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.
--- | Since the grid size is necessarily positive, all tetrahedrons
+-- | 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.
prop_all_volumes_positive :: Cube -> Bool
prop_all_volumes_positive cube =
null nonpositive_volumes
where
- ts = tetrahedrons cube
+ ts = tetrahedra cube
volumes = map volume ts
nonpositive_volumes = filter (<= 0) volumes
-- | In fact, since all of the tetrahedra are identical, we should
-- already know their volumes. There's 24 tetrahedra to a cube, so
-- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron0_volumes_exact :: Cube -> Bool
-prop_tetrahedron0_volumes_exact cube =
- volume (tetrahedron0 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron1_volumes_exact :: Cube -> Bool
-prop_tetrahedron1_volumes_exact cube =
- volume (tetrahedron1 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron2_volumes_exact :: Cube -> Bool
-prop_tetrahedron2_volumes_exact cube =
- volume (tetrahedron2 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron3_volumes_exact :: Cube -> Bool
-prop_tetrahedron3_volumes_exact cube =
- volume (tetrahedron3 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron4_volumes_exact :: Cube -> Bool
-prop_tetrahedron4_volumes_exact cube =
- volume (tetrahedron4 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron5_volumes_exact :: Cube -> Bool
-prop_tetrahedron5_volumes_exact cube =
- volume (tetrahedron5 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron6_volumes_exact :: Cube -> Bool
-prop_tetrahedron6_volumes_exact cube =
- volume (tetrahedron6 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron7_volumes_exact :: Cube -> Bool
-prop_tetrahedron7_volumes_exact cube =
- volume (tetrahedron7 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron8_volumes_exact :: Cube -> Bool
-prop_tetrahedron8_volumes_exact cube =
- volume (tetrahedron8 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron9_volumes_exact :: Cube -> Bool
-prop_tetrahedron9_volumes_exact cube =
- volume (tetrahedron9 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron10_volumes_exact :: Cube -> Bool
-prop_tetrahedron10_volumes_exact cube =
- volume (tetrahedron10 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron11_volumes_exact :: Cube -> Bool
-prop_tetrahedron11_volumes_exact cube =
- volume (tetrahedron11 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron12_volumes_exact :: Cube -> Bool
-prop_tetrahedron12_volumes_exact cube =
- volume (tetrahedron12 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron13_volumes_exact :: Cube -> Bool
-prop_tetrahedron13_volumes_exact cube =
- volume (tetrahedron13 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron14_volumes_exact :: Cube -> Bool
-prop_tetrahedron14_volumes_exact cube =
- volume (tetrahedron14 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron15_volumes_exact :: Cube -> Bool
-prop_tetrahedron15_volumes_exact cube =
- volume (tetrahedron15 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron16_volumes_exact :: Cube -> Bool
-prop_tetrahedron16_volumes_exact cube =
- volume (tetrahedron16 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron17_volumes_exact :: Cube -> Bool
-prop_tetrahedron17_volumes_exact cube =
- volume (tetrahedron17 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron18_volumes_exact :: Cube -> Bool
-prop_tetrahedron18_volumes_exact cube =
- volume (tetrahedron18 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron19_volumes_exact :: Cube -> Bool
-prop_tetrahedron19_volumes_exact cube =
- volume (tetrahedron19 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron20_volumes_exact :: Cube -> Bool
-prop_tetrahedron20_volumes_exact cube =
- volume (tetrahedron20 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron21_volumes_exact :: Cube -> Bool
-prop_tetrahedron21_volumes_exact cube =
- volume (tetrahedron21 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron22_volumes_exact :: Cube -> Bool
-prop_tetrahedron22_volumes_exact cube =
- volume (tetrahedron22 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron23_volumes_exact :: Cube -> Bool
-prop_tetrahedron23_volumes_exact cube =
- volume (tetrahedron23 cube) ~~= (1/24)*(delta^(3::Int))
+prop_all_volumes_exact :: Cube -> Bool
+prop_all_volumes_exact cube =
+ and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
where
delta = h cube
prop_v0_all_equal :: Cube -> Bool
prop_v0_all_equal cube = (v0 t0) == (v0 t1)
where
- t0 = head (tetrahedrons cube) -- Doesn't matter which two we choose.
- t1 = head $ tail (tetrahedrons 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
+ t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
+ t1 = head $ tail (tetrahedra cube)
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
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
+ (Cube _ i j k _ _) = cube
+ f = value_at fvs (i-1) j k
+ b = value_at fvs (i+1) j k
+ l = value_at fvs i (j-1) k
+ r = value_at fvs i (j+1) k
+ d = value_at fvs i j (k-1)
+ t = value_at fvs i j (k+1)
+ fl = value_at fvs (i-1) (j-1) k
+ fr = value_at fvs (i-1) (j+1) k
+ fd = value_at fvs (i-1) j (k-1)
+ ft = value_at fvs (i-1) j (k+1)
+ bl = value_at fvs (i+1) (j-1) k
+ br = value_at fvs (i+1) (j+1) k
+ bd = value_at fvs (i+1) j (k-1)
+ bt = value_at fvs (i+1) j (k+1)
+ ld = value_at fvs i (j-1) (k-1)
+ lt = value_at fvs i (j-1) (k+1)
+ rd = value_at fvs i (j+1) (k-1)
+ rt = value_at fvs i (j+1) (k+1)
+ fld = value_at fvs (i-1) (j-1) (k-1)
+ flt = value_at fvs (i-1) (j-1) (k+1)
+ frd = value_at fvs (i-1) (j+1) (k-1)
+ frt = value_at fvs (i-1) (j+1) (k+1)
+ bld = value_at fvs (i+1) (j-1) (k-1)
+ blt = value_at fvs (i+1) (j-1) (k+1)
+ brd = value_at fvs (i+1) (j+1) (k-1)
+ brt = value_at fvs (i+1) (j+1) (k+1)
+ int = value_at fvs i j k
+
-- Tests to check that the correct edges are incidental.
prop_t0_shares_edge_with_t1 :: Cube -> Bool
projects / spline3.git / blobdiff