src/Tests/Tetrahedron.hs

   1 module Tests.Tetrahedron
   2 where
   3
   4 import Test.HUnit
   5 import Test.QuickCheck
   6
   7 import Cardinal
   8 import Comparisons
   9 import Point
  10 import FunctionValues
  11 import Tests.FunctionValues()
  12 import Tetrahedron
  13 import ThreeDimensional
  14
  15 instance Arbitrary Tetrahedron where
  16     arbitrary = do
  17       rnd_v0 <- arbitrary :: Gen Point
  18       rnd_v1 <- arbitrary :: Gen Point
  19       rnd_v2 <- arbitrary :: Gen Point
  20       rnd_v3 <- arbitrary :: Gen Point
  21       rnd_fv <- arbitrary :: Gen FunctionValues
  22       return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
  23
  24 -- HUnit Tests
  25
  26
  27 -- | Check the volume of a particular tetrahedron against the value
  28 --   computed by hand. Its vertices are in clockwise order, so the
  29 --   volume should be negative.
  30 test_volume1 :: Assertion
  31 test_volume1 =
  32     assertEqual "volume is correct" True (vol ~= (-1/3))
  33     where
  34       p0 = (0, -0.5, 0)
  35       p1 = (0, 0.5, 0)
  36       p2 = (2, 0, 0)
  37       p3 = (1, 0, 1)
  38       t = Tetrahedron { v0 = p0,
  39                         v1 = p1,
  40                         v2 = p2,
  41                         v3 = p3,
  42                         fv = empty_values }
  43       vol = volume t
  44
  45
  46 -- | Check the volume of a particular tetrahedron against the value
  47 --   computed by hand. Its vertices are in counter-clockwise order, so
  48 --   the volume should be positive.
  49 test_volume2 :: Assertion
  50 test_volume2 =
  51     assertEqual "volume is correct" True (vol ~= (1/3))
  52     where
  53       p0 = (0, -0.5, 0)
  54       p1 = (2, 0, 0)
  55       p2 = (0, 0.5, 0)
  56       p3 = (1, 0, 1)
  57       t = Tetrahedron { v0 = p0,
  58                         v1 = p1,
  59                         v2 = p2,
  60                         v3 = p3,
  61                         fv = empty_values }
  62       vol = volume t
  63
  64
  65 -- | Ensure that a tetrahedron contains a particular point chosen to
  66 --   be inside of it.
  67 test_contains_point1 :: Assertion
  68 test_contains_point1 =
  69     assertEqual "contains an inner point" True (contains_point t inner_point)
  70     where
  71       p0 = (0, -0.5, 0)
  72       p1 = (0, 0.5, 0)
  73       p2 = (2, 0, 0)
  74       p3 = (1, 0, 1)
  75       inner_point = (1, 0, 0.5)
  76       t = Tetrahedron { v0 = p0,
  77                         v1 = p1,
  78                         v2 = p2,
  79                         v3 = p3,
  80                         fv = empty_values }
  81
  82
  83 -- | Ensure that a tetrahedron does not contain a particular point chosen to
  84 --   be outside of it (first test).
  85 test_doesnt_contain_point1 :: Assertion
  86 test_doesnt_contain_point1 =
  87     assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
  88     where
  89       p0 = (0, -0.5, 0)
  90       p1 = (0, 0.5, 0)
  91       p2 = (2, 0, 0)
  92       p3 = (1, 0, 1)
  93       exterior_point = (5, 2, -9.0212)
  94       t = Tetrahedron { v0 = p0,
  95                         v1 = p1,
  96                         v2 = p2,
  97                         v3 = p3,
  98                         fv = empty_values }
  99
 100
 101 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 102 --   be outside of it (second test).
 103 test_doesnt_contain_point2 :: Assertion
 104 test_doesnt_contain_point2 =
 105     assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 106     where
 107       p0 = (0, 1, 1)
 108       p1 = (1, 1, 1)
 109       p2 = (0.5, 0.5, 1)
 110       p3 = (0.5, 0.5, 0.5)
 111       exterior_point = (0, 0, 0)
 112       t = Tetrahedron { v0 = p0,
 113                         v1 = p1,
 114                         v2 = p2,
 115                         v3 = p3,
 116                         fv = empty_values }
 117
 118
 119 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 120 --   be outside of it (third test).
 121 test_doesnt_contain_point3 :: Assertion
 122 test_doesnt_contain_point3 =
 123     assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 124     where
 125       p0 = (1, 1, 1)
 126       p1 = (1, 0, 1)
 127       p2 = (0.5, 0.5, 1)
 128       p3 = (0.5, 0.5, 0.5)
 129       exterior_point = (0, 0, 0)
 130       t = Tetrahedron { v0 = p0,
 131                         v1 = p1,
 132                         v2 = p2,
 133                         v3 = p3,
 134                         fv = empty_values }
 135
 136
 137 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 138 --   be outside of it (fourth test).
 139 test_doesnt_contain_point4 :: Assertion
 140 test_doesnt_contain_point4 =
 141     assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 142     where
 143       p0 = (1, 0, 1)
 144       p1 = (0, 0, 1)
 145       p2 = (0.5, 0.5, 1)
 146       p3 = (0.5, 0.5, 0.5)
 147       exterior_point = (0, 0, 0)
 148       t = Tetrahedron { v0 = p0,
 149                         v1 = p1,
 150                         v2 = p2,
 151                         v3 = p3,
 152                         fv = empty_values }
 153
 154
 155 -- | Ensure that a tetrahedron does not contain a particular point chosen to
 156 --   be outside of it (fifth test).
 157 test_doesnt_contain_point5 :: Assertion
 158 test_doesnt_contain_point5 =
 159     assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 160     where
 161       p0 = (0, 0, 1)
 162       p1 = (0, 1, 1)
 163       p2 = (0.5, 0.5, 1)
 164       p3 = (0.5, 0.5, 0.5)
 165       exterior_point = (0, 0, 0)
 166       t = Tetrahedron { v0 = p0,
 167                         v1 = p1,
 168                         v2 = p2,
 169                         v3 = p3,
 170                         fv = empty_values }
 171
 172
 173 -- | The barycentric coordinate of v0 with respect to itself should
 174 --   be one.
 175 prop_b0_v0_always_unity :: Tetrahedron -> Property
 176 prop_b0_v0_always_unity t =
 177     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 178
 179 -- | The barycentric coordinate of v1 with respect to v0 should
 180 --   be zero.
 181 prop_b0_v1_always_zero :: Tetrahedron -> Property
 182 prop_b0_v1_always_zero t =
 183     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 184
 185 -- | The barycentric coordinate of v2 with respect to v0 should
 186 --   be zero.
 187 prop_b0_v2_always_zero :: Tetrahedron -> Property
 188 prop_b0_v2_always_zero t =
 189     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 190
 191 -- | The barycentric coordinate of v3 with respect to v0 should
 192 --   be zero.
 193 prop_b0_v3_always_zero :: Tetrahedron -> Property
 194 prop_b0_v3_always_zero t =
 195     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 196
 197 -- | The barycentric coordinate of v1 with respect to itself should
 198 --   be one.
 199 prop_b1_v1_always_unity :: Tetrahedron -> Property
 200 prop_b1_v1_always_unity t =
 201     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 202
 203 -- | The barycentric coordinate of v0 with respect to v1 should
 204 --   be zero.
 205 prop_b1_v0_always_zero :: Tetrahedron -> Property
 206 prop_b1_v0_always_zero t =
 207     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 208
 209 -- | The barycentric coordinate of v2 with respect to v1 should
 210 --   be zero.
 211 prop_b1_v2_always_zero :: Tetrahedron -> Property
 212 prop_b1_v2_always_zero t =
 213     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 214
 215 -- | The barycentric coordinate of v3 with respect to v1 should
 216 --   be zero.
 217 prop_b1_v3_always_zero :: Tetrahedron -> Property
 218 prop_b1_v3_always_zero t =
 219     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 220
 221 -- | The barycentric coordinate of v2 with respect to itself should
 222 --   be one.
 223 prop_b2_v2_always_unity :: Tetrahedron -> Property
 224 prop_b2_v2_always_unity t =
 225     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 226
 227 -- | The barycentric coordinate of v0 with respect to v2 should
 228 --   be zero.
 229 prop_b2_v0_always_zero :: Tetrahedron -> Property
 230 prop_b2_v0_always_zero t =
 231     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 232
 233 -- | The barycentric coordinate of v1 with respect to v2 should
 234 --   be zero.
 235 prop_b2_v1_always_zero :: Tetrahedron -> Property
 236 prop_b2_v1_always_zero t =
 237     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 238
 239 -- | The barycentric coordinate of v3 with respect to v2 should
 240 --   be zero.
 241 prop_b2_v3_always_zero :: Tetrahedron -> Property
 242 prop_b2_v3_always_zero t =
 243     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 244
 245 -- | The barycentric coordinate of v3 with respect to itself should
 246 --   be one.
 247 prop_b3_v3_always_unity :: Tetrahedron -> Property
 248 prop_b3_v3_always_unity t =
 249     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 250
 251 -- | The barycentric coordinate of v0 with respect to v3 should
 252 --   be zero.
 253 prop_b3_v0_always_zero :: Tetrahedron -> Property
 254 prop_b3_v0_always_zero t =
 255     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 256
 257 -- | The barycentric coordinate of v1 with respect to v3 should
 258 --   be zero.
 259 prop_b3_v1_always_zero :: Tetrahedron -> Property
 260 prop_b3_v1_always_zero t =
 261     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 262
 263 -- | The barycentric coordinate of v2 with respect to v3 should
 264 --   be zero.
 265 prop_b3_v2_always_zero :: Tetrahedron -> Property
 266 prop_b3_v2_always_zero t =
 267     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 268
 269
 270 -- | Used for convenience in the next few tests; not a test itself.
 271 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 272 p t i j k l = (polynomial t) (xi t i j k l)
 273
 274 -- | Given in Sorokina and Zeilfelder, p. 78.
 275 prop_c3000_identity :: Tetrahedron -> Property
 276 prop_c3000_identity t =
 277     (volume t) > 0 ==>
 278                c t 3 0 0 0 ~= p t 3 0 0 0
 279
 280 -- | Given in Sorokina and Zeilfelder, p. 78.
 281 prop_c2100_identity :: Tetrahedron -> Property
 282 prop_c2100_identity t =
 283     (volume t) > 0 ==>
 284       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 285         where
 286           term1 = (1/3)*(p t 0 3 0 0)
 287           term2 = (5/6)*(p t 3 0 0 0)
 288           term3 = 3*(p t 2 1 0 0)
 289           term4 = (3/2)*(p t 1 2 0 0)
 290
 291 -- | Given in Sorokina and Zeilfelder, p. 78.
 292 prop_c1110_identity :: Tetrahedron -> Property
 293 prop_c1110_identity t =
 294     (volume t) > 0 ==>
 295        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 296         where
 297           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 298           term2 = (9/2)*(p t 1 1 1 0)
 299           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 300           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
 301
 302 prop_x_rotation_doesnt_affect_front :: Tetrahedron -> Bool
 303 prop_x_rotation_doesnt_affect_front t =
 304     expr1 == expr2
 305     where
 306       fv0 = Tetrahedron.fv t
 307       fv1 = rotate cwx (Tetrahedron.fv t)
 308       expr1 = front fv0
 309       expr2 = front fv1
 310
 311 prop_x_rotation_doesnt_affect_back :: Tetrahedron -> Bool
 312 prop_x_rotation_doesnt_affect_back t =
 313     expr1 == expr2
 314     where
 315       fv0 = Tetrahedron.fv t
 316       fv1 = rotate cwx (Tetrahedron.fv t)
 317       expr1 = back fv0
 318       expr2 = back fv1
 319
 320
 321 prop_y_rotation_doesnt_affect_left :: Tetrahedron -> Bool
 322 prop_y_rotation_doesnt_affect_left t =
 323     expr1 == expr2
 324     where
 325       fv0 = Tetrahedron.fv t
 326       fv1 = rotate cwy (Tetrahedron.fv t)
 327       expr1 = left fv0
 328       expr2 = left fv1
 329
 330 prop_y_rotation_doesnt_affect_right :: Tetrahedron -> Bool
 331 prop_y_rotation_doesnt_affect_right t =
 332     expr1 == expr2
 333     where
 334       fv0 = Tetrahedron.fv t
 335       fv1 = rotate cwy (Tetrahedron.fv t)
 336       expr1 = right fv0
 337       expr2 = right fv1
 338
 339
 340 prop_z_rotation_doesnt_affect_down :: Tetrahedron -> Bool
 341 prop_z_rotation_doesnt_affect_down t =
 342     expr1 == expr2
 343     where
 344       fv0 = Tetrahedron.fv t
 345       fv1 = rotate cwz (Tetrahedron.fv t)
 346       expr1 = down fv0
 347       expr2 = down fv1
 348
 349
 350 prop_z_rotation_doesnt_affect_top :: Tetrahedron -> Bool
 351 prop_z_rotation_doesnt_affect_top t =
 352     expr1 == expr2
 353     where
 354       fv0 = Tetrahedron.fv t
 355       fv1 = rotate cwz (Tetrahedron.fv t)
 356       expr1 = top fv0
 357       expr2 = top fv1
 358
 359 prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
 360 prop_swapping_vertices_doesnt_affect_coefficients1 t =
 361       c t 0 0 1 2 == c t' 0 0 1 2
 362         where
 363           t' = t { v0 = (v1 t), v1 = (v0 t) }
 364
 365 prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool
 366 prop_swapping_vertices_doesnt_affect_coefficients2 t =
 367       c t 0 1 1 1 == c t' 0 1 1 1
 368         where
 369           t' = t { v2 = (v3 t), v3 = (v2 t) }
 370
 371 prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool
 372 prop_swapping_vertices_doesnt_affect_coefficients3 t =
 373       c t 2 1 0 0 == c t' 2 1 0 0
 374         where
 375           t' = t { v2 = (v3 t), v3 = (v2 t) }
 376
 377 prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool
 378 prop_swapping_vertices_doesnt_affect_coefficients4 t =
 379       c t 2 0 0 1 == c t' 2 0 0 1
 380         where
 381           t' = t { v0 = (v3 t), v3 = (v0 t) }