src/Tests/Tetrahedron.hs

   1 module Tests.Tetrahedron
   2 where
   3
   4 import Test.HUnit
   5 import Test.QuickCheck
   6
   7 import Cube
   8 import Point
   9 import Tests.Cube()
  10 import Tetrahedron
  11 import ThreeDimensional
  12
  13 instance Arbitrary Tetrahedron where
  14     arbitrary = do
  15       rnd_c0 <- arbitrary :: Gen Cube
  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       return (Tetrahedron rnd_c0 rnd_v0 rnd_v1 rnd_v2 rnd_v3)
  21
  22 almost_equals :: Double -> Double -> Bool
  23 almost_equals x y = (abs (x - y)) < 0.0001
  24
  25 (~=) :: Double -> Double -> Bool
  26 (~=) = almost_equals
  27
  28
  29 -- HUnit Tests
  30
  31 -- Since p0, p1, p2 are in clockwise order, we expect the volume here
  32 -- to be negative.
  33 test_volume1 :: Test
  34 test_volume1 =
  35     TestCase $ assertEqual "volume is correct" True (vol ~= (-1/3))
  36     where
  37       p0 = (0, -0.5, 0)
  38       p1 = (0, 0.5, 0)
  39       p2 = (2, 0, 0)
  40       p3 = (1, 0, 1)
  41       t = Tetrahedron { cube = empty_cube,
  42                         v0 = p0,
  43                         v1 = p1,
  44                         v2 = p2,
  45                         v3 = p3 }
  46       vol = volume t
  47
  48
  49 -- Now, p0, p1, and p2 are in counter-clockwise order. The volume
  50 -- should therefore be positive.
  51 test_volume2 :: Test
  52 test_volume2 =
  53     TestCase $ assertEqual "volume is correct" True (vol ~= (1/3))
  54     where
  55       p0 = (0, -0.5, 0)
  56       p1 = (2, 0, 0)
  57       p2 = (0, 0.5, 0)
  58       p3 = (1, 0, 1)
  59       t = Tetrahedron { cube = empty_cube,
  60                         v0 = p0,
  61                         v1 = p1,
  62                         v2 = p2,
  63                         v3 = p3 }
  64       vol = volume t
  65
  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 { cube = empty_cube,
  76                         v0 = p0,
  77                         v1 = p1,
  78                         v2 = p2,
  79                         v3 = p3 }
  80
  81
  82 test_doesnt_contain_point1 :: Test
  83 test_doesnt_contain_point1 =
  84     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
  85     where
  86       p0 = (0, -0.5, 0)
  87       p1 = (0, 0.5, 0)
  88       p2 = (2, 0, 0)
  89       p3 = (1, 0, 1)
  90       exterior_point = (5, 2, -9.0212)
  91       c_empty = empty_cube
  92       t = Tetrahedron { cube = c_empty,
  93                         v0 = p0,
  94                         v1 = p1,
  95                         v2 = p2,
  96                         v3 = p3 }
  97
  98
  99 test_doesnt_contain_point2 :: Test
 100 test_doesnt_contain_point2 =
 101     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 102     where
 103       p0 = (0, 1, 1)
 104       p1 = (1, 1, 1)
 105       p2 = (0.5, 0.5, 1)
 106       p3 = (0.5, 0.5, 0.5)
 107       exterior_point = (0, 0, 0)
 108       c_empty = empty_cube
 109       t = Tetrahedron { cube = c_empty,
 110                         v0 = p0,
 111                         v1 = p1,
 112                         v2 = p2,
 113                         v3 = p3 }
 114
 115 test_doesnt_contain_point3 :: Test
 116 test_doesnt_contain_point3 =
 117     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 118     where
 119       p0 = (1, 1, 1)
 120       p1 = (1, 0, 1)
 121       p2 = (0.5, 0.5, 1)
 122       p3 = (0.5, 0.5, 0.5)
 123       exterior_point = (0, 0, 0)
 124       c_empty = empty_cube
 125       t = Tetrahedron { cube = c_empty,
 126                         v0 = p0,
 127                         v1 = p1,
 128                         v2 = p2,
 129                         v3 = p3 }
 130
 131 test_doesnt_contain_point4 :: Test
 132 test_doesnt_contain_point4 =
 133     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 134     where
 135       p0 = (1, 0, 1)
 136       p1 = (0, 0, 1)
 137       p2 = (0.5, 0.5, 1)
 138       p3 = (0.5, 0.5, 0.5)
 139       exterior_point = (0, 0, 0)
 140       c_empty = empty_cube
 141       t = Tetrahedron { cube = c_empty,
 142                         v0 = p0,
 143                         v1 = p1,
 144                         v2 = p2,
 145                         v3 = p3 }
 146
 147 test_doesnt_contain_point5 :: Test
 148 test_doesnt_contain_point5 =
 149     TestCase $ 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       c_empty = empty_cube
 157       t = Tetrahedron { cube = c_empty,
 158                         v0 = p0,
 159                         v1 = p1,
 160                         v2 = p2,
 161                         v3 = p3 }
 162
 163 tetrahedron_tests :: [Test]
 164 tetrahedron_tests = [test_volume1,
 165                      test_volume2,
 166                      test_contains_point1,
 167                      test_doesnt_contain_point1,
 168                      test_doesnt_contain_point2,
 169                      test_doesnt_contain_point3,
 170                      test_doesnt_contain_point4,
 171                      test_doesnt_contain_point5 ]
 172
 173 prop_b0_v0_always_unity :: Tetrahedron -> Property
 174 prop_b0_v0_always_unity t =
 175     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 176
 177 prop_b0_v1_always_zero :: Tetrahedron -> Property
 178 prop_b0_v1_always_zero t =
 179     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 180
 181 prop_b0_v2_always_zero :: Tetrahedron -> Property
 182 prop_b0_v2_always_zero t =
 183     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 184
 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 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 prop_b1_v0_always_zero :: Tetrahedron -> Property
 194 prop_b1_v0_always_zero t =
 195     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 196
 197 prop_b1_v2_always_zero :: Tetrahedron -> Property
 198 prop_b1_v2_always_zero t =
 199     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 200
 201 prop_b1_v3_always_zero :: Tetrahedron -> Property
 202 prop_b1_v3_always_zero t =
 203     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 204
 205 prop_b2_v2_always_unity :: Tetrahedron -> Property
 206 prop_b2_v2_always_unity t =
 207     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 208
 209 prop_b2_v0_always_zero :: Tetrahedron -> Property
 210 prop_b2_v0_always_zero t =
 211     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 212
 213 prop_b2_v1_always_zero :: Tetrahedron -> Property
 214 prop_b2_v1_always_zero t =
 215     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 216
 217 prop_b2_v3_always_zero :: Tetrahedron -> Property
 218 prop_b2_v3_always_zero t =
 219     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 220
 221 prop_b3_v3_always_unity :: Tetrahedron -> Property
 222 prop_b3_v3_always_unity t =
 223     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 224
 225 prop_b3_v0_always_zero :: Tetrahedron -> Property
 226 prop_b3_v0_always_zero t =
 227     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 228
 229 prop_b3_v1_always_zero :: Tetrahedron -> Property
 230 prop_b3_v1_always_zero t =
 231     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 232
 233 prop_b3_v2_always_zero :: Tetrahedron -> Property
 234 prop_b3_v2_always_zero t =
 235     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 236
 237
 238 -- Used for convenience in the next few tests.
 239 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 240 p t i j k l = (polynomial t) (xi t i j k l)
 241
 242 -- | Given in Sorokina and Zeilfelder, p. 78.
 243 prop_c3000_identity :: Tetrahedron -> Property
 244 prop_c3000_identity t =
 245     (volume t) > 0 ==>
 246                c t 3 0 0 0 ~= p t 3 0 0 0
 247
 248 -- | Given in Sorokina and Zeilfelder, p. 78.
 249 prop_c2100_identity :: Tetrahedron -> Property
 250 prop_c2100_identity t =
 251     (volume t) > 0 ==>
 252       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 253         where
 254           term1 = (1/3)*(p t 0 3 0 0)
 255           term2 = (5/6)*(p t 3 0 0 0)
 256           term3 = 3*(p t 2 1 0 0)
 257           term4 = (3/2)*(p t 1 2 0 0)
 258
 259 -- | Given in Sorokina and Zeilfelder, p. 78.
 260 prop_c1110_identity :: Tetrahedron -> Property
 261 prop_c1110_identity t =
 262     (volume t) > 0 ==>
 263        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 264         where
 265           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 266           term2 = (9/2)*(p t 1 1 1 0)
 267           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 268           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))