X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=17ea7f8857ee6e0a1bc9f079a7a19b7d8509fe57;hb=1f20ae355d28b53fc2e1e31c4bd131e9ede00a87;hp=78e8e1a82c8a74411880b466c22d9d3007c15538;hpb=f6d0c289ad3397cf392976c24f3afdb17da5d377;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index 78e8e1a..17ea7f8 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -7,15 +7,34 @@ import Cardinal
 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.
@@ -30,217 +49,9 @@ prop_all_volumes_positive 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_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
 
@@ -252,151 +63,6 @@ prop_v0_all_equal cube = (v0 t0) == (v0 t1)
       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
@@ -745,25 +411,35 @@ prop_c_tilde_2100_correct cube =
       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