src/Tests/Cube.hs

   1 module Tests.Cube
   2 where
   3
   4 import Test.QuickCheck
   5
   6 import Comparisons
   7 import Cube
   8 import FunctionValues (FunctionValues(FunctionValues))
   9 import Tests.FunctionValues
  10 import Tetrahedron (v0, volume)
  11
  12 instance Arbitrary Cube where
  13     arbitrary = do
  14       (Positive h') <- arbitrary :: Gen (Positive Double)
  15       i' <- choose (coordmin, coordmax)
  16       j' <- choose (coordmin, coordmax)
  17       k' <- choose (coordmin, coordmax)
  18       fv' <- arbitrary :: Gen FunctionValues
  19       return (Cube h' i' j' k' fv')
  20         where
  21           coordmin = -268435456 -- -(2^29 / 2)
  22           coordmax = 268435456  -- +(2^29 / 2)
  23
  24
  25 -- Quickcheck tests.
  26
  27 -- | Since the grid size is necessarily positive, all tetrahedrons
  28 --   (which comprise cubes of positive volume) must have positive volume
  29 --   as well.
  30 prop_all_volumes_positive :: Cube -> Bool
  31 prop_all_volumes_positive c =
  32     null nonpositive_volumes
  33     where
  34       ts = tetrahedrons c
  35       volumes = map volume ts
  36       nonpositive_volumes = filter (<= 0) volumes
  37
  38 -- | In fact, since all of the tetrahedra are identical, we should
  39 --   already know their volumes. There's 24 tetrahedra to a cube, so
  40 --   we'd expect the volume of each one to be (1/24)*h^3.
  41 prop_all_volumes_exact :: Cube -> Bool
  42 prop_all_volumes_exact c =
  43     volume t ~= (1/24)*(delta^(3::Int))
  44     where
  45       t = head $ tetrahedrons c
  46       delta = h c
  47
  48 -- | All tetrahedron should have their v0 located at the center of the cube.
  49 prop_v0_all_equal :: Cube -> Bool
  50 prop_v0_all_equal c = (v0 t0) == (v0 t1)
  51     where
  52       t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
  53       t1 = head $ tail (tetrahedrons c)
  54
  55
  56 -- | This pretty much repeats the prop_all_volumes_positive property,
  57 --   but will let me know which tetrahedrons's vertices are disoriented.
  58 prop_tetrahedron0_volumes_positive :: Cube -> Bool
  59 prop_tetrahedron0_volumes_positive c =
  60     volume (tetrahedron0 c) > 0
  61
  62 -- | This pretty much repeats the prop_all_volumes_positive property,
  63 --   but will let me know which tetrahedrons's vertices are disoriented.
  64 prop_tetrahedron1_volumes_positive :: Cube -> Bool
  65 prop_tetrahedron1_volumes_positive c =
  66     volume (tetrahedron1 c) > 0
  67
  68 -- | This pretty much repeats the prop_all_volumes_positive property,
  69 --   but will let me know which tetrahedrons's vertices are disoriented.
  70 prop_tetrahedron2_volumes_positive :: Cube -> Bool
  71 prop_tetrahedron2_volumes_positive c =
  72     volume (tetrahedron2 c) > 0
  73
  74 -- | This pretty much repeats the prop_all_volumes_positive property,
  75 --   but will let me know which tetrahedrons's vertices are disoriented.
  76 prop_tetrahedron3_volumes_positive :: Cube -> Bool
  77 prop_tetrahedron3_volumes_positive c =
  78     volume (tetrahedron3 c) > 0
  79
  80 -- | This pretty much repeats the prop_all_volumes_positive property,
  81 --   but will let me know which tetrahedrons's vertices are disoriented.
  82 prop_tetrahedron4_volumes_positive :: Cube -> Bool
  83 prop_tetrahedron4_volumes_positive c =
  84     volume (tetrahedron4 c) > 0
  85
  86 -- | This pretty much repeats the prop_all_volumes_positive property,
  87 --   but will let me know which tetrahedrons's vertices are disoriented.
  88 prop_tetrahedron5_volumes_positive :: Cube -> Bool
  89 prop_tetrahedron5_volumes_positive c =
  90     volume (tetrahedron5 c) > 0
  91
  92 -- | This pretty much repeats the prop_all_volumes_positive property,
  93 --   but will let me know which tetrahedrons's vertices are disoriented.
  94 prop_tetrahedron6_volumes_positive :: Cube -> Bool
  95 prop_tetrahedron6_volumes_positive c =
  96     volume (tetrahedron6 c) > 0
  97
  98 -- | This pretty much repeats the prop_all_volumes_positive property,
  99 --   but will let me know which tetrahedrons's vertices are disoriented.
 100 prop_tetrahedron7_volumes_positive :: Cube -> Bool
 101 prop_tetrahedron7_volumes_positive c =
 102     volume (tetrahedron7 c) > 0