X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=6170d36d612bb7048ad99c356860f20f5052a4c7;hb=9712b55ab9a0672a5edc95cb4943d9ffca145c29;hp=742360f5d799993f47ce2cb38adf3f3cfc46ae6f;hpb=3b111f8df1bde25f32f3d5378844cbcf34404015;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index 742360f..6170d36 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -10,14 +10,17 @@ module Grid (
   )
 where
 
-import Data.Array (Array, array, (!))
 import qualified Data.Array.Repa as R
 import Test.HUnit
 import Test.Framework (Test, testGroup)
 import Test.Framework.Providers.HUnit (testCase)
 import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
-
+import Test.QuickCheck ((==>),
+                        Arbitrary(..),
+                        Gen,
+                        Positive(..),
+                        Property,
+                        choose)
 import Assertions
 import Comparisons
 import Cube (Cube(Cube),
@@ -33,16 +36,12 @@ import ThreeDimensional
 import Values (Values3D, dims, empty3d, zoom_shape)
 
 
-type CubeGrid = Array (Int,Int,Int) Cube
-
-
 -- | Our problem is defined on a Grid. The grid size is given by the
 --   positive number h. The function values are the values of the
 --   function at the grid points, which are distance h from one
 --   another in each direction (x,y,z).
 data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
-                   function_values :: Values3D,
-                   cube_grid :: CubeGrid }
+                   function_values :: Values3D }
           deriving (Eq, Show)
 
 
@@ -58,28 +57,8 @@ instance Arbitrary Grid where
 make_grid :: Double -> Values3D -> Grid
 make_grid grid_size values
     | grid_size <= 0 = error "grid size must be positive"
-    | otherwise = Grid grid_size values (cubes grid_size values)
-
-
--- | Returns a three-dimensional array of cubes centered on the grid
---   points (h*i, h*j, h*k) with the appropriate 'FunctionValues'.
-cubes :: Double -> Values3D -> CubeGrid
-cubes delta fvs 
-  = array (lbounds, ubounds)
-           [ ((i,j,k), cube_ijk)
-                 | i <- [0..xmax],
-                   j <- [0..ymax],
-                   k <- [0..zmax],
-                   let tet_vol = (1/24)*(delta^(3::Int)),
-                   let cube_ijk =
-                         Cube delta i j k (make_values fvs i j k) tet_vol]
-     where
-       xmax = xsize - 1
-       ymax = ysize - 1
-       zmax = zsize - 1
-       lbounds = (0, 0, 0)
-       ubounds = (xmax, ymax, zmax)
-       (xsize, ysize, zsize) = dims fvs
+    | otherwise = Grid grid_size values
+
 
 
 -- | Takes a grid and a position as an argument and returns the cube
@@ -93,10 +72,13 @@ cube_at g i j k
     | j >= ysize = error "j >= ysize in cube_at"
     | k < 0      = error "k < 0 in cube_at"
     | k >= zsize = error "k >= zsize in cube_at"
-    | otherwise = (cube_grid g) ! (i,j,k)
+    | otherwise = Cube delta i j k fvs' tet_vol
       where
         fvs = function_values g
         (xsize, ysize, zsize) = dims fvs
+        fvs' = make_values fvs i j k
+        delta = h g
+        tet_vol = (1/24)*(delta^(3::Int))
 
 --   The first cube along any axis covers (-h/2, h/2). The second
 --   covers (h/2, 3h/2).  The third, (3h/2, 5h/2), and so on.
@@ -131,17 +113,16 @@ find_containing_cube g p =
       k = calculate_containing_cube_coordinate g z
 
 
-{-# INLINE zoom_lookup #-}
-zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
-zoom_lookup g scale_factor _ =
-    zoom_result g scale_factor
+zoom_lookup :: Values3D -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup v3d scale_factor _ =
+    zoom_result v3d scale_factor
 
 
-{-# INLINE zoom_result #-}
-zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
-zoom_result g (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
+zoom_result :: Values3D -> ScaleFactor -> R.DIM3 -> Double
+zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
   f p
   where
+    g = make_grid 1 v3d
     offset = (h g)/2
     m' = (fromIntegral m) / (fromIntegral sfx) - offset
     n' = (fromIntegral n) / (fromIntegral sfy) - offset
@@ -150,18 +131,17 @@ zoom_result g (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
     cube = find_containing_cube g p
     t = find_containing_tetrahedron cube p
     f = polynomial t
-    
-zoom :: Grid -> ScaleFactor -> Values3D
-zoom g scale_factor
+
+
+zoom :: Values3D -> ScaleFactor -> Values3D
+zoom v3d scale_factor
     | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
     | otherwise =
-        R.force $ R.unsafeTraverse arr transExtent (zoom_lookup g scale_factor)
+        R.force $ R.unsafeTraverse v3d transExtent f
           where
-            arr = function_values g
-            (xsize, ysize, zsize) = dims arr
+            (xsize, ysize, zsize) = dims v3d
             transExtent = zoom_shape scale_factor
-
-
+            f = zoom_lookup v3d scale_factor
 
 
 -- | Check all coefficients of tetrahedron0 belonging to the cube
@@ -404,11 +384,117 @@ prop_cube_indices_never_go_out_of_bounds g =
       idx_z <= zsize - 1
 
 
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). Note that the
+--   third and fourth indices of c-t10 have been switched. This is
+--   because we store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share \<v1,v2,v3\> and v0,v0-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0120_identity :: Grid -> Property
+prop_c0120_identity g =
+  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+    c t0 0 1 2 0 ~= (c t0 1 0 2 0 + c t10 1 0 0 2) / 2
+  where
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    cube0 = cube_at g 1 1 1
+    cube1 = cube_at g 0 1 1
+    t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+    t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+--   'prop_c0120_identity'.
+prop_c0111_identity :: Grid -> Property
+prop_c0111_identity g =
+  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+    c t0 0 1 1 1 ~= (c t0 1 0 1 1 + c t10 1 0 1 1) / 2
+  where
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    cube0 = cube_at g 1 1 1
+    cube1 = cube_at g 0 1 1
+    t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+    t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+--   'prop_c0120_identity'.
+prop_c0201_identity :: Grid -> Property
+prop_c0201_identity g =
+  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+    c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t10 1 1 1 0) / 2
+  where
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    cube0 = cube_at g 1 1 1
+    cube1 = cube_at g 0 1 1
+    t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+    t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+--   'prop_c0120_identity'.
+prop_c0102_identity :: Grid -> Property
+prop_c0102_identity g =
+  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+    c t0 0 1 0 2 ~= (c t0 1 0 0 2 + c t10 1 0 2 0) / 2
+  where
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    cube0 = cube_at g 1 1 1
+    cube1 = cube_at g 0 1 1
+    t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+    t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+--   'prop_c0120_identity'.
+prop_c0210_identity :: Grid -> Property
+prop_c0210_identity g =
+  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+    c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t10 1 1 0 1) / 2
+  where
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    cube0 = cube_at g 1 1 1
+    cube1 = cube_at g 0 1 1
+    t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+    t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+--   'prop_c0120_identity'.
+prop_c0300_identity :: Grid -> Property
+prop_c0300_identity g =
+  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+    c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t10 1 2 0 0) / 2
+  where
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    cube0 = cube_at g 1 1 1
+    cube1 = cube_at g 0 1 1
+    t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+    t10 = tetrahedron cube1 10
+
+
+-- | All of the properties from Section (2.9), p. 80. These require a
+--   grid since they refer to two adjacent cubes.
+p80_29_properties :: Test.Framework.Test
+p80_29_properties =
+  testGroup "p. 80, Section (2.9) Properties" [
+    testProperty "c0120 identity" prop_c0120_identity,
+    testProperty "c0111 identity" prop_c0111_identity,
+    testProperty "c0201 identity" prop_c0201_identity,
+    testProperty "c0102 identity" prop_c0102_identity,
+    testProperty "c0210 identity" prop_c0210_identity,
+    testProperty "c0300 identity" prop_c0300_identity ]
+
 
 grid_tests :: Test.Framework.Test
 grid_tests =
     testGroup "Grid Tests" [
       trilinear_c0_t0_tests,
+      p80_29_properties,
       testCase "tetrahedra collision test isn't too sensitive"
          test_tetrahedra_collision_sensitivity,
       testCase "trilinear reproduced" test_trilinear_reproduced,