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 :: Test
  31 test_volume1 =
  32     TestCase $ 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 :: Test
  50 test_volume2 =
  51     TestCase $ 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 :: Test
  68 test_contains_point1 =
  69     TestCase $ 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 :: Test
  86 test_doesnt_contain_point1 =
  87     TestCase $ 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 :: Test
 104 test_doesnt_contain_point2 =
 105     TestCase $ 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 :: Test
 122 test_doesnt_contain_point3 =
 123     TestCase $ 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 :: Test
 140 test_doesnt_contain_point4 =
 141     TestCase $ 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 :: Test
 158 test_doesnt_contain_point5 =
 159     TestCase $ 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 -- | A list of all HUnit tests defined in this module.
 173 tetrahedron_tests :: [Test]
 174 tetrahedron_tests = [test_volume1,
 175                      test_volume2,
 176                      test_contains_point1,
 177                      test_doesnt_contain_point1,
 178                      test_doesnt_contain_point2,
 179                      test_doesnt_contain_point3,
 180                      test_doesnt_contain_point4,
 181                      test_doesnt_contain_point5 ]
 182
 183
 184 -- | The barycentric coordinate of v0 with respect to itself should
 185 --   be one.
 186 prop_b0_v0_always_unity :: Tetrahedron -> Property
 187 prop_b0_v0_always_unity t =
 188     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 189
 190 -- | The barycentric coordinate of v1 with respect to v0 should
 191 --   be zero.
 192 prop_b0_v1_always_zero :: Tetrahedron -> Property
 193 prop_b0_v1_always_zero t =
 194     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 195
 196 -- | The barycentric coordinate of v2 with respect to v0 should
 197 --   be zero.
 198 prop_b0_v2_always_zero :: Tetrahedron -> Property
 199 prop_b0_v2_always_zero t =
 200     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 201
 202 -- | The barycentric coordinate of v3 with respect to v0 should
 203 --   be zero.
 204 prop_b0_v3_always_zero :: Tetrahedron -> Property
 205 prop_b0_v3_always_zero t =
 206     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 207
 208 -- | The barycentric coordinate of v1 with respect to itself should
 209 --   be one.
 210 prop_b1_v1_always_unity :: Tetrahedron -> Property
 211 prop_b1_v1_always_unity t =
 212     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 213
 214 -- | The barycentric coordinate of v0 with respect to v1 should
 215 --   be zero.
 216 prop_b1_v0_always_zero :: Tetrahedron -> Property
 217 prop_b1_v0_always_zero t =
 218     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 219
 220 -- | The barycentric coordinate of v2 with respect to v1 should
 221 --   be zero.
 222 prop_b1_v2_always_zero :: Tetrahedron -> Property
 223 prop_b1_v2_always_zero t =
 224     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 225
 226 -- | The barycentric coordinate of v3 with respect to v1 should
 227 --   be zero.
 228 prop_b1_v3_always_zero :: Tetrahedron -> Property
 229 prop_b1_v3_always_zero t =
 230     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 231
 232 -- | The barycentric coordinate of v2 with respect to itself should
 233 --   be one.
 234 prop_b2_v2_always_unity :: Tetrahedron -> Property
 235 prop_b2_v2_always_unity t =
 236     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 237
 238 -- | The barycentric coordinate of v0 with respect to v2 should
 239 --   be zero.
 240 prop_b2_v0_always_zero :: Tetrahedron -> Property
 241 prop_b2_v0_always_zero t =
 242     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 243
 244 -- | The barycentric coordinate of v1 with respect to v2 should
 245 --   be zero.
 246 prop_b2_v1_always_zero :: Tetrahedron -> Property
 247 prop_b2_v1_always_zero t =
 248     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 249
 250 -- | The barycentric coordinate of v3 with respect to v2 should
 251 --   be zero.
 252 prop_b2_v3_always_zero :: Tetrahedron -> Property
 253 prop_b2_v3_always_zero t =
 254     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 255
 256 -- | The barycentric coordinate of v3 with respect to itself should
 257 --   be one.
 258 prop_b3_v3_always_unity :: Tetrahedron -> Property
 259 prop_b3_v3_always_unity t =
 260     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 261
 262 -- | The barycentric coordinate of v0 with respect to v3 should
 263 --   be zero.
 264 prop_b3_v0_always_zero :: Tetrahedron -> Property
 265 prop_b3_v0_always_zero t =
 266     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 267
 268 -- | The barycentric coordinate of v1 with respect to v3 should
 269 --   be zero.
 270 prop_b3_v1_always_zero :: Tetrahedron -> Property
 271 prop_b3_v1_always_zero t =
 272     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 273
 274 -- | The barycentric coordinate of v2 with respect to v3 should
 275 --   be zero.
 276 prop_b3_v2_always_zero :: Tetrahedron -> Property
 277 prop_b3_v2_always_zero t =
 278     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 279
 280
 281 -- | Used for convenience in the next few tests; not a test itself.
 282 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 283 p t i j k l = (polynomial t) (xi t i j k l)
 284
 285 -- | Given in Sorokina and Zeilfelder, p. 78.
 286 prop_c3000_identity :: Tetrahedron -> Property
 287 prop_c3000_identity t =
 288     (volume t) > 0 ==>
 289                c t 3 0 0 0 ~= p t 3 0 0 0
 290
 291 -- | Given in Sorokina and Zeilfelder, p. 78.
 292 prop_c2100_identity :: Tetrahedron -> Property
 293 prop_c2100_identity t =
 294     (volume t) > 0 ==>
 295       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 296         where
 297           term1 = (1/3)*(p t 0 3 0 0)
 298           term2 = (5/6)*(p t 3 0 0 0)
 299           term3 = 3*(p t 2 1 0 0)
 300           term4 = (3/2)*(p t 1 2 0 0)
 301
 302 -- | Given in Sorokina and Zeilfelder, p. 78.
 303 prop_c1110_identity :: Tetrahedron -> Property
 304 prop_c1110_identity t =
 305     (volume t) > 0 ==>
 306        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 307         where
 308           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 309           term2 = (9/2)*(p t 1 1 1 0)
 310           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 311           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
 312
 313 prop_x_rotation_doesnt_affect_front :: Tetrahedron -> Bool
 314 prop_x_rotation_doesnt_affect_front t =
 315     expr1 == expr2
 316     where
 317       fv0 = Tetrahedron.fv t
 318       fv1 = rotate (Tetrahedron.fv t) cwx
 319       expr1 = front $ fv0
 320       expr2 = front $ fv1
 321
 322 prop_x_rotation_doesnt_affect_back :: Tetrahedron -> Bool
 323 prop_x_rotation_doesnt_affect_back t =
 324     expr1 == expr2
 325     where
 326       fv0 = Tetrahedron.fv t
 327       fv1 = rotate (Tetrahedron.fv t) cwx
 328       expr1 = back $ fv0
 329       expr2 = back $ fv1
 330
 331
 332 prop_y_rotation_doesnt_affect_left :: Tetrahedron -> Bool
 333 prop_y_rotation_doesnt_affect_left t =
 334     expr1 == expr2
 335     where
 336       fv0 = Tetrahedron.fv t
 337       fv1 = rotate (Tetrahedron.fv t) cwy
 338       expr1 = left $ fv0
 339       expr2 = left $ fv1
 340
 341 prop_y_rotation_doesnt_affect_right :: Tetrahedron -> Bool
 342 prop_y_rotation_doesnt_affect_right t =
 343     expr1 == expr2
 344     where
 345       fv0 = Tetrahedron.fv t
 346       fv1 = rotate (Tetrahedron.fv t) cwy
 347       expr1 = right $ fv0
 348       expr2 = right $ fv1
 349
 350
 351 prop_z_rotation_doesnt_affect_down :: Tetrahedron -> Bool
 352 prop_z_rotation_doesnt_affect_down t =
 353     expr1 == expr2
 354     where
 355       fv0 = Tetrahedron.fv t
 356       fv1 = rotate (Tetrahedron.fv t) cwz
 357       expr1 = down $ fv0
 358       expr2 = down $ fv1
 359
 360
 361 prop_z_rotation_doesnt_affect_top :: Tetrahedron -> Bool
 362 prop_z_rotation_doesnt_affect_top t =
 363     expr1 == expr2
 364     where
 365       fv0 = Tetrahedron.fv t
 366       fv1 = rotate (Tetrahedron.fv t) cwz
 367       expr1 = top $ fv0
 368       expr2 = top $ fv1