Art Gallery Theorems and Algorithms

Download or read book Art Gallery Theorems and Algorithms written by Joseph O'Rourke and published by Oxford University Press, USA. This book was released on 1987 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.