module Tests.Cube
where
+import Prelude hiding (LT)
import Test.QuickCheck
+import Cardinal
import Comparisons
import Cube
-import FunctionValues (FunctionValues)
+import FunctionValues
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
-- | 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 =
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.
-- where
-- t0 = tetrahedron0 cube
-- t1 = tetrahedron1 cube
+
+
+
+-- | 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
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