src/Tests/Tetrahedron.hs

   1 module Tests.Tetrahedron
   2 where
   3
   4 import Test.HUnit
   5 import Test.QuickCheck
   6
   7 import Assertions
   8 import Comparisons
   9 import Point
  10 import FunctionValues
  11 import Misc
  12 import Tests.FunctionValues()
  13 import Tetrahedron
  14 import ThreeDimensional
  15
  16 instance Arbitrary Tetrahedron where
  17     arbitrary = do
  18       rnd_v0 <- arbitrary :: Gen Point
  19       rnd_v1 <- arbitrary :: Gen Point
  20       rnd_v2 <- arbitrary :: Gen Point
  21       rnd_v3 <- arbitrary :: Gen Point
  22       rnd_fv <- arbitrary :: Gen FunctionValues
  23       return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
  24
  25 -- HUnit Tests
  26
  27 -- Since p0, p1, p2 are in clockwise order, we expect the volume here
  28 -- to 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 -- Now, p0, p1, and p2 are in counter-clockwise order. The volume
  46 -- should therefore be positive.
  47 test_volume2 :: Test
  48 test_volume2 =
  49     TestCase $ assertEqual "volume is correct" True (vol ~= (1/3))
  50     where
  51       p0 = (0, -0.5, 0)
  52       p1 = (2, 0, 0)
  53       p2 = (0, 0.5, 0)
  54       p3 = (1, 0, 1)
  55       t = Tetrahedron { v0 = p0,
  56                         v1 = p1,
  57                         v2 = p2,
  58                         v3 = p3,
  59                         fv = empty_values }
  60       vol = volume t
  61
  62 test_contains_point1 :: Test
  63 test_contains_point1 =
  64     TestCase $ assertEqual "contains an inner point" True (contains_point t inner_point)
  65     where
  66       p0 = (0, -0.5, 0)
  67       p1 = (0, 0.5, 0)
  68       p2 = (2, 0, 0)
  69       p3 = (1, 0, 1)
  70       inner_point = (1, 0, 0.5)
  71       t = Tetrahedron { v0 = p0,
  72                         v1 = p1,
  73                         v2 = p2,
  74                         v3 = p3,
  75                         fv = empty_values }
  76
  77
  78 test_doesnt_contain_point1 :: Test
  79 test_doesnt_contain_point1 =
  80     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
  81     where
  82       p0 = (0, -0.5, 0)
  83       p1 = (0, 0.5, 0)
  84       p2 = (2, 0, 0)
  85       p3 = (1, 0, 1)
  86       exterior_point = (5, 2, -9.0212)
  87       t = Tetrahedron { v0 = p0,
  88                         v1 = p1,
  89                         v2 = p2,
  90                         v3 = p3,
  91                         fv = empty_values }
  92
  93
  94 test_doesnt_contain_point2 :: Test
  95 test_doesnt_contain_point2 =
  96     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
  97     where
  98       p0 = (0, 1, 1)
  99       p1 = (1, 1, 1)
 100       p2 = (0.5, 0.5, 1)
 101       p3 = (0.5, 0.5, 0.5)
 102       exterior_point = (0, 0, 0)
 103       t = Tetrahedron { v0 = p0,
 104                         v1 = p1,
 105                         v2 = p2,
 106                         v3 = p3,
 107                         fv = empty_values }
 108
 109 test_doesnt_contain_point3 :: Test
 110 test_doesnt_contain_point3 =
 111     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 112     where
 113       p0 = (1, 1, 1)
 114       p1 = (1, 0, 1)
 115       p2 = (0.5, 0.5, 1)
 116       p3 = (0.5, 0.5, 0.5)
 117       exterior_point = (0, 0, 0)
 118       t = Tetrahedron { v0 = p0,
 119                         v1 = p1,
 120                         v2 = p2,
 121                         v3 = p3,
 122                         fv = empty_values }
 123
 124 test_doesnt_contain_point4 :: Test
 125 test_doesnt_contain_point4 =
 126     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 127     where
 128       p0 = (1, 0, 1)
 129       p1 = (0, 0, 1)
 130       p2 = (0.5, 0.5, 1)
 131       p3 = (0.5, 0.5, 0.5)
 132       exterior_point = (0, 0, 0)
 133       t = Tetrahedron { v0 = p0,
 134                         v1 = p1,
 135                         v2 = p2,
 136                         v3 = p3,
 137                         fv = empty_values }
 138
 139 test_doesnt_contain_point5 :: Test
 140 test_doesnt_contain_point5 =
 141     TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
 142     where
 143       p0 = (0, 0, 1)
 144       p1 = (0, 1, 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 tetrahedron_tests :: [Test]
 155 tetrahedron_tests = [test_volume1,
 156                      test_volume2,
 157                      test_contains_point1,
 158                      test_doesnt_contain_point1,
 159                      test_doesnt_contain_point2,
 160                      test_doesnt_contain_point3,
 161                      test_doesnt_contain_point4,
 162                      test_doesnt_contain_point5 ]
 163
 164 prop_b0_v0_always_unity :: Tetrahedron -> Property
 165 prop_b0_v0_always_unity t =
 166     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 167
 168 prop_b0_v1_always_zero :: Tetrahedron -> Property
 169 prop_b0_v1_always_zero t =
 170     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 171
 172 prop_b0_v2_always_zero :: Tetrahedron -> Property
 173 prop_b0_v2_always_zero t =
 174     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 175
 176 prop_b0_v3_always_zero :: Tetrahedron -> Property
 177 prop_b0_v3_always_zero t =
 178     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 179
 180 prop_b1_v1_always_unity :: Tetrahedron -> Property
 181 prop_b1_v1_always_unity t =
 182     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 183
 184 prop_b1_v0_always_zero :: Tetrahedron -> Property
 185 prop_b1_v0_always_zero t =
 186     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 187
 188 prop_b1_v2_always_zero :: Tetrahedron -> Property
 189 prop_b1_v2_always_zero t =
 190     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 191
 192 prop_b1_v3_always_zero :: Tetrahedron -> Property
 193 prop_b1_v3_always_zero t =
 194     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 195
 196 prop_b2_v2_always_unity :: Tetrahedron -> Property
 197 prop_b2_v2_always_unity t =
 198     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 199
 200 prop_b2_v0_always_zero :: Tetrahedron -> Property
 201 prop_b2_v0_always_zero t =
 202     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 203
 204 prop_b2_v1_always_zero :: Tetrahedron -> Property
 205 prop_b2_v1_always_zero t =
 206     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 207
 208 prop_b2_v3_always_zero :: Tetrahedron -> Property
 209 prop_b2_v3_always_zero t =
 210     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 211
 212 prop_b3_v3_always_unity :: Tetrahedron -> Property
 213 prop_b3_v3_always_unity t =
 214     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 215
 216 prop_b3_v0_always_zero :: Tetrahedron -> Property
 217 prop_b3_v0_always_zero t =
 218     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 219
 220 prop_b3_v1_always_zero :: Tetrahedron -> Property
 221 prop_b3_v1_always_zero t =
 222     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 223
 224 prop_b3_v2_always_zero :: Tetrahedron -> Property
 225 prop_b3_v2_always_zero t =
 226     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 227
 228
 229 -- Used for convenience in the next few tests.
 230 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 231 p t i j k l = (polynomial t) (xi t i j k l)
 232
 233 -- | Given in Sorokina and Zeilfelder, p. 78.
 234 prop_c3000_identity :: Tetrahedron -> Property
 235 prop_c3000_identity t =
 236     (volume t) > 0 ==>
 237                c t 3 0 0 0 ~= p t 3 0 0 0
 238
 239 -- | Given in Sorokina and Zeilfelder, p. 78.
 240 prop_c2100_identity :: Tetrahedron -> Property
 241 prop_c2100_identity t =
 242     (volume t) > 0 ==>
 243       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 244         where
 245           term1 = (1/3)*(p t 0 3 0 0)
 246           term2 = (5/6)*(p t 3 0 0 0)
 247           term3 = 3*(p t 2 1 0 0)
 248           term4 = (3/2)*(p t 1 2 0 0)
 249
 250 -- | Given in Sorokina and Zeilfelder, p. 78.
 251 prop_c1110_identity :: Tetrahedron -> Property
 252 prop_c1110_identity t =
 253     (volume t) > 0 ==>
 254        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 255         where
 256           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 257           term2 = (9/2)*(p t 1 1 1 0)
 258           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 259           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))