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