TopQT: A Topological Data-Structure for Quadtrees

In this paper we propose a topological data structure for quadtrees, TopQT. This data structure is somewhat different from others very common in cell-complexes representations such as the famous half-edge. In the main result of this paper, we show that given a cell in the quadtree, TopQT is able to find all four connected neighbor cells in constant time. We give some pseudo algorithms to explain how to access the surrounding cells. These algorithms may point out to many nice applications in the computer graphics comunnity. We will cite some of them, specially the one that motivated this work.