X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=d9fa975eedc7498989d601394b7e686c72ff0d41;hb=b2e1c440b9b1bb99ae564d6600230bbd1f7d204c;hp=b8f1d759e1f268a1e71c33cfa5b7dd3dcb58919a;hpb=394aeb5715f666d2fbdc17223d8eb803e4e1171c;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index b8f1d75..d9fa975 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,16 +4,20 @@
 module Grid
 where
 
+import Data.Array (Array, array, (!))
+import qualified Data.Array.Repa as R
 import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
 
-import Cube (Cube(Cube), find_containing_tetrahedra)
+import Cube (Cube(Cube), find_containing_tetrahedron)
 import FunctionValues
-import Misc (flatten)
 import Point (Point)
+import ScaleFactor
 import Tetrahedron (polynomial)
 import Values (Values3D, dims, empty3d, zoom_shape)
 
-import qualified Data.Array.Repa as R
+
+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
@@ -44,50 +48,63 @@ empty_grid :: Grid
 empty_grid = Grid 1 empty3d
 
 
--- | Returns a three-dimensional list of cubes centered on the grid
+-- | Returns a three-dimensional array of cubes centered on the grid
 --   points of g with the appropriate 'FunctionValues'.
-cubes :: Grid -> [[[Cube]]]
+cubes :: Grid -> CubeGrid
 cubes g
-    | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]]
-    | otherwise =
-        [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
-              | j <- [0..ysize]]
-              | k <- [0..zsize]]
-    where
-      fvs = function_values g
-      (xsize, ysize, zsize) = dims fvs
+  = array (lbounds, ubounds)
+           [ ((i,j,k), cube_ijk)
+                 | i <- [0..xmax],
+                   j <- [0..ymax],
+                   k <- [0..zmax],
+                   let delta = h g,
+                   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)
+       fvs = function_values g
+       (xsize, ysize, zsize) = dims fvs
 
 
 -- | Takes a grid and a position as an argument and returns the cube
 --   centered on that position. If there is no cube there (i.e. the
---   position is outside of the grid), it will return 'Nothing'.
-cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube
+--   position is outside of the grid), it will throw an error.
+cube_at :: Grid -> Int -> Int -> Int -> Cube
 cube_at g i j k
-    | i < 0 = Nothing
-    | j < 0 = Nothing
-    | k < 0 = Nothing
-    | i >= length (cubes g) = Nothing
-    | j >= length ((cubes g) !! i) = Nothing
-    | k >= length (((cubes g) !! i) !! j) = Nothing
-    | otherwise = Just $ (((cubes g) !! i) !! j) !! k
-
-
+    | i < 0      = error "i < 0 in cube_at"
+    | i >= xsize = error "i >= xsize in cube_at"
+    | j < 0      = error "j < 0 in cube_at"
+    | 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 = (cubes g) ! (i,j,k)
+      where
+        fvs = function_values g
+        (xsize, ysize, zsize) = dims fvs
 
 --   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.
 --
---   We translate the (x,y,z) coordinates forward by 'h' so that the
+--   We translate the (x,y,z) coordinates forward by 'h/2' so that the
 --   first covers (0, h), the second covers (h, 2h), etc. This makes
 --   it easy to figure out which cube contains the given point.
 calculate_containing_cube_coordinate :: Grid -> Double -> Int
 calculate_containing_cube_coordinate g coord
-    -- Don't use a cube on the boundary if we can help it.
-    | coord == delta && (xsize > 0 && ysize > 0 && zsize > 0) = 1
-    | otherwise = (ceiling ( (coord + delta) / cube_width )) - 1
+    -- Don't use a cube on the boundary if we can help it. This
+    -- returns cube #1 if we would have returned cube #0 and cube #1
+    -- exists.
+    | coord == offset && (xsize > 0 && ysize > 0 && zsize > 0) = 1
+    | coord < offset = 0
+    | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
     where
       (xsize, ysize, zsize) = dims (function_values g)
-      delta = (h g)
-      cube_width = 2 * delta
+      cube_width = (h g)
+      offset = cube_width / 2
 
 
 -- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
@@ -95,9 +112,7 @@ calculate_containing_cube_coordinate g coord
 --   to check every cube.
 find_containing_cube :: Grid -> Point -> Cube
 find_containing_cube g p =
-    case cube_at g i j k of
-      Just c -> c
-      Nothing -> error "No cube contains the given point."
+    cube_at g i j k
     where
       (x, y, z) = p
       i = calculate_containing_cube_coordinate g x
@@ -106,29 +121,29 @@ find_containing_cube g p =
 
 
 {-# INLINE zoom_lookup #-}
-zoom_lookup :: Grid -> a -> (R.DIM3 -> Double)
-zoom_lookup g _ = zoom_result g
+zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup g scale_factor _ = zoom_result g scale_factor
 
 
 {-# INLINE zoom_result #-}
-zoom_result :: Grid -> R.DIM3 -> Double
-zoom_result g (R.Z R.:. i R.:. j R.:. k) =
+zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
+zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
   f p
   where
-    i' = fromIntegral i
-    j' = fromIntegral j
-    k' = fromIntegral k
+    i' = (fromIntegral i) / (fromIntegral sfx)
+    j' = (fromIntegral j) / (fromIntegral sfy)
+    k' = (fromIntegral k) / (fromIntegral sfz)
     p  = (i', j', k') :: Point
     c = find_containing_cube g p
-    t = head (find_containing_tetrahedra c p)
+    t = find_containing_tetrahedron c p
     f = polynomial t
 
 
-zoom :: Grid -> Int -> Values3D
+zoom :: Grid -> ScaleFactor -> Values3D
 zoom g scale_factor
     | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
     | otherwise =
-        R.force $ R.traverse arr transExtent (zoom_lookup g)
+        R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor)
           where
             arr = function_values g
             (xsize, ysize, zsize) = dims arr