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. 78.
  35 prop_cijk1_identity :: Cube -> Bool
  36 prop_cijk1_identity cube =
  37      and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
  38                             (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
  39                             (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
  40                             (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
  41                                                                     j <- [0..2],
  42                                                                     k <- [0..2],
  43                                                                     i + j + k == 2]
  44       where
  45         t0 = tetrahedron0 (face0 cube)
  46         t1 = tetrahedron1 (face0 cube)
  47         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  48         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  49
  50 -- | Given in Sorokina and Zeilfelder, p. 79.
  51 prop_c0120_identity1 :: Cube -> Bool
  52 prop_c0120_identity1 cube =
  53     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
  54       where
  55         t0 = tetrahedron0 (face0 cube)
  56         t1 = tetrahedron1 (face0 cube)
  57         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  58         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  59
  60
  61 -- | Given in Sorokina and Zeilfelder, p. 79.
  62 prop_c0210_identity1 :: Cube -> Bool
  63 prop_c0210_identity1 cube =
  64     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
  65       where
  66         t0 = tetrahedron0 (face0 cube)
  67         t1 = tetrahedron1 (face0 cube)
  68         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  69         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  70
  71
  72 -- | Given in Sorokina and Zeilfelder, p. 79.
  73 prop_c0300_identity1 :: Cube -> Bool
  74 prop_c0300_identity1 cube =
  75     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
  76       where
  77         t0 = tetrahedron0 (face0 cube)
  78         t1 = tetrahedron1 (face0 cube)
  79         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  80         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  81
  82 -- | Given in Sorokina and Zeilfelder, p. 79.
  83 prop_c1110_identity :: Cube -> Bool
  84 prop_c1110_identity cube =
  85     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
  86       where
  87         t0 = tetrahedron0 (face0 cube)
  88         t1 = tetrahedron1 (face0 cube)
  89         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  90         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  91
  92
  93 -- | Given in Sorokina and Zeilfelder, p. 79.
  94 prop_c1200_identity1 :: Cube -> Bool
  95 prop_c1200_identity1 cube =
  96     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
  97       where
  98         t0 = tetrahedron0 (face0 cube)
  99         t1 = tetrahedron1 (face0 cube)
 100         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 101         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 102
 103
 104 -- | Given in Sorokina and Zeilfelder, p. 79.
 105 prop_c2100_identity1 :: Cube -> Bool
 106 prop_c2100_identity1 cube =
 107     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
 108       where
 109         t0 = tetrahedron0 (face0 cube)
 110         t1 = tetrahedron1 (face0 cube)
 111         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 112         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 113
 114
 115 -- | Given in Sorokina and Zeilfelder, p. 79.
 116 prop_c0102_identity1 :: Cube -> Bool
 117 prop_c0102_identity1 cube =
 118     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
 119       where
 120         t0 = tetrahedron0 (face0 cube)
 121         t3 = tetrahedron3 (face0 cube)
 122         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 123         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 124
 125
 126 -- | Given in Sorokina and Zeilfelder, p. 79.
 127 prop_c0201_identity1 :: Cube -> Bool
 128 prop_c0201_identity1 cube =
 129     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
 130       where
 131         t0 = tetrahedron0 (face0 cube)
 132         t3 = tetrahedron3 (face0 cube)
 133         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 134         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 135
 136
 137 -- | Given in Sorokina and Zeilfelder, p. 79.
 138 prop_c0300_identity2 :: Cube -> Bool
 139 prop_c0300_identity2 cube =
 140     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
 141       where
 142         t0 = tetrahedron0 (face0 cube)
 143         t3 = tetrahedron3 (face0 cube)
 144         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 145         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 146
 147 -- | Given in Sorokina and Zeilfelder, p. 79.
 148 prop_c1101_identity :: Cube -> Bool
 149 prop_c1101_identity cube =
 150     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
 151       where
 152         t0 = tetrahedron0 (face0 cube)
 153         t3 = tetrahedron3 (face0 cube)
 154         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 155         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 156
 157
 158 -- | Given in Sorokina and Zeilfelder, p. 79.
 159 prop_c1200_identity2 :: Cube -> Bool
 160 prop_c1200_identity2 cube =
 161     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
 162       where
 163         t0 = tetrahedron0 (face0 cube)
 164         t3 = tetrahedron3 (face0 cube)
 165         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 166         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 167
 168
 169 -- | Given in Sorokina and Zeilfelder, p. 79.
 170 prop_c2100_identity2 :: Cube -> Bool
 171 prop_c2100_identity2 cube =
 172     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
 173       where
 174         t0 = tetrahedron0 (face0 cube)
 175         t3 = tetrahedron3 (face0 cube)
 176         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 177         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 178
 179
 180 -- | Given in Sorokina and Zeilfelder, p. 79.
 181 prop_c3000_identity :: Cube -> Bool
 182 prop_c3000_identity cube =
 183     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)
 184       where
 185         t0 = tetrahedron0 (face0 cube)
 186         t2 = tetrahedron2 (face5 cube)
 187         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 188         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 189
 190
 191 -- | Given in Sorokina and Zeilfelder, p. 79.
 192 prop_c2010_identity :: Cube -> Bool
 193 prop_c2010_identity cube =
 194     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)
 195       where
 196         t0 = tetrahedron0 (face0 cube)
 197         t2 = tetrahedron2 (face5 cube)
 198         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 199         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 200
 201
 202 -- | Given in Sorokina and Zeilfelder, p. 79.
 203 prop_c2001_identity :: Cube -> Bool
 204 prop_c2001_identity cube =
 205     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)
 206       where
 207         t0 = tetrahedron0 (face0 cube)
 208         t2 = tetrahedron2 (face5 cube)
 209         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 210         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 211
 212 -- | Given in Sorokina and Zeilfelder, p. 79.
 213 prop_c1020_identity :: Cube -> Bool
 214 prop_c1020_identity cube =
 215     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)
 216       where
 217         t0 = tetrahedron0 (face0 cube)
 218         t2 = tetrahedron2 (face5 cube)
 219         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 220         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 221
 222
 223 -- | Given in Sorokina and Zeilfelder, p. 79.
 224 prop_c1002_identity :: Cube -> Bool
 225 prop_c1002_identity cube =
 226     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)
 227       where
 228         t0 = tetrahedron0 (face0 cube)
 229         t2 = tetrahedron2 (face5 cube)
 230         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 231         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 232
 233
 234 -- | Given in Sorokina and Zeilfelder, p. 79.
 235 prop_c1011_identity :: Cube -> Bool
 236 prop_c1011_identity cube =
 237     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)
 238       where
 239         t0 = tetrahedron0 (face0 cube)
 240         t2 = tetrahedron2 (face5 cube)
 241         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 242         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 243
 244
 245 -- | Given in Sorokina and Zeilfelder, p. 80.
 246 prop_c0120_identity2 :: Cube -> Bool
 247 prop_c0120_identity2 cube =
 248         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 249       where
 250         t0 = tetrahedron0 (face0 cube)
 251         t1 = tetrahedron0 (face2 (top cube))
 252         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 253         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 254
 255
 256 -- | Given in Sorokina and Zeilfelder, p. 80.
 257 prop_c0102_identity2 :: Cube -> Bool
 258 prop_c0102_identity2 cube =
 259     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 260       where
 261         t0 = tetrahedron0 (face0 cube)
 262         t1 = tetrahedron0 (face2 (top cube))
 263         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 264         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 265
 266
 267 -- | Given in Sorokina and Zeilfelder, p. 80.
 268 prop_c0111_identity :: Cube -> Bool
 269 prop_c0111_identity cube =
 270     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 271       where
 272         t0 = tetrahedron0 (face0 cube)
 273         t1 = tetrahedron0 (face2 (top cube))
 274         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 275         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 276
 277
 278 -- | Given in Sorokina and Zeilfelder, p. 80.
 279 prop_c0210_identity2 :: Cube -> Bool
 280 prop_c0210_identity2 cube =
 281     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 282       where
 283         t0 = tetrahedron0 (face0 cube)
 284         t1 = tetrahedron0 (face2 (top cube))
 285         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 286         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 287
 288
 289 -- | Given in Sorokina and Zeilfelder, p. 80.
 290 prop_c0201_identity2 :: Cube -> Bool
 291 prop_c0201_identity2 cube =
 292     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 293       where
 294         t0 = tetrahedron0 (face0 cube)
 295         t1 = tetrahedron0 (face2 (top cube))
 296         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 297         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 298
 299
 300 -- | Given in Sorokina and Zeilfelder, p. 80.
 301 prop_c0300_identity3 :: Cube -> Bool
 302 prop_c0300_identity3 cube =
 303     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 304       where
 305         t0 = tetrahedron0 (face0 cube)
 306         t1 = tetrahedron0 (face2 (top cube))
 307         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 308         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)