X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=6a9a8e5edd9ee62907a1486e29c25b334bedc041;hb=c954154b379c5bd444d527298c33142fb150711b;hp=3d636b53a780f465b515c6e45f8ee53b6e7f10ba;hpb=3cf6c69c9c7fed364b13fa54ee78209f7485d304;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index 3d636b5..6a9a8e5 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,17 +4,16 @@
 module Grid
 where
 
+import qualified Data.Array.Repa as R
 import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
 
 import Cube (Cube(Cube), find_containing_tetrahedra)
 import FunctionValues
-import Misc (flatten)
 import Point (Point)
+import ScaleFactor
 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
@@ -61,46 +60,85 @@ cubes g
 
 -- | 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"
+    | j < 0 = error "j < 0 in cube_at"
+    | k < 0 = error "k < 0 in cube_at"
+    | otherwise =
+        let zsize = length (cubes g) in
+          if k >= zsize then
+            error "k >= xsize in cube_at"
+          else
+            let ysize = length ((cubes g) !! k) in
+              if j >= ysize then
+                error "j >= ysize in cube_at"
+              else
+                let xsize = length (((cubes g) !! k) !! j) in
+                  if i >= xsize then
+                    error "i >= xsize in cube_at"
+                  else
+                    (((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 =
+    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
+    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)
+    f = polynomial t
 
 
-zoom :: Grid -> Int -> Values3D
+zoom :: Grid -> ScaleFactor -> Values3D
 zoom g scale_factor
     | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
     | otherwise =
-        R.traverse arr transExtent (\_ -> newlookup)
+        R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor)
           where
-            fvs = function_values g
-            (xsize, ysize, zsize) = dims fvs
-            arr = fvs
+            arr = function_values g
+            (xsize, ysize, zsize) = dims arr
             transExtent = zoom_shape scale_factor
-            newlookup :: R.DIM3 -> Double
-            newlookup (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 = head (find_containing_cubes g p)
-                    t = head (find_containing_tetrahedra c p)
-                    f = polynomial t