X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=8ce2430d186870d7e7322d4bf5ff9e381870273c;hb=ac0e94e82605a5fd1e3ee724cd597f48614689e4;hp=63b2cfa122bc6ba5bbb9d496b77f1a00466eebb6;hpb=46b1f2e3741d6571c2f931371222f8970b6c7f63;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index 63b2cfa..8ce2430 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -8,31 +8,31 @@ import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
 
 import Cube (Cube(Cube), find_containing_tetrahedra)
 import FunctionValues
-import Misc (flatten)
 import Point (Point)
 import Tetrahedron (polynomial)
-import ThreeDimensional (contains_point)
+import Values (Values3D, dims, empty3d, zoom_shape)
 
+import qualified Data.Array.Repa as R
 
 -- | 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 :: [[[Double]]] }
+                   function_values :: Values3D }
           deriving (Eq, Show)
 
 
 instance Arbitrary Grid where
     arbitrary = do
       (Positive h') <- arbitrary :: Gen (Positive Double)
-      fvs <- arbitrary :: Gen [[[Double]]]
+      fvs <- arbitrary :: Gen Values3D
       return (make_grid h' fvs)
 
 
 -- | The constructor that we want people to use. If we're passed a
 --   non-positive grid size, we throw an error.
-make_grid :: Double -> [[[Double]]] -> Grid
+make_grid :: Double -> Values3D -> Grid
 make_grid grid_size values
     | grid_size <= 0 = error "grid size must be positive"
     | otherwise = Grid grid_size values
@@ -40,24 +40,21 @@ make_grid grid_size values
 
 -- | Creates an empty grid with grid size 1.
 empty_grid :: Grid
-empty_grid = Grid 1 [[[]]]
+empty_grid = Grid 1 empty3d
 
 
 -- | Returns a three-dimensional list of cubes centered on the grid
 --   points of g with the appropriate 'FunctionValues'.
 cubes :: Grid -> [[[Cube]]]
 cubes g
-    | fvs == [[[]]] = [[[]]]
-    | head fvs == [[]] = [[[]]]
+    | 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
-      zsize = (length fvs) - 1
-      ysize = length (head fvs) - 1
-      xsize = length (head $ head fvs) - 1
+      (xsize, ysize, zsize) = dims fvs
 
 
 -- | Takes a grid and a position as an argument and returns the cube
@@ -68,43 +65,72 @@ 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
+    | k >= length (cubes g) = Nothing
+    | j >= length ((cubes g) !! k) = Nothing
+    | i >= length (((cubes g) !! k) !! j) = Nothing
+    | otherwise = Just $ (((cubes g) !! k) !! j) !! i
+
+
+
+--   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/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. This
+    -- returns cube #1 if we would have returned cube #0 and cube #1
+    -- exists.
+    | coord == offset && (xsize > 0 && ysize > 0 && zsize > 0) = 1
+    | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
+    where
+      (xsize, ysize, zsize) = dims (function_values g)
+      cube_width = (h g)
+      offset = cube_width / 2
+
+
+-- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
+--   Since our grid is rectangular, we can figure this out without having
+--   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."
+    where
+      (x, y, z) = p
+      i = calculate_containing_cube_coordinate g x
+      j = calculate_containing_cube_coordinate g y
+      k = calculate_containing_cube_coordinate g z
 
 
--- | Takes a 'Grid', and returns all 'Cube's belonging to it that
---   contain the given 'Point'.
-find_containing_cubes :: Grid -> Point -> [Cube]
-find_containing_cubes g p =
-    filter contains_our_point all_cubes
-    where
-      all_cubes = flatten $ cubes g
-      contains_our_point = flip contains_point p
+{-# INLINE zoom_lookup #-}
+zoom_lookup :: Grid -> a -> (R.DIM3 -> Double)
+zoom_lookup g _ = zoom_result g
 
 
+{-# INLINE zoom_result #-}
+zoom_result :: Grid -> R.DIM3 -> Double
+zoom_result g (R.Z R.:. i R.:. j R.:. k) =
+  f p
+  where
+    i' = fromIntegral i
+    j' = fromIntegral j
+    k' = fromIntegral k
+    p  = (i', j', k') :: Point
+    c = find_containing_cube g p
+    t = head (find_containing_tetrahedra c p)
+    f = polynomial t
 
-zoom :: Grid -> Int -> [[[Double]]]
+
+zoom :: Grid -> Int -> Values3D
 zoom g scale_factor
-    | fvs == [[[]]] = []
-    | head fvs == [[]] = []
+    | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
     | otherwise =
-        [[[f p | i <- [0..scaled_zsize],
-                 let i' = scale_dimension i,
-                 let j' = scale_dimension j,
-                 let k' = scale_dimension k,
-                 let p = (i', j', k') :: Point,
-                 let c = (find_containing_cubes g p) !! 0,
-                 let t = (find_containing_tetrahedra c p) !! 0,
-                 let f = polynomial t]
-                 | j <- [0..scaled_ysize]]
-                   | k <- [0..scaled_xsize]]
-  where
-    scale_dimension :: Int -> Double
-    scale_dimension x = (fromIntegral x) / (fromIntegral scale_factor)
-
-    fvs = function_values g
-    scaled_zsize = ((length fvs) - 1) * scale_factor
-    scaled_ysize = (length (head fvs) - 1) * scale_factor
-    scaled_xsize = (length (head $ head fvs) - 1) * scale_factor
+        R.force $ R.traverse arr transExtent (zoom_lookup g)
+          where
+            arr = function_values g
+            (xsize, ysize, zsize) = dims arr
+            transExtent = zoom_shape scale_factor