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 against the value
  20 --   computed by hand. Its vertices are in clockwise order, so the
  21 --   volume should be negative.
  22 test_volume1 :: Assertion
  23 test_volume1 =
  24     assertEqual "volume is correct" True (vol ~= (-1/3))
  25     where
  26       p0 = (0, -0.5, 0)
  27       p1 = (0, 0.5, 0)
  28       p2 = (2, 0, 0)
  29       p3 = (1, 0, 1)
  30       t = Tetrahedron { v0 = p0,
  31                         v1 = p1,
  32                         v2 = p2,
  33                         v3 = p3,
  34                         fv = empty_values }
  35       vol = volume t
  36
  37
  38 -- | Check the volume of a particular tetrahedron (computed by hand)
  39 --   and whether or not it contains a specific point chosen to be
  40 --   inside of it. Its vertices are in counter-clockwise order, so the
  41 --   volume should be positive.
  42 tetrahedron2_geometry_tests :: Test.Framework.Test
  43 tetrahedron2_geometry_tests =
  44   testGroup "tetrahedron2 geometry"
  45               [ testCase "volume1" volume1,
  46                 testCase "contains point1" contains_point1]
  47   where
  48     p0 = (0, -0.5, 0)
  49     p1 = (2, 0, 0)
  50     p2 = (0, 0.5, 0)
  51     p3 = (1, 0, 1)
  52     t = Tetrahedron { v0 = p0,
  53                       v1 = p1,
  54                       v2 = p2,
  55                       v3 = p3,
  56                       fv = empty_values }
  57
  58     volume1 :: Assertion
  59     volume1 = assertEqual "volume1 is correct" True (vol ~= (1/3))
  60       where
  61         vol = volume t
  62
  63     contains_point1 :: Assertion
  64     contains_point1 = assertEqual "contains an inner point" True contained
  65         where
  66           inner_point = (1, 0, 0.5)
  67           contained = contains_point t inner_point
  68
  69
  70 -- | Ensure that a tetrahedron does not contain a particular point chosen to
  71 --   be outside of it (first test).
  72 test_doesnt_contain_point1 :: Assertion
  73 test_doesnt_contain_point1 =
  74     assertEqual "doesn't contain an exterior point" False contained
  75     where
  76       p0 = (0, -0.5, 0)
  77       p1 = (0, 0.5, 0)
  78       p2 = (2, 0, 0)
  79       p3 = (1, 0, 1)
  80       exterior_point = (5, 2, -9.0212)
  81       t = Tetrahedron { v0 = p0,
  82                         v1 = p1,
  83                         v2 = p2,
  84                         v3 = p3,
  85                         fv = empty_values }
  86       contained = contains_point t exterior_point
  87
  88
  89 -- | Ensure that a tetrahedron does not contain a particular point chosen to
  90 --   be outside of it (second test).
  91 test_doesnt_contain_point2 :: Assertion
  92 test_doesnt_contain_point2 =
  93     assertEqual "doesn't contain an exterior point" False contained
  94     where
  95       p0 = (0, 1, 1)
  96       p1 = (1, 1, 1)
  97       p2 = (0.5, 0.5, 1)
  98       p3 = (0.5, 0.5, 0.5)
  99       exterior_point = (0, 0, 0)
 100       t = Tetrahedron { v0 = p0,
 101                         v1 = p1,
 102                         v2 = p2,
 103                         v3 = p3,
 104                         fv = empty_values }
 105       contained = contains_point t exterior_point
 106
 107
 108 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 109 --   be outside of it (third test).
 110 test_doesnt_contain_point3 :: Assertion
 111 test_doesnt_contain_point3 =
 112     assertEqual "doesn't contain an exterior point" False contained
 113     where
 114       p0 = (1, 1, 1)
 115       p1 = (1, 0, 1)
 116       p2 = (0.5, 0.5, 1)
 117       p3 = (0.5, 0.5, 0.5)
 118       exterior_point = (0, 0, 0)
 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 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 128 --   be outside of it (fourth test).
 129 test_doesnt_contain_point4 :: Assertion
 130 test_doesnt_contain_point4 =
 131     assertEqual "doesn't contain an exterior point" False contained
 132     where
 133       p0 = (1, 0, 1)
 134       p1 = (0, 0, 1)
 135       p2 = (0.5, 0.5, 1)
 136       p3 = (0.5, 0.5, 0.5)
 137       exterior_point = (0, 0, 0)
 138       t = Tetrahedron { v0 = p0,
 139                         v1 = p1,
 140                         v2 = p2,
 141                         v3 = p3,
 142                         fv = empty_values }
 143       contained = contains_point t exterior_point
 144
 145
 146 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 147 --   be outside of it (fifth test).
 148 test_doesnt_contain_point5 :: Assertion
 149 test_doesnt_contain_point5 =
 150     assertEqual "doesn't contain an exterior point" False contained
 151     where
 152       p0 = (0, 0, 1)
 153       p1 = (0, 1, 1)
 154       p2 = (0.5, 0.5, 1)
 155       p3 = (0.5, 0.5, 0.5)
 156       exterior_point = (0, 0, 0)
 157       t = Tetrahedron { v0 = p0,
 158                         v1 = p1,
 159                         v2 = p2,
 160                         v3 = p3,
 161                         fv = empty_values }
 162       contained = contains_point t exterior_point
 163
 164
 165 -- | The barycentric coordinate of v0 with respect to itself should
 166 --   be one.
 167 prop_b0_v0_always_unity :: Tetrahedron -> Property
 168 prop_b0_v0_always_unity t =
 169     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 170
 171 -- | The barycentric coordinate of v1 with respect to v0 should
 172 --   be zero.
 173 prop_b0_v1_always_zero :: Tetrahedron -> Property
 174 prop_b0_v1_always_zero t =
 175     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 176
 177 -- | The barycentric coordinate of v2 with respect to v0 should
 178 --   be zero.
 179 prop_b0_v2_always_zero :: Tetrahedron -> Property
 180 prop_b0_v2_always_zero t =
 181     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 182
 183 -- | The barycentric coordinate of v3 with respect to v0 should
 184 --   be zero.
 185 prop_b0_v3_always_zero :: Tetrahedron -> Property
 186 prop_b0_v3_always_zero t =
 187     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 188
 189 -- | The barycentric coordinate of v1 with respect to itself should
 190 --   be one.
 191 prop_b1_v1_always_unity :: Tetrahedron -> Property
 192 prop_b1_v1_always_unity t =
 193     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 194
 195 -- | The barycentric coordinate of v0 with respect to v1 should
 196 --   be zero.
 197 prop_b1_v0_always_zero :: Tetrahedron -> Property
 198 prop_b1_v0_always_zero t =
 199     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 200
 201 -- | The barycentric coordinate of v2 with respect to v1 should
 202 --   be zero.
 203 prop_b1_v2_always_zero :: Tetrahedron -> Property
 204 prop_b1_v2_always_zero t =
 205     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 206
 207 -- | The barycentric coordinate of v3 with respect to v1 should
 208 --   be zero.
 209 prop_b1_v3_always_zero :: Tetrahedron -> Property
 210 prop_b1_v3_always_zero t =
 211     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 212
 213 -- | The barycentric coordinate of v2 with respect to itself should
 214 --   be one.
 215 prop_b2_v2_always_unity :: Tetrahedron -> Property
 216 prop_b2_v2_always_unity t =
 217     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 218
 219 -- | The barycentric coordinate of v0 with respect to v2 should
 220 --   be zero.
 221 prop_b2_v0_always_zero :: Tetrahedron -> Property
 222 prop_b2_v0_always_zero t =
 223     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 224
 225 -- | The barycentric coordinate of v1 with respect to v2 should
 226 --   be zero.
 227 prop_b2_v1_always_zero :: Tetrahedron -> Property
 228 prop_b2_v1_always_zero t =
 229     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 230
 231 -- | The barycentric coordinate of v3 with respect to v2 should
 232 --   be zero.
 233 prop_b2_v3_always_zero :: Tetrahedron -> Property
 234 prop_b2_v3_always_zero t =
 235     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 236
 237 -- | The barycentric coordinate of v3 with respect to itself should
 238 --   be one.
 239 prop_b3_v3_always_unity :: Tetrahedron -> Property
 240 prop_b3_v3_always_unity t =
 241     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 242
 243 -- | The barycentric coordinate of v0 with respect to v3 should
 244 --   be zero.
 245 prop_b3_v0_always_zero :: Tetrahedron -> Property
 246 prop_b3_v0_always_zero t =
 247     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 248
 249 -- | The barycentric coordinate of v1 with respect to v3 should
 250 --   be zero.
 251 prop_b3_v1_always_zero :: Tetrahedron -> Property
 252 prop_b3_v1_always_zero t =
 253     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 254
 255 -- | The barycentric coordinate of v2 with respect to v3 should
 256 --   be zero.
 257 prop_b3_v2_always_zero :: Tetrahedron -> Property
 258 prop_b3_v2_always_zero t =
 259     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 260
 261
 262 -- | Used for convenience in the next few tests; not a test itself.
 263 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 264 p t i j k l = (polynomial t) (xi t i j k l)
 265
 266 -- | Given in Sorokina and Zeilfelder, p. 78.
 267 prop_c3000_identity :: Tetrahedron -> Property
 268 prop_c3000_identity t =
 269     (volume t) > 0 ==>
 270                c t 3 0 0 0 ~= p t 3 0 0 0
 271
 272 -- | Given in Sorokina and Zeilfelder, p. 78.
 273 prop_c2100_identity :: Tetrahedron -> Property
 274 prop_c2100_identity t =
 275     (volume t) > 0 ==>
 276       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 277         where
 278           term1 = (1/3)*(p t 0 3 0 0)
 279           term2 = (5/6)*(p t 3 0 0 0)
 280           term3 = 3*(p t 2 1 0 0)
 281           term4 = (3/2)*(p t 1 2 0 0)
 282
 283 -- | Given in Sorokina and Zeilfelder, p. 78.
 284 prop_c1110_identity :: Tetrahedron -> Property
 285 prop_c1110_identity t =
 286     (volume t) > 0 ==>
 287        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 288         where
 289           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 290           term2 = (9/2)*(p t 1 1 1 0)
 291           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 292           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
 293
 294 prop_x_rotation_doesnt_affect_front :: Tetrahedron -> Bool
 295 prop_x_rotation_doesnt_affect_front t =
 296     expr1 == expr2
 297     where
 298       fv0 = Tetrahedron.fv t
 299       fv1 = rotate cwx (Tetrahedron.fv t)
 300       expr1 = front fv0
 301       expr2 = front fv1
 302
 303 prop_x_rotation_doesnt_affect_back :: Tetrahedron -> Bool
 304 prop_x_rotation_doesnt_affect_back t =
 305     expr1 == expr2
 306     where
 307       fv0 = Tetrahedron.fv t
 308       fv1 = rotate cwx (Tetrahedron.fv t)
 309       expr1 = back fv0
 310       expr2 = back fv1
 311
 312
 313 prop_y_rotation_doesnt_affect_left :: Tetrahedron -> Bool
 314 prop_y_rotation_doesnt_affect_left t =
 315     expr1 == expr2
 316     where
 317       fv0 = Tetrahedron.fv t
 318       fv1 = rotate cwy (Tetrahedron.fv t)
 319       expr1 = left fv0
 320       expr2 = left fv1
 321
 322 prop_y_rotation_doesnt_affect_right :: Tetrahedron -> Bool
 323 prop_y_rotation_doesnt_affect_right t =
 324     expr1 == expr2
 325     where
 326       fv0 = Tetrahedron.fv t
 327       fv1 = rotate cwy (Tetrahedron.fv t)
 328       expr1 = right fv0
 329       expr2 = right fv1
 330
 331
 332 prop_z_rotation_doesnt_affect_down :: Tetrahedron -> Bool
 333 prop_z_rotation_doesnt_affect_down t =
 334     expr1 == expr2
 335     where
 336       fv0 = Tetrahedron.fv t
 337       fv1 = rotate cwz (Tetrahedron.fv t)
 338       expr1 = down fv0
 339       expr2 = down fv1
 340
 341
 342 prop_z_rotation_doesnt_affect_top :: Tetrahedron -> Bool
 343 prop_z_rotation_doesnt_affect_top t =
 344     expr1 == expr2
 345     where
 346       fv0 = Tetrahedron.fv t
 347       fv1 = rotate cwz (Tetrahedron.fv t)
 348       expr1 = top fv0
 349       expr2 = top fv1
 350
 351 prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
 352 prop_swapping_vertices_doesnt_affect_coefficients1 t =
 353       c t 0 0 1 2 == c t' 0 0 1 2
 354         where
 355           t' = t { v0 = (v1 t), v1 = (v0 t) }
 356
 357 prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool
 358 prop_swapping_vertices_doesnt_affect_coefficients2 t =
 359       c t 0 1 1 1 == c t' 0 1 1 1
 360         where
 361           t' = t { v2 = (v3 t), v3 = (v2 t) }
 362
 363 prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool
 364 prop_swapping_vertices_doesnt_affect_coefficients3 t =
 365       c t 2 1 0 0 == c t' 2 1 0 0
 366         where
 367           t' = t { v2 = (v3 t), v3 = (v2 t) }
 368
 369 prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool
 370 prop_swapping_vertices_doesnt_affect_coefficients4 t =
 371       c t 2 0 0 1 == c t' 2 0 0 1
 372         where
 373           t' = t { v0 = (v3 t), v3 = (v0 t) }