src/Tests/Face.hs

   1 module Tests.Face
   2 where
   3
   4 import Test.QuickCheck
   5
   6 import Comparisons
   7 import Cube (Cube(grid), top)
   8 import Face (face0,
   9              face2,
  10              face5,
  11              tetrahedron0,
  12              tetrahedron1,
  13              tetrahedron2,
  14              tetrahedron3,
  15              tetrahedrons)
  16 import Grid (Grid(h))
  17 import Tetrahedron
  18
  19 -- QuickCheck Tests.
  20
  21 -- | Since the grid size is necessarily positive, all tetrahedrons
  22 --   (which comprise cubes of positive volume) must have positive volume
  23 --   as well.
  24 prop_all_volumes_positive :: Cube -> Property
  25 prop_all_volumes_positive c =
  26     (delta > 0) ==> (null nonpositive_volumes)
  27     where
  28       delta = h (grid c)
  29       ts = tetrahedrons c
  30       volumes = map volume ts
  31       nonpositive_volumes = filter (<= 0) volumes
  32
  33
  34 -- | Given in Sorokina and Zeilfelder, p. 79.
  35 prop_c0120_identity1 :: Cube -> Bool
  36 prop_c0120_identity1 cube =
  37     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
  38       where
  39         t0 = tetrahedron0 (face0 cube)
  40         t1 = tetrahedron1 (face0 cube)
  41         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  42         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  43
  44
  45 -- | Given in Sorokina and Zeilfelder, p. 79.
  46 prop_c0210_identity1 :: Cube -> Bool
  47 prop_c0210_identity1 cube =
  48     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
  49       where
  50         t0 = tetrahedron0 (face0 cube)
  51         t1 = tetrahedron1 (face0 cube)
  52         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  53         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  54
  55
  56 -- | Given in Sorokina and Zeilfelder, p. 79.
  57 prop_c0300_identity1 :: Cube -> Bool
  58 prop_c0300_identity1 cube =
  59     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
  60       where
  61         t0 = tetrahedron0 (face0 cube)
  62         t1 = tetrahedron1 (face0 cube)
  63         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  64         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  65
  66 -- | Given in Sorokina and Zeilfelder, p. 79.
  67 prop_c1110_identity :: Cube -> Bool
  68 prop_c1110_identity cube =
  69     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
  70       where
  71         t0 = tetrahedron0 (face0 cube)
  72         t1 = tetrahedron1 (face0 cube)
  73         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  74         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  75
  76
  77 -- | Given in Sorokina and Zeilfelder, p. 79.
  78 prop_c1200_identity1 :: Cube -> Bool
  79 prop_c1200_identity1 cube =
  80     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
  81       where
  82         t0 = tetrahedron0 (face0 cube)
  83         t1 = tetrahedron1 (face0 cube)
  84         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  85         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  86
  87
  88 -- | Given in Sorokina and Zeilfelder, p. 79.
  89 prop_c2100_identity1 :: Cube -> Bool
  90 prop_c2100_identity1 cube =
  91     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
  92       where
  93         t0 = tetrahedron0 (face0 cube)
  94         t1 = tetrahedron1 (face0 cube)
  95         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  96         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  97
  98
  99 -- | Given in Sorokina and Zeilfelder, p. 79.
 100 prop_c0102_identity1 :: Cube -> Bool
 101 prop_c0102_identity1 cube =
 102     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
 103       where
 104         t0 = tetrahedron0 (face0 cube)
 105         t3 = tetrahedron3 (face0 cube)
 106         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 107         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 108
 109
 110 -- | Given in Sorokina and Zeilfelder, p. 79.
 111 prop_c0201_identity1 :: Cube -> Bool
 112 prop_c0201_identity1 cube =
 113     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
 114       where
 115         t0 = tetrahedron0 (face0 cube)
 116         t3 = tetrahedron3 (face0 cube)
 117         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 118         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 119
 120
 121 -- | Given in Sorokina and Zeilfelder, p. 79.
 122 prop_c0300_identity2 :: Cube -> Bool
 123 prop_c0300_identity2 cube =
 124     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
 125       where
 126         t0 = tetrahedron0 (face0 cube)
 127         t3 = tetrahedron3 (face0 cube)
 128         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 129         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 130
 131 -- | Given in Sorokina and Zeilfelder, p. 79.
 132 prop_c1101_identity :: Cube -> Bool
 133 prop_c1101_identity cube =
 134     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
 135       where
 136         t0 = tetrahedron0 (face0 cube)
 137         t3 = tetrahedron3 (face0 cube)
 138         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 139         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 140
 141
 142 -- | Given in Sorokina and Zeilfelder, p. 79.
 143 prop_c1200_identity2 :: Cube -> Bool
 144 prop_c1200_identity2 cube =
 145     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
 146       where
 147         t0 = tetrahedron0 (face0 cube)
 148         t3 = tetrahedron3 (face0 cube)
 149         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 150         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 151
 152
 153 -- | Given in Sorokina and Zeilfelder, p. 79.
 154 prop_c2100_identity2 :: Cube -> Bool
 155 prop_c2100_identity2 cube =
 156     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
 157       where
 158         t0 = tetrahedron0 (face0 cube)
 159         t3 = tetrahedron3 (face0 cube)
 160         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 161         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 162
 163
 164 -- | Given in Sorokina and Zeilfelder, p. 79.
 165 prop_c3000_identity :: Cube -> Bool
 166 prop_c3000_identity cube =
 167     c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
 168       where
 169         t0 = tetrahedron0 (face0 cube)
 170         t2 = tetrahedron2 (face5 cube)
 171         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 172         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 173
 174
 175 -- | Given in Sorokina and Zeilfelder, p. 79.
 176 prop_c2010_identity :: Cube -> Bool
 177 prop_c2010_identity cube =
 178     c t0' 2 0 1 0 ~= c t0' 1 1 1 0 + c t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
 179       where
 180         t0 = tetrahedron0 (face0 cube)
 181         t2 = tetrahedron2 (face5 cube)
 182         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 183         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 184
 185
 186 -- | Given in Sorokina and Zeilfelder, p. 79.
 187 prop_c2001_identity :: Cube -> Bool
 188 prop_c2001_identity cube =
 189     c t0' 2 0 0 1 ~= c t0' 1 1 0 1 + c t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
 190       where
 191         t0 = tetrahedron0 (face0 cube)
 192         t2 = tetrahedron2 (face5 cube)
 193         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 194         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 195
 196 -- | Given in Sorokina and Zeilfelder, p. 79.
 197 prop_c1020_identity :: Cube -> Bool
 198 prop_c1020_identity cube =
 199     c t0' 1 0 2 0 ~= c t0' 0 1 2 0 + c t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
 200       where
 201         t0 = tetrahedron0 (face0 cube)
 202         t2 = tetrahedron2 (face5 cube)
 203         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 204         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 205
 206
 207 -- | Given in Sorokina and Zeilfelder, p. 79.
 208 prop_c1002_identity :: Cube -> Bool
 209 prop_c1002_identity cube =
 210     c t0' 1 0 0 2 ~= c t0' 0 1 0 2 + c t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
 211       where
 212         t0 = tetrahedron0 (face0 cube)
 213         t2 = tetrahedron2 (face5 cube)
 214         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 215         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 216
 217
 218 -- | Given in Sorokina and Zeilfelder, p. 79.
 219 prop_c1011_identity :: Cube -> Bool
 220 prop_c1011_identity cube =
 221     c t0' 1 0 1 1 ~= c t0' 0 1 1 1 + c t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
 222       where
 223         t0 = tetrahedron0 (face0 cube)
 224         t2 = tetrahedron2 (face5 cube)
 225         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 226         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 227
 228
 229 -- | Given in Sorokina and Zeilfelder, p. 80.
 230 prop_c0120_identity2 :: Cube -> Bool
 231 prop_c0120_identity2 cube =
 232         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 233       where
 234         t0 = tetrahedron0 (face0 cube)
 235         t1 = tetrahedron0 (face2 (top cube))
 236         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 237         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 238
 239
 240 -- | Given in Sorokina and Zeilfelder, p. 80.
 241 prop_c0102_identity2 :: Cube -> Bool
 242 prop_c0102_identity2 cube =
 243     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 244       where
 245         t0 = tetrahedron0 (face0 cube)
 246         t1 = tetrahedron0 (face2 (top cube))
 247         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 248         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 249
 250
 251 -- | Given in Sorokina and Zeilfelder, p. 80.
 252 prop_c0111_identity :: Cube -> Bool
 253 prop_c0111_identity cube =
 254     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 255       where
 256         t0 = tetrahedron0 (face0 cube)
 257         t1 = tetrahedron0 (face2 (top cube))
 258         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 259         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 260
 261
 262 -- | Given in Sorokina and Zeilfelder, p. 80.
 263 prop_c0210_identity2 :: Cube -> Bool
 264 prop_c0210_identity2 cube =
 265     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 266       where
 267         t0 = tetrahedron0 (face0 cube)
 268         t1 = tetrahedron0 (face2 (top cube))
 269         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 270         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 271
 272
 273 -- | Given in Sorokina and Zeilfelder, p. 80.
 274 prop_c0201_identity2 :: Cube -> Bool
 275 prop_c0201_identity2 cube =
 276     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 277       where
 278         t0 = tetrahedron0 (face0 cube)
 279         t1 = tetrahedron0 (face2 (top cube))
 280         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 281         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 282
 283
 284 -- | Given in Sorokina and Zeilfelder, p. 80.
 285 prop_c0300_identity3 :: Cube -> Bool
 286 prop_c0300_identity3 cube =
 287     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 288       where
 289         t0 = tetrahedron0 (face0 cube)
 290         t1 = tetrahedron0 (face2 (top cube))
 291         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 292         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)