Basic Algorithms and Combinatorics in Computational Geometry∗

Computational geometry is, in its broadest sense, the study of geometric problems from a computational point of view. At the core of the field is a set of techniques for the design and analysis of geometric algorithms. These algorithms often operate on, and are guided by, a set of data structures that are ubiquitous in geometric computing. These include arrangements, Voronoi diagrams, and Delaunay triangulations. It is the purpose of this paper to present a tutorial introduction to these basic geometric data structures.