X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=dac4f80749f019b0f76dd2f29e77b235eeeea82e;hb=6753d25156abb39ec68b715782b49f525e70b991;hp=11159b5bc6f668a6e14f0976646c5e50398d1236;hpb=f07f76b231a3df623aab8b6035ac6000ce2a5eb2;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index 11159b5..dac4f80 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -1,13 +1,16 @@
 module Tests.Cube
 where
 
+import Prelude hiding (LT)
 import Test.QuickCheck
 
+import Cardinal
 import Comparisons
 import Cube
-import FunctionValues (FunctionValues)
+import FunctionValues
+import Misc (all_equal)
 import Tests.FunctionValues ()
-import Tetrahedron (b0, b1, b2, b3, c,
+import Tetrahedron (b0, b1, b2, b3, c, fv,
                     v0, v1, v2, v3, volume)
 
 instance Arbitrary Cube where
@@ -264,7 +267,7 @@ prop_tetrahedron23_volumes_positive 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
+--   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 =
@@ -274,10 +277,59 @@ prop_c0120_identity1 cube =
        t3 = tetrahedron3 cube
 
 
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+--   prop_c0120_identity2 with tetrahedrons 3 and 2.
+prop_c0120_identity2 :: Cube -> Bool
+prop_c0120_identity2 cube =
+   c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
+     where
+       t3 = tetrahedron3 cube
+       t2 = tetrahedron2 cube
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+--   prop_c0120_identity1 with tetrahedrons 2 and 1.
+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
+       t2 = tetrahedron2 cube
+       t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+--   prop_c0120_identity1 with tetrahedrons 4 and 7.
+prop_c0120_identity4 :: Cube -> Bool
+prop_c0120_identity4 cube =
+   c t4 0 1 2 0 ~= (c t4 0 0 2 1 + c t7 0 0 1 2) / 2
+     where
+       t4 = tetrahedron4 cube
+       t7 = tetrahedron7 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+--   prop_c0120_identity1 with tetrahedrons 7 and 6.
+prop_c0120_identity5 :: Cube -> Bool
+prop_c0120_identity5 cube =
+   c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
+     where
+       t7 = tetrahedron7 cube
+       t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+--   prop_c0120_identity1 with tetrahedrons 6 and 5.
+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
+       t6 = tetrahedron6 cube
+       t5 = tetrahedron5 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
+--   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 =
@@ -290,7 +342,7 @@ prop_c0210_identity1 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
+--   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 =
@@ -303,7 +355,7 @@ prop_c0300_identity1 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
+--   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 =
@@ -316,7 +368,7 @@ prop_c1110_identity 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
+--   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 =
@@ -329,7 +381,7 @@ prop_c1200_identity1 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
+--   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 =
@@ -343,7 +395,7 @@ prop_c2100_identity1 cube =
 -- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+--   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 --   in opposite directions, one of them has to have negative volume!
 prop_c0102_identity1 :: Cube -> Bool
 prop_c0102_identity1 cube =
@@ -356,7 +408,7 @@ prop_c0102_identity1 cube =
 -- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+--   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 --   in opposite directions, one of them has to have negative volume!
 prop_c0201_identity1 :: Cube -> Bool
 prop_c0201_identity1 cube =
@@ -369,7 +421,7 @@ prop_c0201_identity1 cube =
 -- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+--   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 --   in opposite directions, one of them has to have negative volume!
 prop_c0300_identity2 :: Cube -> Bool
 prop_c0300_identity2 cube =
@@ -382,7 +434,7 @@ prop_c0300_identity2 cube =
 -- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+--   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 --   in opposite directions, one of them has to have negative volume!
 prop_c1101_identity :: Cube -> Bool
 prop_c1101_identity cube =
@@ -395,7 +447,7 @@ prop_c1101_identity cube =
 -- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+--   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 --   in opposite directions, one of them has to have negative volume!
 prop_c1200_identity2 :: Cube -> Bool
 prop_c1200_identity2 cube =
@@ -408,7 +460,7 @@ prop_c1200_identity2 cube =
 -- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+--   positive. If T and T-tilde share \<v0,v1,v3\> and v2,v2-tilde point
 --   in opposite directions, one of them has to have negative volume!
 prop_c2100_identity2 :: Cube -> Bool
 prop_c2100_identity2 cube =
@@ -418,21 +470,13 @@ prop_c2100_identity2 cube =
         t1 = tetrahedron1 cube
 
 
-prop_t0_shares_edge_with_t6 :: Cube -> Bool
-prop_t0_shares_edge_with_t6 cube =
-    (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
-      where
-        t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
-
-
 -- | 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 t6 2 1 0 0 - ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
       where
         t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
+        t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79.
@@ -494,3 +538,205 @@ prop_c1011_identity cube =
 --       where
 --         t0 = tetrahedron0 cube
 --         t1 = tetrahedron1 cube
+
+
+
+-- | The function values at the interior should be the same for all tetrahedra.
+prop_interior_values_all_identical :: Cube -> Bool
+prop_interior_values_all_identical cube =
+    all_equal [i0, i1, i2, i3, i4, i5, i6, i7, i8,
+               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
+
+
+-- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
+--   This test checks the rotation works as expected.
+prop_c_tilde_2100_rotation_correct :: Cube -> Bool
+prop_c_tilde_2100_rotation_correct cube =
+    expr1 == expr2
+    where
+      t0 = tetrahedron0 cube
+      t6 = tetrahedron6 cube
+
+      -- What gets computed for c2100 of t6.
+      expr1 = eval (Tetrahedron.fv t6) $
+          (3/8)*I +
+          (1/12)*(T + R + L + D) +
+          (1/64)*(FT + FR + FL + FD) +
+          (7/48)*F +
+          (1/48)*B +
+          (1/96)*(RT + LD + LT + RD) +
+          (1/192)*(BT + BR + BL + BD)
+
+      -- What should be computed for c2100 of t6.
+      expr2 = eval (Tetrahedron.fv t0) $
+              (3/8)*I +
+              (1/12)*(F + R + L + B) +
+              (1/64)*(FT + RT + LT + BT) +
+              (7/48)*T +
+              (1/48)*D +
+              (1/96)*(FR + FL + BR + BL) +
+              (1/192)*(FD + RD + LD + BD)
+
+
+-- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
+--   This test checks the actual value based on the FunctionValues of the cube.
+prop_c_tilde_2100_correct :: Cube -> Bool
+prop_c_tilde_2100_correct cube =
+    c t6 2 1 0 0 == (3/8)*int + (1/12)*(f + r + l + b) + (1/64)*(ft + rt + lt + bt)
+                              + (7/48)*t + (1/48)*d + (1/96)*(fr + fl + br + bl)
+                              + (1/192)*(fd + rd + ld + bd)
+    where
+      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
+
+-- Tests to check that the correct edges are incidental.
+prop_t0_shares_edge_with_t1 :: Cube -> Bool
+prop_t0_shares_edge_with_t1 cube =
+    (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+prop_t0_shares_edge_with_t3 :: Cube -> Bool
+prop_t0_shares_edge_with_t3 cube =
+    (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+prop_t0_shares_edge_with_t6 :: Cube -> Bool
+prop_t0_shares_edge_with_t6 cube =
+    (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+prop_t1_shares_edge_with_t2 :: Cube -> Bool
+prop_t1_shares_edge_with_t2 cube =
+    (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
+      where
+        t1 = tetrahedron1 cube
+        t2 = tetrahedron2 cube
+
+prop_t1_shares_edge_with_t19 :: Cube -> Bool
+prop_t1_shares_edge_with_t19 cube =
+    (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
+      where
+        t1 = tetrahedron1 cube
+        t19 = tetrahedron19 cube
+
+prop_t2_shares_edge_with_t3 :: Cube -> Bool
+prop_t2_shares_edge_with_t3 cube =
+    (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
+      where
+        t1 = tetrahedron1 cube
+        t2 = tetrahedron2 cube
+
+prop_t2_shares_edge_with_t12 :: Cube -> Bool
+prop_t2_shares_edge_with_t12 cube =
+    (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
+      where
+        t2 = tetrahedron2 cube
+        t12 = tetrahedron12 cube
+
+prop_t3_shares_edge_with_t21 :: Cube -> Bool
+prop_t3_shares_edge_with_t21 cube =
+    (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
+      where
+        t3 = tetrahedron3 cube
+        t21 = tetrahedron21 cube
+
+prop_t4_shares_edge_with_t5 :: Cube -> Bool
+prop_t4_shares_edge_with_t5 cube =
+    (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
+      where
+        t4 = tetrahedron4 cube
+        t5 = tetrahedron5 cube
+
+prop_t4_shares_edge_with_t7 :: Cube -> Bool
+prop_t4_shares_edge_with_t7 cube =
+    (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
+      where
+        t4 = tetrahedron4 cube
+        t7 = tetrahedron7 cube
+
+prop_t4_shares_edge_with_t10 :: Cube -> Bool
+prop_t4_shares_edge_with_t10 cube =
+    (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
+      where
+        t4 = tetrahedron4 cube
+        t10 = tetrahedron10 cube
+
+prop_t5_shares_edge_with_t6 :: Cube -> Bool
+prop_t5_shares_edge_with_t6 cube =
+    (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
+      where
+        t5 = tetrahedron5 cube
+        t6 = tetrahedron6 cube
+
+prop_t5_shares_edge_with_t16 :: Cube -> Bool
+prop_t5_shares_edge_with_t16 cube =
+    (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
+      where
+        t5 = tetrahedron5 cube
+        t16 = tetrahedron16 cube
+
+prop_t6_shares_edge_with_t7 :: Cube -> Bool
+prop_t6_shares_edge_with_t7 cube =
+    (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
+      where
+        t6 = tetrahedron6 cube
+        t7 = tetrahedron7 cube
+
+prop_t7_shares_edge_with_t20 :: Cube -> Bool
+prop_t7_shares_edge_with_t20 cube =
+    (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
+      where
+        t7 = tetrahedron7 cube
+        t20 = tetrahedron20 cube