Topics in Computational Geometry

This book presents work in two of the most popularareas of geometric computation: Robust GeometricComputing and Optimal Visibility Coverage. Both areashave been extensively researched in recent years andattracted the attention of many researchers andsoftware developers. (1) Implementation of geometricalgorithms is generally difficult because one mustdeal with both precision problems and degenerateinput. Overlooking these issues often result inprogram errors or crashes. The first part of thisbook presents algorithms to approximate anarrangement of line segments which is a basic andimportant geometric data structure in order to makeit more robust for further manipulation andcomputation. (2) The optimal visibility coverageproblem often called the art gallery problem isone of the classic geometric problems. The input forthe problem is a geometric domain and the challengeis to minimize the number of guards that cover orsee the domain. This topic is motivated by problemsin surveillance sensor networking illumination andmore. The second part of this book presentsalgorithms for some of the most popular visibilitycoverage problems.