Non-interleaved quadtree node codification

Abstract

The usual quadtree node non-pointer codification is based on interleaved binary representations of node coordinates, in such a way that every operation that concerns to the spatial position or to the specific orientation of the region represented by the node needs to undo this interleaving process. So, the computation time of such operations is linear with the node depth. In this paper an alternative codification is presented called "non-interleaved codification". The new codification has a simpler management and a higher intuitiveness than current codifications that use the interleaving approach. The proposed codification is more efficient than previous ones for the following set of operations: generating the node codes from the spatial coordinates, recovering original coordinates from the node codes, and performing topological operations where explicit or implicit reference is made to node location, for instance, checking if two nodes are adjacent, evaluating distances between nodes, evaluating relative orientation, etc. The proposed codification performs all these operations in O(1) time, independently from the node depth. © Springer-Verlag 2004.