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_tetrahedron0_volumes_exact :: Cube -> Bool
  42 prop_tetrahedron0_volumes_exact c =
  43     volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
  44     where
  45       delta = h c
  46
  47 -- | In fact, since all of the tetrahedra are identical, we should
  48 --   already know their volumes. There's 24 tetrahedra to a cube, so
  49 --   we'd expect the volume of each one to be (1/24)*h^3.
  50 prop_tetrahedron1_volumes_exact :: Cube -> Bool
  51 prop_tetrahedron1_volumes_exact c =
  52     volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
  53     where
  54       delta = h c
  55
  56 -- | In fact, since all of the tetrahedra are identical, we should
  57 --   already know their volumes. There's 24 tetrahedra to a cube, so
  58 --   we'd expect the volume of each one to be (1/24)*h^3.
  59 prop_tetrahedron2_volumes_exact :: Cube -> Bool
  60 prop_tetrahedron2_volumes_exact c =
  61     volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
  62     where
  63       delta = h c
  64
  65 -- | In fact, since all of the tetrahedra are identical, we should
  66 --   already know their volumes. There's 24 tetrahedra to a cube, so
  67 --   we'd expect the volume of each one to be (1/24)*h^3.
  68 prop_tetrahedron3_volumes_exact :: Cube -> Bool
  69 prop_tetrahedron3_volumes_exact c =
  70     volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
  71     where
  72       delta = h c
  73
  74 -- | In fact, since all of the tetrahedra are identical, we should
  75 --   already know their volumes. There's 24 tetrahedra to a cube, so
  76 --   we'd expect the volume of each one to be (1/24)*h^3.
  77 prop_tetrahedron4_volumes_exact :: Cube -> Bool
  78 prop_tetrahedron4_volumes_exact c =
  79     volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
  80     where
  81       delta = h c
  82
  83 -- | In fact, since all of the tetrahedra are identical, we should
  84 --   already know their volumes. There's 24 tetrahedra to a cube, so
  85 --   we'd expect the volume of each one to be (1/24)*h^3.
  86 prop_tetrahedron5_volumes_exact :: Cube -> Bool
  87 prop_tetrahedron5_volumes_exact c =
  88     volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
  89     where
  90       delta = h c
  91
  92 -- | In fact, since all of the tetrahedra are identical, we should
  93 --   already know their volumes. There's 24 tetrahedra to a cube, so
  94 --   we'd expect the volume of each one to be (1/24)*h^3.
  95 prop_tetrahedron6_volumes_exact :: Cube -> Bool
  96 prop_tetrahedron6_volumes_exact c =
  97     volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
  98     where
  99       delta = h c
 100
 101 -- | In fact, since all of the tetrahedra are identical, we should
 102 --   already know their volumes. There's 24 tetrahedra to a cube, so
 103 --   we'd expect the volume of each one to be (1/24)*h^3.
 104 prop_tetrahedron7_volumes_exact :: Cube -> Bool
 105 prop_tetrahedron7_volumes_exact c =
 106     volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
 107     where
 108       delta = h c
 109
 110 -- | All tetrahedron should have their v0 located at the center of the cube.
 111 prop_v0_all_equal :: Cube -> Bool
 112 prop_v0_all_equal c = (v0 t0) == (v0 t1)
 113     where
 114       t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
 115       t1 = head $ tail (tetrahedrons c)
 116
 117
 118 -- | This pretty much repeats the prop_all_volumes_positive property,
 119 --   but will let me know which tetrahedrons's vertices are disoriented.
 120 prop_tetrahedron0_volumes_positive :: Cube -> Bool
 121 prop_tetrahedron0_volumes_positive c =
 122     volume (tetrahedron0 c) > 0
 123
 124 -- | This pretty much repeats the prop_all_volumes_positive property,
 125 --   but will let me know which tetrahedrons's vertices are disoriented.
 126 prop_tetrahedron1_volumes_positive :: Cube -> Bool
 127 prop_tetrahedron1_volumes_positive c =
 128     volume (tetrahedron1 c) > 0
 129
 130 -- | This pretty much repeats the prop_all_volumes_positive property,
 131 --   but will let me know which tetrahedrons's vertices are disoriented.
 132 prop_tetrahedron2_volumes_positive :: Cube -> Bool
 133 prop_tetrahedron2_volumes_positive c =
 134     volume (tetrahedron2 c) > 0
 135
 136 -- | This pretty much repeats the prop_all_volumes_positive property,
 137 --   but will let me know which tetrahedrons's vertices are disoriented.
 138 prop_tetrahedron3_volumes_positive :: Cube -> Bool
 139 prop_tetrahedron3_volumes_positive c =
 140     volume (tetrahedron3 c) > 0
 141
 142 -- | This pretty much repeats the prop_all_volumes_positive property,
 143 --   but will let me know which tetrahedrons's vertices are disoriented.
 144 prop_tetrahedron4_volumes_positive :: Cube -> Bool
 145 prop_tetrahedron4_volumes_positive c =
 146     volume (tetrahedron4 c) > 0
 147
 148 -- | This pretty much repeats the prop_all_volumes_positive property,
 149 --   but will let me know which tetrahedrons's vertices are disoriented.
 150 prop_tetrahedron5_volumes_positive :: Cube -> Bool
 151 prop_tetrahedron5_volumes_positive c =
 152     volume (tetrahedron5 c) > 0
 153
 154 -- | This pretty much repeats the prop_all_volumes_positive property,
 155 --   but will let me know which tetrahedrons's vertices are disoriented.
 156 prop_tetrahedron6_volumes_positive :: Cube -> Bool
 157 prop_tetrahedron6_volumes_positive c =
 158     volume (tetrahedron6 c) > 0
 159
 160 -- | This pretty much repeats the prop_all_volumes_positive property,
 161 --   but will let me know which tetrahedrons's vertices are disoriented.
 162 prop_tetrahedron7_volumes_positive :: Cube -> Bool
 163 prop_tetrahedron7_volumes_positive c =
 164     volume (tetrahedron7 c) > 0
 165
 166 -- | This pretty much repeats the prop_all_volumes_positive property,
 167 --   but will let me know which tetrahedrons's vertices are disoriented.
 168 prop_tetrahedron8_volumes_positive :: Cube -> Bool
 169 prop_tetrahedron8_volumes_positive c =
 170     volume (tetrahedron8 c) > 0
 171
 172 -- | This pretty much repeats the prop_all_volumes_positive property,
 173 --   but will let me know which tetrahedrons's vertices are disoriented.
 174 prop_tetrahedron9_volumes_positive :: Cube -> Bool
 175 prop_tetrahedron9_volumes_positive c =
 176     volume (tetrahedron9 c) > 0
 177
 178 -- | This pretty much repeats the prop_all_volumes_positive property,
 179 --   but will let me know which tetrahedrons's vertices are disoriented.
 180 prop_tetrahedron10_volumes_positive :: Cube -> Bool
 181 prop_tetrahedron10_volumes_positive c =
 182     volume (tetrahedron10 c) > 0
 183
 184 -- | This pretty much repeats the prop_all_volumes_positive property,
 185 --   but will let me know which tetrahedrons's vertices are disoriented.
 186 prop_tetrahedron11_volumes_positive :: Cube -> Bool
 187 prop_tetrahedron11_volumes_positive c =
 188     volume (tetrahedron11 c) > 0
 189
 190 -- | This pretty much repeats the prop_all_volumes_positive property,
 191 --   but will let me know which tetrahedrons's vertices are disoriented.
 192 prop_tetrahedron12_volumes_positive :: Cube -> Bool
 193 prop_tetrahedron12_volumes_positive c =
 194     volume (tetrahedron12 c) > 0
 195
 196 -- | This pretty much repeats the prop_all_volumes_positive property,
 197 --   but will let me know which tetrahedrons's vertices are disoriented.
 198 prop_tetrahedron13_volumes_positive :: Cube -> Bool
 199 prop_tetrahedron13_volumes_positive c =
 200     volume (tetrahedron13 c) > 0
 201
 202 -- | This pretty much repeats the prop_all_volumes_positive property,
 203 --   but will let me know which tetrahedrons's vertices are disoriented.
 204 prop_tetrahedron14_volumes_positive :: Cube -> Bool
 205 prop_tetrahedron14_volumes_positive c =
 206     volume (tetrahedron14 c) > 0
 207
 208 -- | This pretty much repeats the prop_all_volumes_positive property,
 209 --   but will let me know which tetrahedrons's vertices are disoriented.
 210 prop_tetrahedron15_volumes_positive :: Cube -> Bool
 211 prop_tetrahedron15_volumes_positive c =
 212     volume (tetrahedron15 c) > 0