import Comparisons
import Cube hiding (i, j, k)
import FunctionValues
-import Misc (all_equal)
-import Tests.FunctionValues ()
+import Misc (all_equal, disjoint)
import Tetrahedron (b0, b1, b2, b3, c, fv,
v0, v1, v2, v3, volume)
-
-- Quickcheck tests.
+-- | The 'front_half_tetrahedra' and 'back_half_tetrahedra' should
+-- have no tetrahedra in common.
+prop_front_back_tetrahedra_disjoint :: Cube -> Bool
+prop_front_back_tetrahedra_disjoint c =
+ disjoint (front_half_tetrahedra c) (back_half_tetrahedra c)
+
+
+-- | The 'top_half_tetrahedra' and 'down_half_tetrahedra' should
+-- have no tetrahedra in common.
+prop_top_down_tetrahedra_disjoint :: Cube -> Bool
+prop_top_down_tetrahedra_disjoint c =
+ disjoint (top_half_tetrahedra c) (down_half_tetrahedra c)
+
+
+-- | The 'left_half_tetrahedra' and 'right_half_tetrahedra' should
+-- have no tetrahedra in common.
+prop_left_right_tetrahedra_disjoint :: Cube -> Bool
+prop_left_right_tetrahedra_disjoint c =
+ disjoint (left_half_tetrahedra c) (right_half_tetrahedra c)
+
+
-- | Since the grid size is necessarily positive, all tetrahedra
-- (which comprise cubes of positive volume) must have positive volume
-- as well.
(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.
+-- | 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.
+--
+-- If 'prop_c_tilde_2100_rotation_correct' passes, then this test is
+-- even meaningful!
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)
+ c t6 2 1 0 0 == expected
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
+ expected = eval fvs $
+ (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)
+
-- Tests to check that the correct edges are incidental.
prop_t0_shares_edge_with_t1 :: Cube -> Bool