000 =
 143       assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 144
 145     test_trilinear_f0_t0_v0 :: Assertion
 146     test_trilinear_f0_t0_v0 =
 147       assertEqual "v0 is correct" (v0 t) (1, 1, 1)
 148
 149     test_trilinear_f0_t0_v1 :: Assertion
 150     test_trilinear_f0_t0_v1 =
 151       assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
 152
 153     test_trilinear_f0_t0_v2 :: Assertion
 154     test_trilinear_f0_t0_v2 =
 155       assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
 156
 157     test_trilinear_f0_t0_v3 :: Assertion
 158     test_trilinear_f0_t0_v3 =
 159       assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
 160
 161
 162 test_trilinear_reproduced :: Assertion
 163 test_trilinear_reproduced =
 164     assertTrue "trilinears are reproduced correctly" $
 165              and [p (i', j', k') ~= value_at trilinear i j k
 166                     | i <- [0..2],
 167                       j <- [0..2],
 168                       k <- [0..2],
 169                       t <- tetrahedra c0,
 170                       let p = polynomial t,
 171                       let i' = fromIntegral i,
 172                       let j' = fromIntegral j,
 173                       let k' = fromIntegral k]
 174     where
 175       g = make_grid 1 trilinear
 176       c0 = cube_at g 1 1 1
 177
 178
 179 test_zeros_reproduced :: Assertion
 180 test_zeros_reproduced =
 181     assertTrue "the zero function is reproduced correctly" $
 182              and [p (i', j', k') ~= value_at zeros i j k
 183                     | i <- [0..2],
 184                       j <- [0..2],
 185                       k <- [0..2],
 186                       let i' = fromIntegral i,
 187                       let j' = fromIntegral j,
 188                       let k' = fromIntegral k]
 189     where
 190       g = make_grid 1 zeros
 191       c0 = cube_at g 1 1 1
 192       t0 = tetrahedron0 c0
 193       p = polynomial t0
 194
 195
 196 -- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
 197 test_trilinear9x9x9_reproduced :: Assertion
 198 test_trilinear9x9x9_reproduced =
 199     assertTrue "trilinear 9x9x9 is reproduced correctly" $
 200       and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
 201             | i <- [0..8],
 202               j <- [0..8],
 203               k <- [0..8],
 204               t <- tetrahedra c0,
 205               let p = polynomial t,
 206               let i' = (fromIntegral i) * 0.5,
 207               let j' = (fromIntegral j) * 0.5,
 208               let k' = (fromIntegral k) * 0.5]
 209     where
 210       g = make_grid 1 trilinear
 211       c0 = cube_at g 1 1 1
 212
 213
 214 -- | The point 'p' in this test lies on the boundary of tetrahedra 12 and 15.
 215 --   However, the 'contains_point' test fails due to some numerical innacuracy.
 216 --   This bug should have been fixed by setting a positive tolerance level.
 217 --
 218 --   Example from before the fix:
 219 --
 220 --   > b0 (tetrahedron15 c) p
 221 --   -3.4694469519536365e-18
 222 --
 223 test_tetrahedra_collision_sensitivity :: Assertion
 224 test_tetrahedra_collision_sensitivity =
 225   assertTrue "tetrahedron collision tests isn't too sensitive" $
 226              contains_point t15 p
 227   where
 228     g = make_grid 1 naturals_1d
 229     c = cube_at g 0 17 1
 230     p = (0, 16.75, 0.5) :: Point
 231     t15 = tetrahedron15 c
 232
 233
 234 prop_cube_indices_never_go_out_of_bounds :: Grid -> Gen Bool
 235 prop_cube_indices_never_go_out_of_bounds g =
 236   do
 237     let delta = Grid.h g
 238     let coordmin = negate (delta/2)
 239
 240     let (xsize, ysize, zsize) = dims $ function_values g
 241     let xmax = delta*(fromIntegral xsize) - (delta/2)
 242     let ymax = delta*(fromIntegral ysize) - (delta/2)
 243     let zmax = delta*(fromIntegral zsize) - (delta/2)
 244
 245     x <- choose (coordmin, xmax)
 246     y <- choose (coordmin, ymax)
 247     z <- choose (coordmin, zmax)
 248
 249     let p = (x,y,z) :: Point
 250     let idx_x = calculate_containing_cube_coordinate g x
 251     let idx_y = calculate_containing_cube_coordinate g y
 252     let idx_z = calculate_containing_cube_coordinate g z
 253
 254     return $
 255       idx_x >= 0 &&
 256       idx_x <= xsize - 1 &&
 257       idx_y >= 0 &&
 258       idx_y <= ysize - 1 &&
 259       idx_z >= 0 &&
 260       idx_z <= zsize - 1