X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=17ea7f8857ee6e0a1bc9f079a7a19b7d8509fe57;hb=1f20ae355d28b53fc2e1e31c4bd131e9ede00a87;hp=631af5f54545564bf314531cf612d94ac4ef41f3;hpb=131df3514c868c055c22c090e17674b07d25d8ca;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index 631af5f..17ea7f8 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -2,257 +2,56 @@ module Tests.Cube
 where
 
 import Prelude hiding (LT)
-import Test.QuickCheck
 
 import Cardinal
 import Comparisons
-import Cube
+import Cube hiding (i, j, k)
 import FunctionValues
-import Misc (all_equal)
-import Tests.FunctionValues ()
+import Misc (all_equal, disjoint)
 import Tetrahedron (b0, b1, b2, b3, c, fv,
                     v0, v1, v2, v3, volume)
 
-instance Arbitrary Cube where
-    arbitrary = do
-      (Positive h') <- arbitrary :: Gen (Positive Double)
-      i' <- choose (coordmin, coordmax)
-      j' <- choose (coordmin, coordmax)
-      k' <- choose (coordmin, coordmax)
-      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
+-- | The 'front_half_tetrahedra' and 'back_half_tetrahedra' should
+--   have no tetrahedra in common.
+prop_front_back_tetrahedra_disjoint :: Cube -> Bool
+prop_front_back_tetrahedra_disjoint c =
+    disjoint (front_half_tetrahedra c) (back_half_tetrahedra c)
+
+
+-- | The 'top_half_tetrahedra' and 'down_half_tetrahedra' should
+--   have no tetrahedra in common.
+prop_top_down_tetrahedra_disjoint :: Cube -> Bool
+prop_top_down_tetrahedra_disjoint c =
+    disjoint (top_half_tetrahedra c) (down_half_tetrahedra c)
+
+
+-- | The 'left_half_tetrahedra' and 'right_half_tetrahedra' should
+--   have no tetrahedra in common.
+prop_left_right_tetrahedra_disjoint :: Cube -> Bool
+prop_left_right_tetrahedra_disjoint c =
+    disjoint (left_half_tetrahedra c) (right_half_tetrahedra c)
+
+
+-- | Since the grid size is necessarily positive, all tetrahedra
 --   (which comprise cubes of positive volume) must have positive volume
 --   as well.
 prop_all_volumes_positive :: Cube -> Bool
 prop_all_volumes_positive cube =
     null nonpositive_volumes
     where
-      ts = tetrahedrons cube
+      ts = tetrahedra cube
       volumes = map volume ts
       nonpositive_volumes = filter (<= 0) volumes
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron0_volumes_exact :: Cube -> Bool
-prop_tetrahedron0_volumes_exact cube =
-    volume (tetrahedron0 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron1_volumes_exact :: Cube -> Bool
-prop_tetrahedron1_volumes_exact cube =
-    volume (tetrahedron1 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron2_volumes_exact :: Cube -> Bool
-prop_tetrahedron2_volumes_exact cube =
-    volume (tetrahedron2 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron3_volumes_exact :: Cube -> Bool
-prop_tetrahedron3_volumes_exact cube =
-    volume (tetrahedron3 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron4_volumes_exact :: Cube -> Bool
-prop_tetrahedron4_volumes_exact cube =
-    volume (tetrahedron4 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron5_volumes_exact :: Cube -> Bool
-prop_tetrahedron5_volumes_exact cube =
-    volume (tetrahedron5 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron6_volumes_exact :: Cube -> Bool
-prop_tetrahedron6_volumes_exact cube =
-    volume (tetrahedron6 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron7_volumes_exact :: Cube -> Bool
-prop_tetrahedron7_volumes_exact cube =
-    volume (tetrahedron7 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron8_volumes_exact :: Cube -> Bool
-prop_tetrahedron8_volumes_exact cube =
-    volume (tetrahedron8 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron9_volumes_exact :: Cube -> Bool
-prop_tetrahedron9_volumes_exact cube =
-    volume (tetrahedron9 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron10_volumes_exact :: Cube -> Bool
-prop_tetrahedron10_volumes_exact cube =
-    volume (tetrahedron10 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron11_volumes_exact :: Cube -> Bool
-prop_tetrahedron11_volumes_exact cube =
-    volume (tetrahedron11 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron12_volumes_exact :: Cube -> Bool
-prop_tetrahedron12_volumes_exact cube =
-    volume (tetrahedron12 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron13_volumes_exact :: Cube -> Bool
-prop_tetrahedron13_volumes_exact cube =
-    volume (tetrahedron13 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron14_volumes_exact :: Cube -> Bool
-prop_tetrahedron14_volumes_exact cube =
-    volume (tetrahedron14 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron15_volumes_exact :: Cube -> Bool
-prop_tetrahedron15_volumes_exact cube =
-    volume (tetrahedron15 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron16_volumes_exact :: Cube -> Bool
-prop_tetrahedron16_volumes_exact cube =
-    volume (tetrahedron16 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron17_volumes_exact :: Cube -> Bool
-prop_tetrahedron17_volumes_exact cube =
-    volume (tetrahedron17 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron18_volumes_exact :: Cube -> Bool
-prop_tetrahedron18_volumes_exact cube =
-    volume (tetrahedron18 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron19_volumes_exact :: Cube -> Bool
-prop_tetrahedron19_volumes_exact cube =
-    volume (tetrahedron19 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron20_volumes_exact :: Cube -> Bool
-prop_tetrahedron20_volumes_exact cube =
-    volume (tetrahedron20 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron21_volumes_exact :: Cube -> Bool
-prop_tetrahedron21_volumes_exact cube =
-    volume (tetrahedron21 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron22_volumes_exact :: Cube -> Bool
-prop_tetrahedron22_volumes_exact cube =
-    volume (tetrahedron22 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
---   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron23_volumes_exact :: Cube -> Bool
-prop_tetrahedron23_volumes_exact cube =
-    volume (tetrahedron23 cube) ~~= (1/24)*(delta^(3::Int))
+prop_all_volumes_exact :: Cube -> Bool
+prop_all_volumes_exact cube =
+    and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
     where
       delta = h cube
 
@@ -260,187 +59,46 @@ prop_tetrahedron23_volumes_exact cube =
 prop_v0_all_equal :: Cube -> Bool
 prop_v0_all_equal cube = (v0 t0) == (v0 t1)
     where
-      t0 = head (tetrahedrons cube) -- Doesn't matter which two we choose.
-      t1 = head $ tail (tetrahedrons cube)
-
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron0_volumes_positive :: Cube -> Bool
-prop_tetrahedron0_volumes_positive cube =
-    volume (tetrahedron0 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron1_volumes_positive :: Cube -> Bool
-prop_tetrahedron1_volumes_positive cube =
-    volume (tetrahedron1 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron2_volumes_positive :: Cube -> Bool
-prop_tetrahedron2_volumes_positive cube =
-    volume (tetrahedron2 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron3_volumes_positive :: Cube -> Bool
-prop_tetrahedron3_volumes_positive cube =
-    volume (tetrahedron3 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron4_volumes_positive :: Cube -> Bool
-prop_tetrahedron4_volumes_positive cube =
-    volume (tetrahedron4 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron5_volumes_positive :: Cube -> Bool
-prop_tetrahedron5_volumes_positive cube =
-    volume (tetrahedron5 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron6_volumes_positive :: Cube -> Bool
-prop_tetrahedron6_volumes_positive cube =
-    volume (tetrahedron6 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron7_volumes_positive :: Cube -> Bool
-prop_tetrahedron7_volumes_positive cube =
-    volume (tetrahedron7 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron8_volumes_positive :: Cube -> Bool
-prop_tetrahedron8_volumes_positive cube =
-    volume (tetrahedron8 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron9_volumes_positive :: Cube -> Bool
-prop_tetrahedron9_volumes_positive cube =
-    volume (tetrahedron9 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron10_volumes_positive :: Cube -> Bool
-prop_tetrahedron10_volumes_positive cube =
-    volume (tetrahedron10 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron11_volumes_positive :: Cube -> Bool
-prop_tetrahedron11_volumes_positive cube =
-    volume (tetrahedron11 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron12_volumes_positive :: Cube -> Bool
-prop_tetrahedron12_volumes_positive cube =
-    volume (tetrahedron12 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron13_volumes_positive :: Cube -> Bool
-prop_tetrahedron13_volumes_positive cube =
-    volume (tetrahedron13 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron14_volumes_positive :: Cube -> Bool
-prop_tetrahedron14_volumes_positive cube =
-    volume (tetrahedron14 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron15_volumes_positive :: Cube -> Bool
-prop_tetrahedron15_volumes_positive cube =
-    volume (tetrahedron15 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron16_volumes_positive :: Cube -> Bool
-prop_tetrahedron16_volumes_positive cube =
-    volume (tetrahedron16 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron17_volumes_positive :: Cube -> Bool
-prop_tetrahedron17_volumes_positive cube =
-    volume (tetrahedron17 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron18_volumes_positive :: Cube -> Bool
-prop_tetrahedron18_volumes_positive cube =
-    volume (tetrahedron18 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron19_volumes_positive :: Cube -> Bool
-prop_tetrahedron19_volumes_positive cube =
-    volume (tetrahedron19 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron20_volumes_positive :: Cube -> Bool
-prop_tetrahedron20_volumes_positive cube =
-    volume (tetrahedron20 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron21_volumes_positive :: Cube -> Bool
-prop_tetrahedron21_volumes_positive cube =
-    volume (tetrahedron21 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron22_volumes_positive :: Cube -> Bool
-prop_tetrahedron22_volumes_positive cube =
-    volume (tetrahedron22 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
---   but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron23_volumes_positive :: Cube -> Bool
-prop_tetrahedron23_volumes_positive cube =
-    volume (tetrahedron23 cube) > 0
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). It appears that
---   the assumptions in sections (2.6) and (2.7) have been
---   switched. From the description, one would expect 'tetrahedron0'
---   and 'tetrahedron3' to share face \<v0,v1,v2\>; however, we have
---   to use 'tetrahedron0' and 'tetahedron1' for all of the tests in
---   section (2.6). Also note that the third and fourth indices of
---   c-t1 have been switched. This is because we store the triangles
---   oriented such that their volume is positive. If T and T-tilde
---   share \<v0,v1,v2\> and v3,v3-tilde point in opposite directions,
---   one of them has to have negative volume!
+      t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
+      t1 = head $ tail (tetrahedra cube)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
+--   third and fourth indices of c-t1 have been switched. This is
+--   because we store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
 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 1 2) / 2
+   c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
      where
        t0 = tetrahedron0 cube
-       t1 = tetrahedron1 cube
+       t3 = tetrahedron3 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 --   'prop_c0120_identity1' with tetrahedrons 1 and 2.
 prop_c0120_identity2 :: Cube -> Bool
 prop_c0120_identity2 cube =
-   c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t2 0 0 1 2) / 2
+   c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
+     where
+       t0 = tetrahedron0 cube
+       t1 = tetrahedron1 cube
+            
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+--   'prop_c0120_identity1' with tetrahedrons 1 and 2.
+prop_c0120_identity3 :: Cube -> Bool
+prop_c0120_identity3 cube =
+   c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
      where
        t1 = tetrahedron1 cube
        t2 = tetrahedron2 cube
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 --   'prop_c0120_identity1' with tetrahedrons 2 and 3.
-prop_c0120_identity3 :: Cube -> Bool
-prop_c0120_identity3 cube =
-   c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t3 0 0 1 2) / 2
+prop_c0120_identity4 :: Cube -> Bool
+prop_c0120_identity4 cube =
+   c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
      where
        t2 = tetrahedron2 cube
        t3 = tetrahedron3 cube
@@ -448,176 +106,146 @@ prop_c0120_identity3 cube =
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 --   'prop_c0120_identity1' with tetrahedrons 4 and 5.
--- prop_c0120_identity4 :: Cube -> Bool
--- prop_c0120_identity4 cube =
---     sum [trace ("c_t4_0120: " ++ (show tmp1)) tmp1,
---          trace ("c_t5_0012: " ++ (show tmp2)) tmp2,
---          trace ("c_t5_0102: " ++ (show tmp3)) tmp3,
---          trace ("c_t5_1002: " ++ (show tmp4)) tmp4,
---          trace ("c_t5_0120: " ++ (show tmp5)) tmp5,
---          trace ("c_t5_1020: " ++ (show tmp6)) tmp6,
---          trace ("c_t5_1200: " ++ (show tmp7)) tmp7,
---          trace ("c_t5_0021: " ++ (show tmp8)) tmp8,
---          trace ("c_t5_0201: " ++ (show tmp9)) tmp9,
---          trace ("c_t5_2001: " ++ (show tmp10)) tmp10,
---          trace ("c_t5_0210: " ++ (show tmp11)) tmp11,
---          trace ("c_t5_2010: " ++ (show tmp12)) tmp12,
---          trace ("c_t5_2100: " ++ (show tmp13)) tmp13] == 10
--- --   c t4 0 1 2 0 ~= (c t4 0 0 2 1 + c t5 0 0 1 2) / 2
---      where
---        t4 = tetrahedron4 cube
---        t5 = tetrahedron5 cube
---        tmp1 = c t4 0 1 2 0
---        tmp2 = (c t4 0 0 2 1 + c t5 0 0 1 2) / 2
---        tmp3 = (c t4 0 0 2 1 + c t5 0 1 0 2) / 2
---        tmp4 = (c t4 0 0 2 1 + c t5 1 0 0 2) / 2
---        tmp5 = (c t4 0 0 2 1 + c t5 0 1 2 0) / 2
---        tmp6 = (c t4 0 0 2 1 + c t5 1 0 2 0) / 2
---        tmp7 = (c t4 0 0 2 1 + c t5 1 2 0 0) / 2
---        tmp8 = (c t4 0 0 2 1 + c t5 0 0 2 1) / 2
---        tmp9 = (c t4 0 0 2 1 + c t5 0 2 0 1) / 2
---        tmp10 = (c t4 0 0 2 1 + c t5 2 0 0 1) / 2
---        tmp11 = (c t4 0 0 2 1 + c t5 0 2 1 0) / 2
---        tmp12 = (c t4 0 0 2 1 + c t5 2 0 1 0) / 2
---        tmp13 = (c t4 0 0 2 1 + c t5 2 1 0 0) / 2
+prop_c0120_identity5 :: Cube -> Bool
+prop_c0120_identity5 cube =
+    c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
+    where
+      t4 = tetrahedron4 cube
+      t5 = tetrahedron5 cube
 
 -- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 -- --   'prop_c0120_identity1' with tetrahedrons 5 and 6.
--- prop_c0120_identity5 :: Cube -> Bool
--- prop_c0120_identity5 cube =
---    c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t6 0 0 1 2) / 2
---      where
---        t5 = tetrahedron5 cube
---        t6 = tetrahedron6 cube
+prop_c0120_identity6 :: Cube -> Bool
+prop_c0120_identity6 cube =
+   c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
+     where
+       t5 = tetrahedron5 cube
+       t6 = tetrahedron6 cube
 
 
 -- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 -- --   'prop_c0120_identity1' with tetrahedrons 6 and 7.
--- prop_c0120_identity6 :: Cube -> Bool
--- prop_c0120_identity6 cube =
---    c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t7 0 0 1 2) / 2
---      where
---        t6 = tetrahedron6 cube
---        t7 = tetrahedron7 cube
+prop_c0120_identity7 :: Cube -> Bool
+prop_c0120_identity7 cube =
+   c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
+     where
+       t6 = tetrahedron6 cube
+       t7 = tetrahedron7 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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
+    c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
       where
         t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t3 = tetrahedron3 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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 1 0) / 2
+    c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
       where
         t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t3 = tetrahedron3 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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
+    c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
       where
         t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t3 = tetrahedron3 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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 1 0) / 2
+    c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
       where
         t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t3 = tetrahedron3 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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 1 0) / 2
+    c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
       where
         t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t3 = tetrahedron3 cube
 
 
 
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). It appears that
---   the assumptions in sections (2.6) and (2.7) have been
---   switched. From the description, one would expect 'tetrahedron0'
---   and 'tetrahedron1' to share face \<v0,v1,v3\>; however, we have
---   to use 'tetrahedron0' and 'tetahedron3' for all of the tests in
---   section (2.7). Also note that the third and fourth indices of
---   c-t3 have been switched. This is because we store the triangles
---   oriented such that their volume is positive. If T and T-tilde
---   share \<v0,v1,v2\> and v3,v3-tilde point in opposite directions,
---   one of them has to have negative volume!
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). Note that the
+--   third and fourth indices of c-t3 have been switched. This is
+--   because we store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
+--   point in opposite directions, one of them has to have negative
+--   volume!
 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 2 1) / 2
+    c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
       where
         t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t1 = tetrahedron1 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 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
+    c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
       where
         t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t1 = tetrahedron1 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 prop_c0300_identity2 :: Cube -> Bool
 prop_c0300_identity2 cube =
-    c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t3 0 2 0 1) / 2
+    c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
       where
         t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t1 = tetrahedron1 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 prop_c1101_identity :: Cube -> Bool
 prop_c1101_identity cube =
-    c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+    c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
       where
         t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t1 = tetrahedron1 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 prop_c1200_identity2 :: Cube -> Bool
 prop_c1200_identity2 cube =
-    c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t3 1 1 0 1) / 2
+    c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
       where
         t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t1 = tetrahedron1 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 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 0 1) / 2
+    c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
       where
         t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t1 = tetrahedron1 cube
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
@@ -692,20 +320,19 @@ prop_c1011_identity cube =
 
 
 -- | 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 cube
---         t1 = tetrahedron1 cube
-
+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 cube
+        t1 = tetrahedron1 cube
 
 
 -- | The function values at the interior should be the same for all tetrahedra.
@@ -715,30 +342,30 @@ prop_interior_values_all_identical cube =
                i9, i10, i11, i12, i13, i14, i15, i16,
                i17, i18, i19, i20, i21, i22, i23]
     where
-      i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) $ I
-      i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) $ I
-      i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) $ I
-      i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) $ I
-      i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) $ I
-      i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) $ I
-      i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) $ I
-      i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) $ I
-      i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) $ I
-      i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) $ I
-      i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) $ I
-      i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) $ I
-      i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) $ I
-      i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) $ I
-      i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) $ I
-      i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) $ I
-      i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) $ I
-      i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) $ I
-      i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) $ I
-      i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) $ I
-      i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) $ I
-      i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) $ I
-      i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) $ I
-      i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) $ I
+      i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) I
+      i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) I
+      i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) I
+      i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) I
+      i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) I
+      i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) I
+      i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) I
+      i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) I
+      i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) I
+      i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) I
+      i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) I
+      i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) I
+      i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) I
+      i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) I
+      i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) I
+      i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) I
+      i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) I
+      i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) I
+      i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) I
+      i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) I
+      i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) I
+      i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) I
+      i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) I
+      i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) I
 
 
 -- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
@@ -784,25 +411,35 @@ prop_c_tilde_2100_correct cube =
       t0 = tetrahedron0 cube
       t6 = tetrahedron6 cube
       fvs = Tetrahedron.fv t0
-      int = interior fvs
-      f = front fvs
-      r = right fvs
-      l = left fvs
-      b = back fvs
-      ft = front_top fvs
-      rt = right_top fvs
-      lt = left_top fvs
-      bt = back_top fvs
-      t = top fvs
-      d = down fvs
-      fr = front_right fvs
-      fl = front_left fvs
-      br = back_right fvs
-      bl = back_left fvs
-      fd = front_down fvs
-      rd = right_down fvs
-      ld = left_down fvs
-      bd = back_down fvs
+      (Cube _ i j k _ _) = cube
+      f  = value_at fvs (i-1) j k
+      b  = value_at fvs (i+1) j k
+      l  = value_at fvs i (j-1) k
+      r  = value_at fvs i (j+1) k
+      d  = value_at fvs i j (k-1)
+      t  = value_at fvs i j (k+1)
+      fl = value_at fvs (i-1) (j-1) k
+      fr = value_at fvs (i-1) (j+1) k
+      fd = value_at fvs (i-1) j (k-1)
+      ft = value_at fvs (i-1) j (k+1)
+      bl = value_at fvs (i+1) (j-1) k
+      br = value_at fvs (i+1) (j+1) k
+      bd = value_at fvs (i+1) j (k-1)
+      bt = value_at fvs (i+1) j (k+1)
+      ld = value_at fvs i (j-1) (k-1)
+      lt = value_at fvs i (j-1) (k+1)
+      rd = value_at fvs i (j+1) (k-1)
+      rt = value_at fvs i (j+1) (k+1)
+      fld = value_at fvs (i-1) (j-1) (k-1)
+      flt = value_at fvs (i-1) (j-1) (k+1)
+      frd = value_at fvs (i-1) (j+1) (k-1)
+      frt = value_at fvs (i-1) (j+1) (k+1)
+      bld = value_at fvs (i+1) (j-1) (k-1)
+      blt = value_at fvs (i+1) (j-1) (k+1)
+      brd = value_at fvs (i+1) (j+1) (k-1)
+      brt = value_at fvs (i+1) (j+1) (k+1)
+      int = value_at fvs i j k
+
 
 -- Tests to check that the correct edges are incidental.
 prop_t0_shares_edge_with_t1 :: Cube -> Bool