src/Tests/Tetrahedron.hs

   1 module Tests.Tetrahedron
   2 where
   3
   4 import Test.Framework (Test, testGroup)
   5 import Test.Framework.Providers.HUnit (testCase)
   6 import Test.HUnit
   7 import Test.QuickCheck (Property, (==>))
   8
   9 import Cardinal
  10 import Comparisons
  11 import FunctionValues
  12 import Tetrahedron
  13 import ThreeDimensional
  14
  15 -- HUnit Tests
  16
  17
  18 -- | Check the volume of a particular tetrahedron (computed by hand)
  19 --   and whether or not it contains a specific point chosen to be
  20 --   outside of it. Its vertices are in clockwise order, so the volume
  21 --   should be negative.
  22 tetrahedron1_geometry_tests :: Test.Framework.Test
  23 tetrahedron1_geometry_tests =
  24   testGroup "tetrahedron1 geometry"
  25               [ testCase "volume1" volume1,
  26                 testCase "doesn't contain point1" doesnt_contain_point1]
  27   where
  28     p0 = (0, -0.5, 0)
  29     p1 = (0, 0.5, 0)
  30     p2 = (2, 0, 0)
  31     p3 = (1, 0, 1)
  32     t = Tetrahedron { v0 = p0,
  33                       v1 = p1,
  34                       v2 = p2,
  35                       v3 = p3,
  36                       fv = empty_values,
  37                       precomputed_volume = 0,
  38                       number = 0 }
  39
  40     volume1 :: Assertion
  41     volume1 =
  42       assertEqual "volume is correct" True (vol ~= (-1/3))
  43       where
  44         vol = volume t
  45
  46     doesnt_contain_point1 :: Assertion
  47     doesnt_contain_point1 =
  48       assertEqual "doesn't contain an exterior point" False contained
  49       where
  50         exterior_point = (5, 2, -9.0212)
  51         contained = contains_point t exterior_point
  52
  53
  54 -- | Check the volume of a particular tetrahedron (computed by hand)
  55 --   and whether or not it contains a specific point chosen to be
  56 --   inside of it. Its vertices are in counter-clockwise order, so the
  57 --   volume should be positive.
  58 tetrahedron2_geometry_tests :: Test.Framework.Test
  59 tetrahedron2_geometry_tests =
  60   testGroup "tetrahedron2 geometry"
  61               [ testCase "volume1" volume1,
  62                 testCase "contains point1" contains_point1]
  63   where
  64     p0 = (0, -0.5, 0)
  65     p1 = (2, 0, 0)
  66     p2 = (0, 0.5, 0)
  67     p3 = (1, 0, 1)
  68     t = Tetrahedron { v0 = p0,
  69                       v1 = p1,
  70                       v2 = p2,
  71                       v3 = p3,
  72                       fv = empty_values,
  73                       precomputed_volume = 0,
  74                       number = 0 }
  75
  76     volume1 :: Assertion
  77     volume1 = assertEqual "volume1 is correct" True (vol ~= (1/3))
  78       where
  79         vol = volume t
  80
  81     contains_point1 :: Assertion
  82     contains_point1 = assertEqual "contains an inner point" True contained
  83         where
  84           inner_point = (1, 0, 0.5)
  85           contained = contains_point t inner_point
  86
  87
  88 -- | Ensure that tetrahedra do not contain a particular point chosen to
  89 --   be outside of them.
  90 containment_tests :: Test.Framework.Test
  91 containment_tests =
  92   testGroup "containment tests"
  93               [ testCase "doesn't contain point2" doesnt_contain_point2,
  94                 testCase "doesn't contain point3" doesnt_contain_point3,
  95                 testCase "doesn't contain point4" doesnt_contain_point4,
  96                 testCase "doesn't contain point5" doesnt_contain_point5]
  97   where
  98     p2 = (0.5, 0.5, 1)
  99     p3 = (0.5, 0.5, 0.5)
 100     exterior_point = (0, 0, 0)
 101
 102     doesnt_contain_point2 :: Assertion
 103     doesnt_contain_point2 =
 104       assertEqual "doesn't contain an exterior point" False contained
 105       where
 106         p0 = (0, 1, 1)
 107         p1 = (1, 1, 1)
 108         t = Tetrahedron { v0 = p0,
 109                           v1 = p1,
 110                           v2 = p2,
 111                           v3 = p3,
 112                           fv = empty_values,
 113                           precomputed_volume = 0,
 114                           number = 0 }
 115         contained = contains_point t exterior_point
 116
 117
 118     doesnt_contain_point3 :: Assertion
 119     doesnt_contain_point3 =
 120       assertEqual "doesn't contain an exterior point" False contained
 121       where
 122         p0 = (1, 1, 1)
 123         p1 = (1, 0, 1)
 124         t = Tetrahedron { v0 = p0,
 125                           v1 = p1,
 126                           v2 = p2,
 127                           v3 = p3,
 128                           fv = empty_values,
 129                           precomputed_volume = 0,
 130                           number = 0 }
 131         contained = contains_point t exterior_point
 132
 133
 134     doesnt_contain_point4 :: Assertion
 135     doesnt_contain_point4 =
 136       assertEqual "doesn't contain an exterior point" False contained
 137       where
 138         p0 = (1, 0, 1)
 139         p1 = (0, 0, 1)
 140         t = Tetrahedron { v0 = p0,
 141                           v1 = p1,
 142                           v2 = p2,
 143                           v3 = p3,
 144                           fv = empty_values,
 145                           precomputed_volume = 0,
 146                           number = 0 }
 147         contained = contains_point t exterior_point
 148
 149
 150     doesnt_contain_point5 :: Assertion
 151     doesnt_contain_point5 =
 152       assertEqual "doesn't contain an exterior point" False contained
 153       where
 154         p0 = (0, 0, 1)
 155         p1 = (0, 1, 1)
 156         t = Tetrahedron { v0 = p0,
 157                           v1 = p1,
 158                           v2 = p2,
 159                           v3 = p3,
 160                           fv = empty_values,
 161                           precomputed_volume = 0,
 162                           number = 0 }
 163         contained = contains_point t exterior_point
 164
 165
 166 -- | The barycentric coordinate of v0 with respect to itself should
 167 --   be one.
 168 prop_b0_v0_always_unity :: Tetrahedron -> Property
 169 prop_b0_v0_always_unity t =
 170     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 171
 172 -- | The barycentric coordinate of v1 with respect to v0 should
 173 --   be zero.
 174 prop_b0_v1_always_zero :: Tetrahedron -> Property
 175 prop_b0_v1_always_zero t =
 176     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 177
 178 -- | The barycentric coordinate of v2 with respect to v0 should
 179 --   be zero.
 180 prop_b0_v2_always_zero :: Tetrahedron -> Property
 181 prop_b0_v2_always_zero t =
 182     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 183
 184 -- | The barycentric coordinate of v3 with respect to v0 should
 185 --   be zero.
 186 prop_b0_v3_always_zero :: Tetrahedron -> Property
 187 prop_b0_v3_always_zero t =
 188     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 189
 190 -- | The barycentric coordinate of v1 with respect to itself should
 191 --   be one.
 192 prop_b1_v1_always_unity :: Tetrahedron -> Property
 193 prop_b1_v1_always_unity t =
 194     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 195
 196 -- | The barycentric coordinate of v0 with respect to v1 should
 197 --   be zero.
 198 prop_b1_v0_always_zero :: Tetrahedron -> Property
 199 prop_b1_v0_always_zero t =
 200     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 201
 202 -- | The barycentric coordinate of v2 with respect to v1 should
 203 --   be zero.
 204 prop_b1_v2_always_zero :: Tetrahedron -> Property
 205 prop_b1_v2_always_zero t =
 206     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 207
 208 -- | The barycentric coordinate of v3 with respect to v1 should
 209 --   be zero.
 210 prop_b1_v3_always_zero :: Tetrahedron -> Property
 211 prop_b1_v3_always_zero t =
 212     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 213
 214 -- | The barycentric coordinate of v2 with respect to itself should
 215 --   be one.
 216 prop_b2_v2_always_unity :: Tetrahedron -> Property
 217 prop_b2_v2_always_unity t =
 218     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 219
 220 -- | The barycentric coordinate of v0 with respect to v2 should
 221 --   be zero.
 222 prop_b2_v0_always_zero :: Tetrahedron -> Property
 223 prop_b2_v0_always_zero t =
 224     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 225
 226 -- | The barycentric coordinate of v1 with respect to v2 should
 227 --   be zero.
 228 prop_b2_v1_always_zero :: Tetrahedron -> Property
 229 prop_b2_v1_always_zero t =
 230     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 231
 232 -- | The barycentric coordinate of v3 with respect to v2 should
 233 --   be zero.
 234 prop_b2_v3_always_zero :: Tetrahedron -> Property
 235 prop_b2_v3_always_zero t =
 236     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 237
 238 -- | The barycentric coordinate of v3 with respect to itself should
 239 --   be one.
 240 prop_b3_v3_always_unity :: Tetrahedron -> Property
 241 prop_b3_v3_always_unity t =
 242     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 243
 244 -- | The barycentric coordinate of v0 with respect to v3 should
 245 --   be zero.
 246 prop_b3_v0_always_zero :: Tetrahedron -> Property
 247 prop_b3_v0_always_zero t =
 248     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 249
 250 -- | The barycentric coordinate of v1 with respect to v3 should
 251 --   be zero.
 252 prop_b3_v1_always_zero :: Tetrahedron -> Property
 253 prop_b3_v1_always_zero t =
 254     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 255
 256 -- | The barycentric coordinate of v2 with respect to v3 should
 257 --   be zero.
 258 prop_b3_v2_always_zero :: Tetrahedron -> Property
 259 prop_b3_v2_always_zero t =
 260     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 261
 262
 263 -- | Used for convenience in the next few tests; not a test itself.
 264 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 265 p t i j k l = (polynomial t) (xi t i j k l)
 266
 267 -- | Given in Sorokina and Zeilfelder, p. 78.
 268 prop_c3000_identity :: Tetrahedron -> Property
 269 prop_c3000_identity t =
 270     (volume t) > 0 ==>
 271                c t 3 0 0 0 ~= p t 3 0 0 0
 272
 273 -- | Given in Sorokina and Zeilfelder, p. 78.
 274 prop_c2100_identity :: Tetrahedron -> Property
 275 prop_c2100_identity t =
 276     (volume t) > 0 ==>
 277       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 278         where
 279           term1 = (1/3)*(p t 0 3 0 0)
 280           term2 = (5/6)*(p t 3 0 0 0)
 281           term3 = 3*(p t 2 1 0 0)
 282           term4 = (3/2)*(p t 1 2 0 0)
 283
 284 -- | Given in Sorokina and Zeilfelder, p. 78.
 285 prop_c1110_identity :: Tetrahedron -> Property
 286 prop_c1110_identity t =
 287     (volume t) > 0 ==>
 288        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 289         where
 290           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 291           term2 = (9/2)*(p t 1 1 1 0)
 292           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 293           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
 294
 295
 296 prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
 297 prop_swapping_vertices_doesnt_affect_coefficients1 t =
 298       c t 0 0 1 2 == c t' 0 0 1 2
 299         where
 300           t' = t { v0 = (v1 t), v1 = (v0 t) }
 301
 302 prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool
 303 prop_swapping_vertices_doesnt_affect_coefficients2 t =
 304       c t 0 1 1 1 == c t' 0 1 1 1
 305         where
 306           t' = t { v2 = (v3 t), v3 = (v2 t) }
 307
 308 prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool
 309 prop_swapping_vertices_doesnt_affect_coefficients3 t =
 310       c t 2 1 0 0 == c t' 2 1 0 0
 311         where
 312           t' = t { v2 = (v3 t), v3 = (v2 t) }
 313
 314 prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool
 315 prop_swapping_vertices_doesnt_affect_coefficients4 t =
 316       c t 2 0 0 1 == c t' 2 0 0 1
 317         where
 318           t' = t { v0 = (v3 t), v3 = (v0 t) }