Computational Geometry: Methods and Applications

In this book, we concentrate on four major directions in computational geometry: the construction of convex hulls, proximity problems, searching problems and intersection problems. Computational geometry is of practical importance because Euclidean space of two and three dimensions forms the arena in which real physical objects are arranged. A large number of applications areas such as pattern recognition, computer graphics, image processing, operations research, statistics, computer-aided design, robotics, etc., have been the incubation bed of the discipline since they provide inherently geo metric problems for which efficient algorithms have to be developed. A large number of manufacturing problems involve wire layout, facilities location, cutting-stock and related geometric optimization problems. Solving these efficiently on a high-speed computer requires the development of new geo metrical tools, as well as the application of fast-algorithm techniques, and is not simply a matter of translating well-known theorems into computer programs. From a theoretical standpoint, the complexity of geometric algo rithms is of interest because it sheds new light on the intrinsic difficulty of computation.