From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 4 May 2011 03:04:05 +0000 (-0400)
Subject: Begin fixing some of the tests. Commented out most of them.
X-Git-Tag: 0.0.1~342
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=33998c9e4eac925df771d224befc5c0974f877bf;p=spline3.git

Begin fixing some of the tests. Commented out most of them.
Added an Arbitrary instance for FunctionValues.
---

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index eee5444..a832f5a 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -3,18 +3,33 @@ where
 
 import Test.QuickCheck
 
-import Cube
-import Grid (Grid)
-import Tests.Grid ()
+import Cube (Cube(Cube))
+import FunctionValues (FunctionValues(FunctionValues))
+import Tests.FunctionValues
 
 instance Arbitrary Cube where
     arbitrary = do
-      g' <- arbitrary :: Gen Grid
+      (Positive h') <- arbitrary :: Gen (Positive Double)
       i' <- choose (coordmin, coordmax)
       j' <- choose (coordmin, coordmax)
       k' <- choose (coordmin, coordmax)
-      d' <- arbitrary :: Gen Double
-      return (Cube g' i' j' k' d')
+      fv' <- arbitrary :: Gen FunctionValues
+      return (Cube h' i' j' k' fv')
         where
           coordmin = -268435456 -- -(2^29 / 2)
           coordmax = 268435456  -- +(2^29 / 2)
+
+
+-- 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
diff --git a/src/Tests/Face.hs b/src/Tests/Face.hs
index decb77a..4a1e9b8 100644
--- a/src/Tests/Face.hs
+++ b/src/Tests/Face.hs
@@ -6,15 +6,7 @@ import Test.HUnit
 import Test.QuickCheck
 
 import Comparisons
-import Cube (Cube(grid), cube_at, top)
-import Face (face0,
-             face2,
-             face5,
-             tetrahedron0,
-             tetrahedron1,
-             tetrahedron2,
-             tetrahedron3,
-             tetrahedrons)
+import Face
 import Grid (Grid(h), make_grid)
 import Point
 import Tetrahedron
@@ -57,596 +49,584 @@ trilinear = [ [ [ 1, 2, 3 ],
 -- | Check the value of c0030 for any tetrahedron belonging to the
 --   cube centered on (1,1,1) with a grid constructed from the
 --   trilinear values. See example one in the paper.
-test_trilinear_c0030 :: Test
-test_trilinear_c0030 =
-    TestCase $ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0003 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0003 :: Test
-test_trilinear_c0003 =
-    TestCase $ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0021 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0021 :: Test
-test_trilinear_c0021 =
-    TestCase $ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0012 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0012 :: Test
-test_trilinear_c0012 =
-    TestCase $ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0120 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0120 :: Test
-test_trilinear_c0120 =
-    TestCase $ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0102 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0102 :: Test
-test_trilinear_c0102 =
-    TestCase $ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0111 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0111 :: Test
-test_trilinear_c0111 =
-    TestCase $ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0210 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0210 :: Test
-test_trilinear_c0210 =
-    TestCase $ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0201 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0201 :: Test
-test_trilinear_c0201 =
-    TestCase $ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c0300 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c0300 :: Test
-test_trilinear_c0300 =
-    TestCase $ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c1020 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c1020 :: Test
-test_trilinear_c1020 =
-    TestCase $ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c1002 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c1002 :: Test
-test_trilinear_c1002 =
-    TestCase $ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c1011 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c1011 :: Test
-test_trilinear_c1011 =
-    TestCase $ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c1110 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c1110 :: Test
-test_trilinear_c1110 =
-    TestCase $ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c1101 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c1101 :: Test
-test_trilinear_c1101 =
-    TestCase $ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c1200 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c1200 :: Test
-test_trilinear_c1200 =
-    TestCase $ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c2010 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c2010 :: Test
-test_trilinear_c2010 =
-    TestCase $ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c2001 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c2001 :: Test
-test_trilinear_c2001 =
-    TestCase $ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c2100 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c2100 :: Test
-test_trilinear_c2100 =
-    TestCase $ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
--- | Check the value of c3000 for any tetrahedron belonging to the
---   cube centered on (1,1,1) with a grid constructed from the
---   trilinear values. See example one in the paper.
-test_trilinear_c3000 :: Test
-test_trilinear_c3000 =
-    TestCase $ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
-      where
-        g = make_grid 1 trilinear
-        cube = cube_at g 1 1 1
-        t = head (tetrahedrons cube) -- Any one will do.
-
-
-
-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 = [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.
-
--- | 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)
+-- test_trilinear_c0030 :: Test
+-- test_trilinear_c0030 =
+--     TestCase $ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0003 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0003 :: Test
+-- test_trilinear_c0003 =
+--     TestCase $ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0021 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0021 :: Test
+-- test_trilinear_c0021 =
+--     TestCase $ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0012 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0012 :: Test
+-- test_trilinear_c0012 =
+--     TestCase $ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0120 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0120 :: Test
+-- test_trilinear_c0120 =
+--     TestCase $ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0102 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0102 :: Test
+-- test_trilinear_c0102 =
+--     TestCase $ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0111 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0111 :: Test
+-- test_trilinear_c0111 =
+--     TestCase $ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0210 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0210 :: Test
+-- test_trilinear_c0210 =
+--     TestCase $ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0201 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0201 :: Test
+-- test_trilinear_c0201 =
+--     TestCase $ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c0300 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c0300 :: Test
+-- test_trilinear_c0300 =
+--     TestCase $ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c1020 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c1020 :: Test
+-- test_trilinear_c1020 =
+--     TestCase $ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c1002 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c1002 :: Test
+-- test_trilinear_c1002 =
+--     TestCase $ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c1011 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c1011 :: Test
+-- test_trilinear_c1011 =
+--     TestCase $ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c1110 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c1110 :: Test
+-- test_trilinear_c1110 =
+--     TestCase $ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c1101 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c1101 :: Test
+-- test_trilinear_c1101 =
+--     TestCase $ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c1200 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c1200 :: Test
+-- test_trilinear_c1200 =
+--     TestCase $ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c2010 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c2010 :: Test
+-- test_trilinear_c2010 =
+--     TestCase $ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c2001 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c2001 :: Test
+-- test_trilinear_c2001 =
+--     TestCase $ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c2100 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- test_trilinear_c2100 :: Test
+-- test_trilinear_c2100 =
+--     TestCase $ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+--       where
+--         g = make_grid 1 trilinear
+--         cube = cube_at g 1 1 1
+--         t = head (tetrahedrons cube) -- Any one will do.
+
+
+-- -- | Check the value of c3000 for any tetrahedron belonging to the
+-- --   cube centered on (1,1,1) with a grid constructed from the
+-- --   trilinear values. See example one in the paper.
+-- -- test_trilinear_c3000 :: Test
+-- -- test_trilinear_c3000 =
+-- --     TestCase $ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
+-- --       where
+-- --         g = make_grid 1 trilinear
+-- --         cube = cube_at g 1 1 1
+-- --         t = head (tetrahedrons cube) -- Any one will do.
+
+
+
+-- -- 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 = [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)
diff --git a/src/Tests/FunctionValues.hs b/src/Tests/FunctionValues.hs
new file mode 100644
index 0000000..ce9a351
--- /dev/null
+++ b/src/Tests/FunctionValues.hs
@@ -0,0 +1,64 @@
+module Tests.FunctionValues
+where
+
+import Test.QuickCheck
+
+import FunctionValues
+
+instance Arbitrary FunctionValues where
+    arbitrary = do
+      front'  <- arbitrary :: Gen Double
+      back'   <- arbitrary :: Gen Double
+      left'   <- arbitrary :: Gen Double
+      right'  <- arbitrary :: Gen Double
+      top'    <- arbitrary :: Gen Double
+      down'   <- arbitrary :: Gen Double
+      front_left' <- arbitrary :: Gen Double
+      front_right' <- arbitrary :: Gen Double
+      front_top' <- arbitrary :: Gen Double
+      front_down' <- arbitrary :: Gen Double
+      back_left' <- arbitrary :: Gen Double
+      back_right' <- arbitrary :: Gen Double
+      back_top' <- arbitrary :: Gen Double
+      back_down' <- arbitrary :: Gen Double
+      left_top' <- arbitrary :: Gen Double
+      left_down' <- arbitrary :: Gen Double
+      right_top' <- arbitrary :: Gen Double
+      right_down' <- arbitrary :: Gen Double
+      front_left_top' <- arbitrary :: Gen Double
+      front_left_down' <- arbitrary :: Gen Double
+      front_right_top' <- arbitrary :: Gen Double
+      front_right_down' <- arbitrary :: Gen Double
+      back_left_top' <- arbitrary :: Gen Double
+      back_left_down' <- arbitrary :: Gen Double
+      back_right_top' <- arbitrary :: Gen Double
+      back_right_down' <- arbitrary :: Gen Double
+      interior' <- arbitrary :: Gen Double
+
+      return empty_values { front = front',
+                            back  = back',
+                            left  = left',
+                            right = right',
+                            top   = top',
+                            down  = down',
+                            front_left = front_left',
+                            front_right = front_right',
+                            front_top = front_top',
+                            front_down = front_down',
+                            back_left = back_left',
+                            back_right = back_right',
+                            back_top = back_top',
+                            back_down = back_down',
+                            left_top = left_top',
+                            left_down = left_down',
+                            right_top = right_top',
+                            right_down = right_down',
+                            front_left_top = front_left_top',
+                            front_left_down = front_left_down',
+                            front_right_top = front_right_top',
+                            front_right_down = front_right_down',
+                            back_left_top = back_left_top',
+                            back_left_down = back_left_down',
+                            back_right_top = back_right_top',
+                            back_right_down = back_right_down',
+                            interior = interior' }
diff --git a/src/Tests/Tetrahedron.hs b/src/Tests/Tetrahedron.hs
index bc13876..d4b7b9b 100644
--- a/src/Tests/Tetrahedron.hs
+++ b/src/Tests/Tetrahedron.hs
@@ -5,20 +5,20 @@ import Test.HUnit
 import Test.QuickCheck
 
 import Comparisons
-import Cube
 import Point
-import Tests.Cube()
+import FunctionValues
+import Tests.FunctionValues()
 import Tetrahedron
 import ThreeDimensional
 
 instance Arbitrary Tetrahedron where
     arbitrary = do
-      rnd_c0 <- arbitrary :: Gen Cube
       rnd_v0 <- arbitrary :: Gen Point
       rnd_v1 <- arbitrary :: Gen Point
       rnd_v2 <- arbitrary :: Gen Point
       rnd_v3 <- arbitrary :: Gen Point
-      return (Tetrahedron rnd_c0 rnd_v0 rnd_v1 rnd_v2 rnd_v3)
+      rnd_fv <- arbitrary :: Gen FunctionValues
+      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
 
 -- HUnit Tests
 
@@ -32,11 +32,11 @@ test_volume1 =
       p1 = (0, 0.5, 0)
       p2 = (2, 0, 0)
       p3 = (1, 0, 1)
-      t = Tetrahedron { cube = empty_cube,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
       vol = volume t
 
 
@@ -50,11 +50,11 @@ test_volume2 =
       p1 = (2, 0, 0)
       p2 = (0, 0.5, 0)
       p3 = (1, 0, 1)
-      t = Tetrahedron { cube = empty_cube,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
       vol = volume t
 
 test_contains_point1 :: Test
@@ -66,11 +66,11 @@ test_contains_point1 =
       p2 = (2, 0, 0)
       p3 = (1, 0, 1)
       inner_point = (1, 0, 0.5)
-      t = Tetrahedron { cube = empty_cube,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
 
 
 test_doesnt_contain_point1 :: Test
@@ -82,12 +82,11 @@ test_doesnt_contain_point1 =
       p2 = (2, 0, 0)
       p3 = (1, 0, 1)
       exterior_point = (5, 2, -9.0212)
-      c_empty = empty_cube
-      t = Tetrahedron { cube = c_empty,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
 
 
 test_doesnt_contain_point2 :: Test
@@ -99,12 +98,11 @@ test_doesnt_contain_point2 =
       p2 = (0.5, 0.5, 1)
       p3 = (0.5, 0.5, 0.5)
       exterior_point = (0, 0, 0)
-      c_empty = empty_cube
-      t = Tetrahedron { cube = c_empty,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
 
 test_doesnt_contain_point3 :: Test
 test_doesnt_contain_point3 =
@@ -115,12 +113,11 @@ test_doesnt_contain_point3 =
       p2 = (0.5, 0.5, 1)
       p3 = (0.5, 0.5, 0.5)
       exterior_point = (0, 0, 0)
-      c_empty = empty_cube
-      t = Tetrahedron { cube = c_empty,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
 
 test_doesnt_contain_point4 :: Test
 test_doesnt_contain_point4 =
@@ -131,12 +128,11 @@ test_doesnt_contain_point4 =
       p2 = (0.5, 0.5, 1)
       p3 = (0.5, 0.5, 0.5)
       exterior_point = (0, 0, 0)
-      c_empty = empty_cube
-      t = Tetrahedron { cube = c_empty,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
 
 test_doesnt_contain_point5 :: Test
 test_doesnt_contain_point5 =
@@ -147,12 +143,11 @@ test_doesnt_contain_point5 =
       p2 = (0.5, 0.5, 1)
       p3 = (0.5, 0.5, 0.5)
       exterior_point = (0, 0, 0)
-      c_empty = empty_cube
-      t = Tetrahedron { cube = c_empty,
-                        v0 = p0,
+      t = Tetrahedron { v0 = p0,
                         v1 = p1,
                         v2 = p2,
-                        v3 = p3 }
+                        v3 = p3,
+                        fv = empty_values }
 
 tetrahedron_tests :: [Test]
 tetrahedron_tests = [test_volume1,