- | 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