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 Tests.FunctionValues()
  13 import Tetrahedron
  14 import ThreeDimensional
  15
  16 -- HUnit Tests
  17
  18
  19 -- | Check the volume of a particular tetrahedron (computed by hand)
  20 --   and whether or not it contains a specific point chosen to be
  21 --   outside of it. Its vertices are in clockwise order, so the volume
  22 --   should be negative.
  23 tetrahedron1_geometry_tests :: Test.Framework.Test
  24 tetrahedron1_geometry_tests =
  25   testGroup "tetrahedron1 geometry"
  26               [ testCase "volume1" volume1,
  27                 testCase "doesn't contain point1" doesnt_contain_point1]
  28   where
  29     p0 = (0, -0.5, 0)
  30     p1 = (0, 0.5, 0)
  31     p2 = (2, 0, 0)
  32     p3 = (1, 0, 1)
  33     t = Tetrahedron { v0 = p0,
  34                       v1 = p1,
  35                       v2 = p2,
  36                       v3 = p3,
  37                       fv = empty_values }
  38
  39     volume1 :: Assertion
  40     volume1 =
  41       assertEqual "volume is correct" True (vol ~= (-1/3))
  42       where
  43         vol = volume t
  44
  45     doesnt_contain_point1 :: Assertion
  46     doesnt_contain_point1 =
  47       assertEqual "doesn't contain an exterior point" False contained
  48       where
  49         exterior_point = (5, 2, -9.0212)
  50         contained = contains_point t exterior_point
  51
  52
  53 -- | Check the volume of a particular tetrahedron (computed by hand)
  54 --   and whether or not it contains a specific point chosen to be
  55 --   inside of it. Its vertices are in counter-clockwise order, so the
  56 --   volume should be positive.
  57 tetrahedron2_geometry_tests :: Test.Framework.Test
  58 tetrahedron2_geometry_tests =
  59   testGroup "tetrahedron2 geometry"
  60               [ testCase "volume1" volume1,
  61                 testCase "contains point1" contains_point1]
  62   where
  63     p0 = (0, -0.5, 0)
  64     p1 = (2, 0, 0)
  65     p2 = (0, 0.5, 0)
  66     p3 = (1, 0, 1)
  67     t = Tetrahedron { v0 = p0,
  68                       v1 = p1,
  69                       v2 = p2,
  70                       v3 = p3,
  71                       fv = empty_values }
  72
  73     volume1 :: Assertion
  74     volume1 = assertEqual "volume1 is correct" True (vol ~= (1/3))
  75       where
  76         vol = volume t
  77
  78     contains_point1 :: Assertion
  79     contains_point1 = assertEqual "contains an inner point" True contained
  80         where
  81           inner_point = (1, 0, 0.5)
  82           contained = contains_point t inner_point
  83
  84
  85 -- | Ensure that tetrahedra do not contain a particular point chosen to
  86 --   be outside of them.
  87 containment_tests :: Test.Framework.Test
  88 containment_tests =
  89   testGroup "containment tests"
  90               [ testCase "doesn't contain point2" doesnt_contain_point2,
  91                 testCase "doesn't contain point3" doesnt_contain_point3,
  92                 testCase "doesn't contain point4" doesnt_contain_point4,
  93                 testCase "doesn't contain point5" doesnt_contain_point5]
  94   where
  95     p2 = (0.5, 0.5, 1)
  96     p3 = (0.5, 0.5, 0.5)
  97     exterior_point = (0, 0, 0)
  98
  99     doesnt_contain_point2 :: Assertion
 100     doesnt_contain_point2 =
 101       assertEqual "doesn't contain an exterior point" False contained
 102       where
 103         p0 = (0, 1, 1)
 104         p1 = (1, 1, 1)
 105         t = Tetrahedron { v0 = p0,
 106                           v1 = p1,
 107                           v2 = p2,
 108                           v3 = p3,
 109                           fv = empty_values }
 110         contained = contains_point t exterior_point
 111
 112
 113     doesnt_contain_point3 :: Assertion
 114     doesnt_contain_point3 =
 115       assertEqual "doesn't contain an exterior point" False contained
 116       where
 117         p0 = (1, 1, 1)
 118         p1 = (1, 0, 1)
 119         t = Tetrahedron { v0 = p0,
 120                           v1 = p1,
 121                           v2 = p2,
 122                           v3 = p3,
 123                           fv = empty_values }
 124         contained = contains_point t exterior_point
 125
 126
 127     doesnt_contain_point4 :: Assertion
 128     doesnt_contain_point4 =
 129       assertEqual "doesn't contain an exterior point" False contained
 130       where
 131         p0 = (1, 0, 1)
 132         p1 = (0, 0, 1)
 133         t = Tetrahedron { v0 = p0,
 134                           v1 = p1,
 135                           v2 = p2,
 136                           v3 = p3,
 137                           fv = empty_values }
 138         contained = contains_point t exterior_point
 139
 140
 141     doesnt_contain_point5 :: Assertion
 142     doesnt_contain_point5 =
 143       assertEqual "doesn't contain an exterior point" False contained
 144       where
 145         p0 = (0, 0, 1)
 146         p1 = (0, 1, 1)
 147         t = Tetrahedron { v0 = p0,
 148                           v1 = p1,
 149                           v2 = p2,
 150                           v3 = p3,
 151                           fv = empty_values }
 152         contained = contains_point t exterior_point
 153
 154
 155 -- | The barycentric coordinate of v0 with respect to itself should
 156 --   be one.
 157 prop_b0_v0_always_unity :: Tetrahedron -> Property
 158 prop_b0_v0_always_unity t =
 159     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 160
 161 -- | The barycentric coordinate of v1 with respect to v0 should
 162 --   be zero.
 163 prop_b0_v1_always_zero :: Tetrahedron -> Property
 164 prop_b0_v1_always_zero t =
 165     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 166
 167 -- | The barycentric coordinate of v2 with respect to v0 should
 168 --   be zero.
 169 prop_b0_v2_always_zero :: Tetrahedron -> Property
 170 prop_b0_v2_always_zero t =
 171     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 172
 173 -- | The barycentric coordinate of v3 with respect to v0 should
 174 --   be zero.
 175 prop_b0_v3_always_zero :: Tetrahedron -> Property
 176 prop_b0_v3_always_zero t =
 177     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 178
 179 -- | The barycentric coordinate of v1 with respect to itself should
 180 --   be one.
 181 prop_b1_v1_always_unity :: Tetrahedron -> Property
 182 prop_b1_v1_always_unity t =
 183     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 184
 185 -- | The barycentric coordinate of v0 with respect to v1 should
 186 --   be zero.
 187 prop_b1_v0_always_zero :: Tetrahedron -> Property
 188 prop_b1_v0_always_zero t =
 189     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 190
 191 -- | The barycentric coordinate of v2 with respect to v1 should
 192 --   be zero.
 193 prop_b1_v2_always_zero :: Tetrahedron -> Property
 194 prop_b1_v2_always_zero t =
 195     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 196
 197 -- | The barycentric coordinate of v3 with respect to v1 should
 198 --   be zero.
 199 prop_b1_v3_always_zero :: Tetrahedron -> Property
 200 prop_b1_v3_always_zero t =
 201     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 202
 203 -- | The barycentric coordinate of v2 with respect to itself should
 204 --   be one.
 205 prop_b2_v2_always_unity :: Tetrahedron -> Property
 206 prop_b2_v2_always_unity t =
 207     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 208
 209 -- | The barycentric coordinate of v0 with respect to v2 should
 210 --   be zero.
 211 prop_b2_v0_always_zero :: Tetrahedron -> Property
 212 prop_b2_v0_always_zero t =
 213     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 214
 215 -- | The barycentric coordinate of v1 with respect to v2 should
 216 --   be zero.
 217 prop_b2_v1_always_zero :: Tetrahedron -> Property
 218 prop_b2_v1_always_zero t =
 219     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 220
 221 -- | The barycentric coordinate of v3 with respect to v2 should
 222 --   be zero.
 223 prop_b2_v3_always_zero :: Tetrahedron -> Property
 224 prop_b2_v3_always_zero t =
 225     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 226
 227 -- | The barycentric coordinate of v3 with respect to itself should
 228 --   be one.
 229 prop_b3_v3_always_unity :: Tetrahedron -> Property
 230 prop_b3_v3_always_unity t =
 231     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 232
 233 -- | The barycentric coordinate of v0 with respect to v3 should
 234 --   be zero.
 235 prop_b3_v0_always_zero :: Tetrahedron -> Property
 236 prop_b3_v0_always_zero t =
 237     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 238
 239 -- | The barycentric coordinate of v1 with respect to v3 should
 240 --   be zero.
 241 prop_b3_v1_always_zero :: Tetrahedron -> Property
 242 prop_b3_v1_always_zero t =
 243     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 244
 245 -- | The barycentric coordinate of v2 with respect to v3 should
 246 --   be zero.
 247 prop_b3_v2_always_zero :: Tetrahedron -> Property
 248 prop_b3_v2_always_zero t =
 249     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 250
 251
 252 -- | Used for convenience in the next few tests; not a test itself.
 253 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 254 p t i j k l = (polynomial t) (xi t i j k l)
 255
 256 -- | Given in Sorokina and Zeilfelder, p. 78.
 257 prop_c3000_identity :: Tetrahedron -> Property
 258 prop_c3000_identity t =
 259     (volume t) > 0 ==>
 260                c t 3 0 0 0 ~= p t 3 0 0 0
 261
 262 -- | Given in Sorokina and Zeilfelder, p. 78.
 263 prop_c2100_identity :: Tetrahedron -> Property
 264 prop_c2100_identity t =
 265     (volume t) > 0 ==>
 266       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 267         where
 268           term1 = (1/3)*(p t 0 3 0 0)
 269           term2 = (5/6)*(p t 3 0 0 0)
 270           term3 = 3*(p t 2 1 0 0)
 271           term4 = (3/2)*(p t 1 2 0 0)
 272
 273 -- | Given in Sorokina and Zeilfelder, p. 78.
 274 prop_c1110_identity :: Tetrahedron -> Property
 275 prop_c1110_identity t =
 276     (volume t) > 0 ==>
 277        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 278         where
 279           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 280           term2 = (9/2)*(p t 1 1 1 0)
 281           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 282           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
 283
 284 prop_x_rotation_doesnt_affect_front :: Tetrahedron -> Bool
 285 prop_x_rotation_doesnt_affect_front t =
 286     expr1 == expr2
 287     where
 288       fv0 = Tetrahedron.fv t
 289       fv1 = rotate cwx (Tetrahedron.fv t)
 290       expr1 = front fv0
 291       expr2 = front fv1
 292
 293 prop_x_rotation_doesnt_affect_back :: Tetrahedron -> Bool
 294 prop_x_rotation_doesnt_affect_back t =
 295     expr1 == expr2
 296     where
 297       fv0 = Tetrahedron.fv t
 298       fv1 = rotate cwx (Tetrahedron.fv t)
 299       expr1 = back fv0
 300       expr2 = back fv1
 301
 302
 303 prop_y_rotation_doesnt_affect_left :: Tetrahedron -> Bool
 304 prop_y_rotation_doesnt_affect_left t =
 305     expr1 == expr2
 306     where
 307       fv0 = Tetrahedron.fv t
 308       fv1 = rotate cwy (Tetrahedron.fv t)
 309       expr1 = left fv0
 310       expr2 = left fv1
 311
 312 prop_y_rotation_doesnt_affect_right :: Tetrahedron -> Bool
 313 prop_y_rotation_doesnt_affect_right t =
 314     expr1 == expr2
 315     where
 316       fv0 = Tetrahedron.fv t
 317       fv1 = rotate cwy (Tetrahedron.fv t)
 318       expr1 = right fv0
 319       expr2 = right fv1
 320
 321
 322 prop_z_rotation_doesnt_affect_down :: Tetrahedron -> Bool
 323 prop_z_rotation_doesnt_affect_down t =
 324     expr1 == expr2
 325     where
 326       fv0 = Tetrahedron.fv t
 327       fv1 = rotate cwz (Tetrahedron.fv t)
 328       expr1 = down fv0
 329       expr2 = down fv1
 330
 331
 332 prop_z_rotation_doesnt_affect_top :: Tetrahedron -> Bool
 333 prop_z_rotation_doesnt_affect_top t =
 334     expr1 == expr2
 335     where
 336       fv0 = Tetrahedron.fv t
 337       fv1 = rotate cwz (Tetrahedron.fv t)
 338       expr1 = top fv0
 339       expr2 = top fv1
 340
 341 prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
 342 prop_swapping_vertices_doesnt_affect_coefficients1 t =
 343       c t 0 0 1 2 == c t' 0 0 1 2
 344         where
 345           t' = t { v0 = (v1 t), v1 = (v0 t) }
 346
 347 prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool
 348 prop_swapping_vertices_doesnt_affect_coefficients2 t =
 349       c t 0 1 1 1 == c t' 0 1 1 1
 350         where
 351           t' = t { v2 = (v3 t), v3 = (v2 t) }
 352
 353 prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool
 354 prop_swapping_vertices_doesnt_affect_coefficients3 t =
 355       c t 2 1 0 0 == c t' 2 1 0 0
 356         where
 357           t' = t { v2 = (v3 t), v3 = (v2 t) }
 358
 359 prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool
 360 prop_swapping_vertices_doesnt_affect_coefficients4 t =
 361       c t 2 0 0 1 == c t' 2 0 0 1
 362         where
 363           t' = t { v0 = (v3 t), v3 = (v0 t) }