Calculate the Hilbert value of a point for use in a Hilbert R-Tree?

Question

I have an application where a Hilbert R-Tree (wikipedia) (citeseer) would seem to be an appropriate data structure. Specifically, it requires reasonably fast spatial querie

Answer 1

Suggestion: A good simple efficient data structure for spatial queries is a multidimensional binary tree.

In a traditional binary tree, there is one "discriminant"; the value that's used to determine whether you take the left branch or the right branch. This can be considered to be the one-dimensional case.

In a multidimensional binary tree, you have multiple discriminants; consecutive levels use different discriminants. For example, for two dimensional spacial data, you could use the X and Y coordinates as discriminants. Consecutive levels would use X, Y, X, Y...

For spatial queries (for example finding all nodes within a rectangle) you do a depth-first search of the tree starting at the root, and you use the discriminant at each level to avoid searching down branches that contain no nodes in the given rectangle.

This allows you to potentially cut the search space in half at each level, making it very efficient for finding small regions in a massive data set. (BTW, this data structure is also useful for partial-match queries, i.e. queries that omit one or more discriminants. You just search down both branches at levels with an omitted discriminant.)

A good paper on this data structure: http://portal.acm.org/citation.cfm?id=361007 This article has good diagrams and algorithm descriptions: http://en.wikipedia.org/wiki/Kd-tree