XOR-Based Compact Triangulations

Abstract

Media, image processing, and geometric-based systems and applications need data structures to model and represent different geometric entities and objects. These data structures have to be time efficient and compact in term of space. Many structures in use are proposed to satisfy those constraints. This paper introduces a novel compact data structure inspired by the XOR-linked lists. The subject of this paper concerns the triangular data structures. Nevertheless, the underlying idea could be used for any other geometrical subdivision. The ability of the bitwise XOR operator to reduce the number of references is used to model triangle and vertex references. The use of the XOR combined references needs to define a context from which the triangle is accessed. The direct access to any triangle is not possible using only the XOR-linked scheme. To allow the direct access, additional information are added to the structure. This additional information permits a constant time access to any element of the triangulation using a local resolution scheme. This information represents an additional cost to the triangulation, but the gain is still maintained. This cost is reduced by including this additional information to a local sub-triangulation and not to each triangle. Sub-triangulations are calculated implicitly according to the catalog-based structure. This approach could be easily extended to other representation models, such as vertex-based structures or edge-based structures. The obtained results are very interesting since the theoretical gain is estimated to 38 % and the practical gain obtained from sample benches is about 34 %.