Computational Geometry I

Abstract

Introduction Computational geometry, since its inception[41] in 1975, has received a great deal of attention from researchers in the area of design and analysis of algorithms. It has evolved into a discipline of its own. It is concerned with the computational complexity of geometric problems that arise in various disciplines such as pattern recognition, computer graphics, geographical information system, computer vision, CAD/CAM, robotics, VLSI layout, operations research, statistics, etc. In contrast with the classical approach to proving mathematical theorems about geometry-related problems, this discipline emphasizes the computational aspect of these problems and attempts to exploit the underlying geometric properties possible, e.g., the metric space, to derive efficient algorithmic solutions. An objective of this discipline in the theoretical context is to study the computational complexity (giving lower bounds) of geometric problems, and to de