X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=666fde8899c168f85b061430ce06f5ee3ca93e1f;hb=5109e41113a39024ef3fe799abb08de4a2ac74b0;hp=5485046ec46b934cc423bb9dedb0054eab9d289b;hpb=01925d099b231a128f6bd51abd61bf9ff9c424b6;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index 5485046..666fde8 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -7,7 +7,9 @@ import Comparisons
 import Cube
 import FunctionValues (FunctionValues)
 import Tests.FunctionValues ()
-import Tetrahedron (v0, volume)
+import Tetrahedron (b0, b1, b2, b3, c,
+                    Tetrahedron(Tetrahedron),
+                    v0, v1, v2, v3, volume)
 
 instance Arbitrary Cube where
     arbitrary = do
@@ -258,3 +260,98 @@ prop_tetrahedron22_volumes_positive c =
 prop_tetrahedron23_volumes_positive :: Cube -> Bool
 prop_tetrahedron23_volumes_positive c =
     volume (tetrahedron23 c) > 0
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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_c0120_identity1 :: Cube -> Bool
+prop_c0120_identity1 cube =
+   c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
+     where
+       t0 = tetrahedron0 cube
+       t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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_c0210_identity1 :: Cube -> Bool
+prop_c0210_identity1 cube =
+    c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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_c0300_identity1 :: Cube -> Bool
+prop_c0300_identity1 cube =
+    c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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_c1110_identity :: Cube -> Bool
+prop_c1110_identity cube =
+    c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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_c1200_identity1 :: Cube -> Bool
+prop_c1200_identity1 cube =
+    c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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_c2100_identity1 :: Cube -> Bool
+prop_c2100_identity1 cube =
+    c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 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