src/Tests/Tetrahedron.hs

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