2D Triangulation Representation Using Stable Catalogs

The problem of representing triangulations has been widely studied to obtain convenient encodings and space efficient data structures. In this paper we propose a new practical approach to reduce the amount of space needed to represent in main memory an arbitrary triangulation, while maintaining constant time for some basic queries. This work focuses on the connectivity information of the triangulation, rather than the geometry information (vertex coordinates), since the combinatorial data represents the main storage part of the structure. The main idea is to gather triangles into patches, to reduce the number of pointers by eliminating the internal pointers in the patches and reducing the multiple references to vertices. To accomplish this, we define stable catalogs of patches that are close under basic standard update operations such as insertion and deletion of vertices, and edge flips. We present some bounds and results concerning special catalogs, and some experimental results for the quadrilateral-triangle catalog