import Comparisons
import Cube hiding (i, j, k)
import FunctionValues
-import Misc (all_equal)
+import Misc (all_equal, disjoint)
import Tests.FunctionValues ()
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.
t1 = head $ tail (tetrahedra cube)
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron0_volumes_positive :: Cube -> Bool
-prop_tetrahedron0_volumes_positive cube =
- volume (tetrahedron0 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron1_volumes_positive :: Cube -> Bool
-prop_tetrahedron1_volumes_positive cube =
- volume (tetrahedron1 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron2_volumes_positive :: Cube -> Bool
-prop_tetrahedron2_volumes_positive cube =
- volume (tetrahedron2 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron3_volumes_positive :: Cube -> Bool
-prop_tetrahedron3_volumes_positive cube =
- volume (tetrahedron3 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron4_volumes_positive :: Cube -> Bool
-prop_tetrahedron4_volumes_positive cube =
- volume (tetrahedron4 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron5_volumes_positive :: Cube -> Bool
-prop_tetrahedron5_volumes_positive cube =
- volume (tetrahedron5 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron6_volumes_positive :: Cube -> Bool
-prop_tetrahedron6_volumes_positive cube =
- volume (tetrahedron6 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron7_volumes_positive :: Cube -> Bool
-prop_tetrahedron7_volumes_positive cube =
- volume (tetrahedron7 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron8_volumes_positive :: Cube -> Bool
-prop_tetrahedron8_volumes_positive cube =
- volume (tetrahedron8 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron9_volumes_positive :: Cube -> Bool
-prop_tetrahedron9_volumes_positive cube =
- volume (tetrahedron9 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron10_volumes_positive :: Cube -> Bool
-prop_tetrahedron10_volumes_positive cube =
- volume (tetrahedron10 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron11_volumes_positive :: Cube -> Bool
-prop_tetrahedron11_volumes_positive cube =
- volume (tetrahedron11 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron12_volumes_positive :: Cube -> Bool
-prop_tetrahedron12_volumes_positive cube =
- volume (tetrahedron12 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron13_volumes_positive :: Cube -> Bool
-prop_tetrahedron13_volumes_positive cube =
- volume (tetrahedron13 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron14_volumes_positive :: Cube -> Bool
-prop_tetrahedron14_volumes_positive cube =
- volume (tetrahedron14 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron15_volumes_positive :: Cube -> Bool
-prop_tetrahedron15_volumes_positive cube =
- volume (tetrahedron15 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron16_volumes_positive :: Cube -> Bool
-prop_tetrahedron16_volumes_positive cube =
- volume (tetrahedron16 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron17_volumes_positive :: Cube -> Bool
-prop_tetrahedron17_volumes_positive cube =
- volume (tetrahedron17 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron18_volumes_positive :: Cube -> Bool
-prop_tetrahedron18_volumes_positive cube =
- volume (tetrahedron18 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron19_volumes_positive :: Cube -> Bool
-prop_tetrahedron19_volumes_positive cube =
- volume (tetrahedron19 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron20_volumes_positive :: Cube -> Bool
-prop_tetrahedron20_volumes_positive cube =
- volume (tetrahedron20 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron21_volumes_positive :: Cube -> Bool
-prop_tetrahedron21_volumes_positive cube =
- volume (tetrahedron21 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron22_volumes_positive :: Cube -> Bool
-prop_tetrahedron22_volumes_positive cube =
- volume (tetrahedron22 cube) > 0
-
--- | This pretty much repeats the prop_all_volumes_positive property,
--- but will let me know which tetrahedrons's vertices are disoriented.
-prop_tetrahedron23_volumes_positive :: Cube -> Bool
-prop_tetrahedron23_volumes_positive cube =
- volume (tetrahedron23 cube) > 0
-
-
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). 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