Computational geometry

Abstract

Computational geometry evolves from the classical discipline of design and analysis of algorithms, and has received a great deal of attention in the past two decades since its identification in 1975 by Shamos. It is concerned with the computational complexity of geometric problems that arise in various disciplines such as pattern recognition, computer graphics, computer vision, robotics, very large-scale integrated (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.