X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FFace.hs;h=027b6b9d7562bd8439b43223ba2520f7b4265403;hb=62e6ea5912a0ef9b21d034590700d6b450f942fb;hp=2de60605b255c9d2cfe2a6bc07022de48a7c86b4;hpb=57c28cdd36989e49e59f556a5d7569768ea5ebb3;p=spline3.git

diff --git a/src/Tests/Face.hs b/src/Tests/Face.hs
index 2de6060..027b6b9 100644
--- a/src/Tests/Face.hs
+++ b/src/Tests/Face.hs
@@ -1,308 +1,365 @@
 module Tests.Face
 where
 
+import Control.Monad (unless)
+import Test.HUnit
 import Test.QuickCheck
 
+import Assertions
 import Comparisons
-import Cube (Cube(grid), top)
-import Face (face0,
-             face2,
-             face5,
-             tetrahedron0,
-             tetrahedron1,
-             tetrahedron2,
-             tetrahedron3,
-             tetrahedrons)
-import Grid (Grid(h))
+import Face
+import Grid (Grid(h), make_grid)
+import Point
 import Tetrahedron
 
--- QuickCheck Tests.
-
--- | Since the grid size is necessarily positive, all tetrahedrons
---   (which comprise cubes of positive volume) must have positive volume
---   as well.
-prop_all_volumes_positive :: Cube -> Property
-prop_all_volumes_positive c =
-    (delta > 0) ==> (null nonpositive_volumes)
-    where
-      delta = h (grid c)
-      ts = tetrahedrons c
-      volumes = map volume ts
-      nonpositive_volumes = filter (<= 0) volumes
-
-
--- | Given in Sorokina and Zeilfelder, p. 78.
-prop_cijk1_identity :: Cube -> Bool
-prop_cijk1_identity cube =
-     and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
-                            (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
-                            (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
-                            (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
-                                                                    j <- [0..2],
-                                                                    k <- [0..2],
-                                                                    i + j + k == 2]
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0120_identity1 :: Cube -> Bool
-prop_c0120_identity1 cube =
-    c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0210_identity1 :: Cube -> Bool
-prop_c0210_identity1 cube =
-    c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0300_identity1 :: Cube -> Bool
-prop_c0300_identity1 cube =
-    c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1110_identity :: Cube -> Bool
-prop_c1110_identity cube =
-    c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1200_identity1 :: Cube -> Bool
-prop_c1200_identity1 cube =
-    c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c2100_identity1 :: Cube -> Bool
-prop_c2100_identity1 cube =
-    c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron1 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0102_identity1 :: Cube -> Bool
-prop_c0102_identity1 cube =
-    c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t3 = tetrahedron3 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0201_identity1 :: Cube -> Bool
-prop_c0201_identity1 cube =
-    c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t3 = tetrahedron3 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0300_identity2 :: Cube -> Bool
-prop_c0300_identity2 cube =
-    c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t3 = tetrahedron3 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1101_identity :: Cube -> Bool
-prop_c1101_identity cube =
-    c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t3 = tetrahedron3 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1200_identity2 :: Cube -> Bool
-prop_c1200_identity2 cube =
-    c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t3 = tetrahedron3 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c2100_identity2 :: Cube -> Bool
-prop_c2100_identity2 cube =
-    c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t3 = tetrahedron3 (face0 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c3000_identity :: Cube -> Bool
-prop_c3000_identity cube =
-    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)
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t2 = tetrahedron2 (face5 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c2010_identity :: Cube -> Bool
-prop_c2010_identity cube =
-    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)
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t2 = tetrahedron2 (face5 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c2001_identity :: Cube -> Bool
-prop_c2001_identity cube =
-    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)
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t2 = tetrahedron2 (face5 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1020_identity :: Cube -> Bool
-prop_c1020_identity cube =
-    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)
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t2 = tetrahedron2 (face5 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1002_identity :: Cube -> Bool
-prop_c1002_identity cube =
-    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)
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t2 = tetrahedron2 (face5 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1011_identity :: Cube -> Bool
-prop_c1011_identity cube =
-    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)
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t2 = tetrahedron2 (face5 cube)
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0120_identity2 :: Cube -> Bool
-prop_c0120_identity2 cube =
-        c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron0 (face2 (top cube))
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0102_identity2 :: Cube -> Bool
-prop_c0102_identity2 cube =
-    c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron0 (face2 (top cube))
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0111_identity :: Cube -> Bool
-prop_c0111_identity cube =
-    c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron0 (face2 (top cube))
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0210_identity2 :: Cube -> Bool
-prop_c0210_identity2 cube =
-    c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron0 (face2 (top cube))
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0201_identity2 :: Cube -> Bool
-prop_c0201_identity2 cube =
-    c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron0 (face2 (top cube))
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0300_identity3 :: Cube -> Bool
-prop_c0300_identity3 cube =
-    c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
-      where
-        t0 = tetrahedron0 (face0 cube)
-        t1 = tetrahedron0 (face2 (top cube))
-        t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
-        t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+-- HUnit tests.
+
+
+
+
+
+-- -- test_trilinear_f0_t0_v0 :: Test
+-- -- test_trilinear_f0_t0_v0 =
+-- --     TestCase $ assertClose "v0 is correct" (v0 t) (0.5, 1.5, 1.5)
+-- --       where
+-- --         g = make_grid 1 trilinear
+-- --         cube = cube_at g 1 1 1
+-- --         t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+-- -- test_trilinear_f0_t0_v1 :: Test
+-- -- test_trilinear_f0_t0_v1 =
+-- --     TestCase $ assertClose "v1 is correct" (v1 t) (1.5, 1.5, 1.5)
+-- --       where
+-- --         g = make_grid 1 trilinear
+-- --         cube = cube_at g 1 1 1
+-- --         t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+-- -- test_trilinear_f0_t0_v2 :: Test
+-- -- test_trilinear_f0_t0_v2 =
+-- --     TestCase $ assertClose "v2 is correct" (v2 t) (1, 1, 1.5)
+-- --       where
+-- --         g = make_grid 1 trilinear
+-- --         cube = cube_at g 1 1 1
+-- --         t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+
+-- -- test_trilinear_f0_t0_v3 :: Test
+-- -- test_trilinear_f0_t0_v3 =
+-- --     TestCase $ assertClose "v3 is correct" (v3 t) (1, 1, 1)
+-- --       where
+-- --         g = make_grid 1 trilinear
+-- --         cube = cube_at g 1 1 1
+-- --         t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+
+-- face_tests :: [Test]
+face_tests = []
+-- face_tests = [test_trilinear_c0030,
+--               test_trilinear_c0003,
+--               test_trilinear_c0021,
+--               test_trilinear_c0012,
+--               test_trilinear_c0120,
+--               test_trilinear_c0102,
+--               test_trilinear_c0111,
+--               test_trilinear_c0210,
+--               test_trilinear_c0201,
+--               test_trilinear_c0300,
+--               test_trilinear_c1020,
+--               test_trilinear_c1002,
+--               test_trilinear_c1011,
+--               test_trilinear_c1110,
+--               test_trilinear_c1101,
+--               test_trilinear_c1200,
+--               test_trilinear_c2010,
+--               test_trilinear_c2001,
+--               test_trilinear_c2100,
+--               test_trilinear_c3000,
+--               test_trilinear_f0_t0_v0,
+--               test_trilinear_f0_t0_v1,
+--               test_trilinear_f0_t0_v2,
+--               test_trilinear_f0_t0_v3]
+
+
+-- -- QuickCheck Tests.
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 78.
+-- prop_cijk1_identity :: Cube -> Bool
+-- prop_cijk1_identity cube =
+--      and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
+--                             (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
+--                             (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
+--                             (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
+--                                                                     j <- [0..2],
+--                                                                     k <- [0..2],
+--                                                                     i + j + k == 2]
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0120_identity1 :: Cube -> Bool
+-- prop_c0120_identity1 cube =
+--     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0210_identity1 :: Cube -> Bool
+-- prop_c0210_identity1 cube =
+--     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0300_identity1 :: Cube -> Bool
+-- prop_c0300_identity1 cube =
+--     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1110_identity :: Cube -> Bool
+-- prop_c1110_identity cube =
+--     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1200_identity1 :: Cube -> Bool
+-- prop_c1200_identity1 cube =
+--     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c2100_identity1 :: Cube -> Bool
+-- prop_c2100_identity1 cube =
+--     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron1 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0102_identity1 :: Cube -> Bool
+-- prop_c0102_identity1 cube =
+--     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t3 = tetrahedron3 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0201_identity1 :: Cube -> Bool
+-- prop_c0201_identity1 cube =
+--     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t3 = tetrahedron3 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0300_identity2 :: Cube -> Bool
+-- prop_c0300_identity2 cube =
+--     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t3 = tetrahedron3 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1101_identity :: Cube -> Bool
+-- prop_c1101_identity cube =
+--     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t3 = tetrahedron3 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1200_identity2 :: Cube -> Bool
+-- prop_c1200_identity2 cube =
+--     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t3 = tetrahedron3 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c2100_identity2 :: Cube -> Bool
+-- prop_c2100_identity2 cube =
+--     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t3 = tetrahedron3 (face0 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c3000_identity :: Cube -> Bool
+-- prop_c3000_identity cube =
+--     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)
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t2 = tetrahedron2 (face5 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c2010_identity :: Cube -> Bool
+-- prop_c2010_identity cube =
+--     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)
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t2 = tetrahedron2 (face5 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c2001_identity :: Cube -> Bool
+-- prop_c2001_identity cube =
+--     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)
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t2 = tetrahedron2 (face5 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1020_identity :: Cube -> Bool
+-- prop_c1020_identity cube =
+--     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)
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t2 = tetrahedron2 (face5 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1002_identity :: Cube -> Bool
+-- prop_c1002_identity cube =
+--     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)
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t2 = tetrahedron2 (face5 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1011_identity :: Cube -> Bool
+-- prop_c1011_identity cube =
+--     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)
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t2 = tetrahedron2 (face5 cube)
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0120_identity2 :: Cube -> Bool
+-- prop_c0120_identity2 cube =
+--         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron0 (face2 (top cube))
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0102_identity2 :: Cube -> Bool
+-- prop_c0102_identity2 cube =
+--     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron0 (face2 (top cube))
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0111_identity :: Cube -> Bool
+-- prop_c0111_identity cube =
+--     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron0 (face2 (top cube))
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0210_identity2 :: Cube -> Bool
+-- prop_c0210_identity2 cube =
+--     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron0 (face2 (top cube))
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0201_identity2 :: Cube -> Bool
+-- prop_c0201_identity2 cube =
+--     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron0 (face2 (top cube))
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0300_identity3 :: Cube -> Bool
+-- prop_c0300_identity3 cube =
+--     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
+--       where
+--         t0 = tetrahedron0 (face0 cube)
+--         t1 = tetrahedron0 (face2 (top cube))
+--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)