Voronoi Diagrams--A Survey of a Fundamental Geometric Data Structure
Voronoi Diagrams — A Survey of a Fundamental Geometric Data Structure FRANZ AURENHAMMER Institute fur Informationsverarbeitung Technische Universitat Graz, Sch iet!stattgasse 4a, Austria This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems–geometrical problems and computations; G. 2.1 [Discrete Mathematics]: Combinatorics— combinatorial algorithms; I. 3.5 [Computer Graphics]: Computational Geometry and Object Modeling—geometric algorithms, languages, and systems General Terms: Algorithms, Theory Additional Key Words and Phrases: Cell complex, clustering, combinatorial complexity, convex hull, crystal structure, divide-and-conquer, geometric data structure, growth model, higher dimensional embedding, hyperplane arrangement, k-set, motion planning, neighbor searching, object modeling, plane-sweep, proximity, randomized insertion, spanning tree, triangulation INTRODUCTION [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner Computational geometry is concerned [1987bl.) with the design and analysis of algo- Readers familiar with the literature of rithms for geometrical problems. In add- computational geometry will have no- ition, other more practically oriented, ticed, especially in the last few years, an areas of computer science— such as com- increasing interest in a geometrical con- puter graphics, computer-aided design, struct called the Voronoi diagram.
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