X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FFace.hs;h=f9de1e7c6f6e8dde049693d08f5d264148d1662c;hb=25c8b387c4b655751265605bd4af033698624f38;hp=14d000b5130bed57d3150d1556d93b4eadc218a0;hpb=7d6bba8440f4327de6272e5c513959425f841c5d;p=spline3.git

diff --git a/src/Tests/Face.hs b/src/Tests/Face.hs
index 14d000b..f9de1e7 100644
--- a/src/Tests/Face.hs
+++ b/src/Tests/Face.hs
@@ -3,17 +3,290 @@ where
 
 import Test.QuickCheck
 
-import Cube (Cube(grid))
-import Face (tetrahedrons)
+import Comparisons
+import Cube (Cube(grid), top)
+import Face (face0,
+             face2,
+             face5,
+             tetrahedron0,
+             tetrahedron1,
+             tetrahedron2,
+             tetrahedron3,
+             tetrahedrons)
 import Grid (Grid(h))
-import Tetrahedron (volume)
+import Tetrahedron
 
 -- QuickCheck Tests.
-prop_all_volumes_nonnegative :: Cube -> Property
-prop_all_volumes_nonnegative c =
-    (delta > 0) ==> (null negative_volumes)
+
+-- | 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
-      negative_volumes = filter (< 0) volumes
+      nonpositive_volumes = filter (<= 0) volumes
+
+
+-- | 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)