-- | 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 =
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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
-- | 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 =
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 =
-- where
-- t0 = tetrahedron0 cube
-- t1 = tetrahedron1 cube
+
+
+-- 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
projects / spline3.git / blobdiff