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.

Autorentext

Dr. Eli Packer works at IBM Research Center in Hawthorne, NewYork. He received a B.Sc. and an M.Sc. in Computer Science from TelAviv University, and a Ph.D. from the Department of ComputerScience at Stony Brook University. His research interests includeComputational Geometry, Computer Graphics, Algorithms andSoftware Engineering.

Klappentext

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.