src/Tests/Tetrahedron.hs

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