Visibility Algorithms in the Plane

The first book entirely devoted to visibility algorithms in computational geometry.

Subir Kumar Ghosh (Author)

9780521875745, Cambridge University Press

Hardback, published 29 March 2007

332 pages, 333 b/w illus. 108 exercises
25.2 x 17.8 x 2 cm, 0.818 kg

'… the book gives a good overview of visibility algorithms in the plane, concentrating on basic algorithms but also covering the state of the art.' Mathematical Reviews

A human observer can effortlessly identify visible portions of geometric objects present in the environment. However, computations of visible portions of objects from a viewpoint involving thousands of objects is a time consuming task even for high speed computers. To solve such visibility problems, efficient algorithms have been designed. This book presents some of these visibility algorithms in two dimensions. Specifically, basic algorithms for point visibility, weak visibility, shortest paths, visibility graphs, link paths and visibility queries are all discussed. Several geometric properties are also established through lemmas and theorems. With over 300 figures and hundreds of exercises, this book is ideal for graduate students and researchers in the field of computational geometry. It will also be useful as a reference for researchers working in algorithms, robotics, computer graphics and geometric graph theory, and some algorithms from the book can be used in a first course in computational geometry.

Preface
1. Background
2. Point visibility
3. Weak visibility and shortest paths
4. L-R visibility and shortest paths
5. Visibility graphs
6. Visibility graph theory
7. Visibility and link paths
8. Visibility and path queries
Bibliography
Index.

Subject Areas: Image processing [UYT], Algorithms & data structures [UMB], Geometry [PBM]