- | 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