From a7f5c0b286ba29cdd586f418638e9ab4a406bf97 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 24 Aug 2011 10:53:28 -0400
Subject: [PATCH] Change "find_containing_cubes" to "find_containing_cube" and
 speed it up considerably.

---
 src/Grid.hs | 40 +++++++++++++++++++++++++++++++---------
 1 file changed, 31 insertions(+), 9 deletions(-)

diff --git a/src/Grid.hs b/src/Grid.hs
index 3d636b5..517e3b1 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -11,7 +11,6 @@ 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
@@ -73,14 +72,37 @@ cube_at g i j k
     | 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
+
+--   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
+--   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
+    where
+      (xsize, ysize, zsize) = dims (function_values g)
+      delta = (h g)
+      cube_width = 2 * delta
+
+
+-- | 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
-      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
 
 
 zoom :: Grid -> Int -> Values3D
@@ -101,6 +123,6 @@ zoom g scale_factor
                     j' = fromIntegral j
                     k' = fromIntegral k
                     p = (i', j', k') :: Point
-                    c = head (find_containing_cubes g p)
+                    c = find_containing_cube g p
                     t = head (find_containing_tetrahedra c p)
                     f = polynomial t
-- 
2.43.2