X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FFace.hs;h=5e5b4c2b98f2b5c4bc9d2f5003975766ee1f1ac5;hb=2064e9a7da32813c6dce843127e2306b841df353;hp=14d000b5130bed57d3150d1556d93b4eadc218a0;hpb=89b8b6e94fcc944a1f4611811265f3c6217af850;p=spline3.git

diff --git a/src/Tests/Face.hs b/src/Tests/Face.hs
index 14d000b..5e5b4c2 100644
--- a/src/Tests/Face.hs
+++ b/src/Tests/Face.hs
@@ -1,19 +1,251 @@
 module Tests.Face
 where
 
-import Test.QuickCheck
-
-import Cube (Cube(grid))
-import Face (tetrahedrons)
-import Grid (Grid(h))
-import Tetrahedron (volume)
-
--- QuickCheck Tests.
-prop_all_volumes_nonnegative :: Cube -> Property
-prop_all_volumes_nonnegative c =
-    (delta > 0) ==> (null negative_volumes)
-    where
-      delta = h (grid c)
-      ts = tetrahedrons c
-      volumes = map volume ts
-      negative_volumes = filter (< 0) volumes
+-- -- | 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)