Topics in Computational Geometry

This book presents work in two of the most popular areas of geometric computation: Robust Geometric Computing and Optimal Visibility Coverage. Both areas have been extensively researched in recent years and attracted the attention of many researchers and software developers. (1) Implementation of geometric algorithms is generally difficult because one must deal with both precision problems and degenerate input. Overlooking these issues often result in program errors or crashes. The first part of this book presents algorithms to approximate an arrangement of line segments, which is a basic and important geometric data structure, in order to make it more robust for further manipulation and computation. (2) The optimal visibility coverage problem, often called the "art gallery problem", is one of the classic geometric problems. The input for the problem is a geometric domain and the challenge is to minimize the number of guards that cover, or see, the domain. This topic is motivated by problems in surveillance, sensor networking, illumination and more. The second part of this book presents algorithms for some of the most popular visibility coverage problems.