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HANDBOOK OF COMPUTATIONAL GEOMETRY
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Preface
Computational Geometry is a young and vibrant field of Computer Science born in the early 1970's. Since its beginning, Computational Geometry has attracted the interest of a large number of researchers, due to its numerous and strong interactions with various fields of Science and Engineering such as Algorithms and Data Structures, Combinatorial Mathematics, Edclidean Geometry, and Optimization. Recently the demand for efficient geometric computing in a variety of areas of applied sciences such as Geographical Information Systems, Visualization, Robotics, Computer Graphics, and CAD has further fueled reseach in Computational Geometry. This has resulted in a wealth of powerful techniques and results of interest to researchers and practitioners.
The need for a comprehensive source of information on the fundamental techniques and tools developed in Computational Geometry is evident. This handbook will be an important source of information for all of us interested in one way or another in Computational Geometry. Readers whose objectives are to use a method for their applications will be able to find and choose different approaches and techniques to solve a large number of problems, most of them described in a comprehensive and concise manner. Researchers interested in theoretical results will find this handbook an invaluable and comprehensive source of information in which most of the results, tools and techniques available in our field are to be found
This handbook presents chapters which survey in detail most of the research available to date in this field. The handbook contains survey papers in the following fundamental topics: Arrangements, Voronoi Diagrams, Geometric Data Structures (incl. point location, convex hull, etc.), Spatial Data Structures, Polygon Decomposition, Randomized Algorithms, Derandomization, Parallel Computational Geometry (deterministic and randomized), Visibility, Art Gallery and Illumination Problems, Closest Point Problems, Link Distance Problems, Similarity of Geometric Objects, Davenport-Schinzel Sequences, and Spanning Trees and Spanners.
There are also three chapters devoted to applications of Computational Geometry to other fields of science: Geographical Information Systems, Geometric Shortest Paths and Network Optimization, and Mesh Generation. In addition, there is a chapter devoted to robustness and numerical issues, and chapters on Animation and Graph Drawing.
We would like to thank for the enthusiasm shown by all the contributors to this handbook, as well as express our gratitude to the numerous anonymous referees whose invaluable contributions made this project possible. We are grateful to Arjen Sevenster of Elsevier Science for this enthusiastic support which made this handbook a reality. Finally, we thank Anil Maheshwari for his help.
J.-R. Sack
J. Urrutia
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