X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=ba8ca2007621c9e31536788d8204e0d0e6306463;hb=957754c693525096c5fd7427decd6404bbb03379;hp=1a436acdc00d9276ceb1e25b7080355577822bf3;hpb=30bc407abc86ffa9a0eb4b26bdb4890f3ea423d1;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index 1a436ac..ba8ca20 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,11 +4,19 @@
 module Grid
 where
 
-import Cube (Cube(Cube))
+import Data.Array (Array, array, (!))
+import qualified Data.Array.Repa as R
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+
+import Cube (Cube(Cube), find_containing_tetrahedron)
 import FunctionValues
-import Misc (flatten)
 import Point (Point)
-import ThreeDimensional (contains_point)
+import ScaleFactor
+import Tetrahedron (polynomial)
+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
@@ -16,59 +24,127 @@ import ThreeDimensional (contains_point)
 --   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,
+                   cube_grid :: CubeGrid }
           deriving (Eq, Show)
 
 
+instance Arbitrary Grid where
+    arbitrary = do
+      (Positive h') <- arbitrary :: Gen (Positive 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
+    | otherwise = Grid grid_size values (cubes grid_size values)
 
 
 -- | Creates an empty grid with grid size 1.
 empty_grid :: Grid
-empty_grid = Grid 1 [[[]]]
+empty_grid = make_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 == [[]] = [[[]]]
-    | 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
+-- | 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
 
 
 -- | 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
-
-
--- | 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
+    | 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 = (cube_grid 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/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 = 0
+    | coord == offset && (xsize > 1 && ysize > 1 && zsize > 1) = 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 =
+    cube_at g i j k
     where
-      all_cubes = flatten $ cubes g
-      contains_our_point = flip contains_point p
+      (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
+
+
+{-# INLINE zoom_lookup #-}
+zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup g scale_factor _ = zoom_result g scale_factor
+
+
+{-# INLINE zoom_result #-}
+zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
+zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
+  f p
+  where
+    offset = (h g)/2
+    i' = (fromIntegral i) / (fromIntegral sfx) - offset
+    j' = (fromIntegral j) / (fromIntegral sfy) - offset
+    k' = (fromIntegral k) / (fromIntegral sfz) - offset
+    p  = (i', j', k') :: Point
+    c = find_containing_cube g p
+    t = find_containing_tetrahedron c p
+    f = polynomial t
+
+
+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 scale_factor)
+          where
+            arr = function_values g
+            (xsize, ysize, zsize) = dims arr
+            transExtent = zoom_shape scale_factor