Art Gallery Theorems and Algorithms by Joseph O'Rourke

Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.
This book is the most comprehensive collection of results on polygons currently available and thus earns its place as a standard text in computational geometry. It is very well written and a pleasure to read. It can be recommended as an introductory book to the beautiful and rich area of discrete and computational geometry.
Suitable as a reference book for a specialist audience, as a text in an advanced course, or as an introduction for the intelligent nonspecialist in the field. It is easy to read. I recommend it for the library of every geometer.
This research monograph is accessible to undergraduates with knowledge of basic graph theory, data structures and algorithms. It can be used as an introduction to computational geometry with plenty of challenging problems.