Computational Geometry

Abstract

Computational geometry deals with the algorithmic aspects of geometrical problems. The typical objects of (plane) computational geometry are points, lines and line segments, polygons, planar subdivisions (= straight-line embeddings of planar graphs) and collections of these objects. Typical questions are e.g. intersection (line-polygon, polygon-polygon,…), point location (point-point, point-polygon, point-planar subdivision) and decomposition problems (polygon into simpler polygons). The questions are motivated by the widespread use of geometric objects in computer graphics and computer aided design. In particular, the computational problems arising in two- and three-dimensional computer graphics and in VLSI design shaped the field and generated a common interest for it.