Handbook of discrete and computational geometry

著者

• Goodman, Jacob E.
• O'Rourke, Joseph

書誌事項

Handbook of discrete and computational geometry

edited by Jacob E. Goodman, Joseph O'Rourke

（Discrete mathematics and its applications / Kenneth H. Rosen, series editor）

CRC Press, c1997

• : hard

注記

Includes bibliographical references and index

内容説明・目次

内容説明

Jacob E. Goodman, co-founder and editor of Discrete & Computational Geometry, the preeminent journal on this area in the international mathematics and computer science community, joins forces with the distinguished computer scientist Joseph O'Rourke and other well-known authorities to produce the definitive handbook on these two interrelated fields. Over the past decade or so, researchers and professionals in discrete geometry and the newer field of computational geometry have developed a highly productive collaborative relationship, where each area benefits from the methods and insights of the other. At the same time that discrete and computational geometry are becoming more closely identified, applications of the results of this work are being used in an increasing number of widely differing areas, from computer graphics and linear programming to manufacturing and robotics. The authors have answered the need for a comprehensive handbook for workers in these and related fields, and for other users of the body of results. While much information can be found on discrete and computational geometry, it is scattered among many sources, and individual books and articles are often narrowly focused. Handbook of Discrete and Computational Geometry brings together, for the first time, all of the major results in both these fields into one volume. Thousands of results - theorems, algorithms, and tables - throughout the volume definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is presented clearly enough to assist the novice, but in enough depth to appeal to the specialist. Every technical term is clearly defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples. Information on current geometric software - what it does, how efficiently it does it, and where to find it - is also included.

目次

Finite point configurations Packing and covering Tilings Helly-type theorems and geometric transversals Pseudoline arrangements Oriented matroids Lattice points and lattice polytopes Euclidean Ramsey theory Discrete aspects of stochastic geometry Geometric discrepancy theory and uniform distribution Topological methods Polyominoes Basic properties of convex polytopes Subdivisions and triangulations of polytopes Face numbers of polytopes and complexes Symmetry of polytopes and polyhedra Polytope skeletons and paths Polyhedral maps Convex hull computations Voronoi diagrams and Delaunay triangulations Arrangements Triangulations Polygons Shortest paths and networks Visibility Geometric reconstruction problems Computational convexity Computational topology Computational real algebraic geometry Point location Range searching Ray shooting and lines in space Geometric intersection Randomized algorithms Robust geometric computation Parallel algorithms in geometry Parametric search Linear programming in low dimensions Mathematical programming Algorithmic motion planning Robotics Computer graphics Pattern recognition Graph drawing Splines and geometric modeling Manufacturing processes Solid modeling Geometric applications of the Grassmann-Cayley algebra Rigidity and scene analysis Sphere packing and coding theory Crystals and quasicrystals Computational geometry software

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA31904725
• ISBN:
  • 0849385245
• LCCN: 97024336
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton, FLA.
• ページ数/冊数: xvi, 991 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA167
  • DC21 : 516/.13
• 件名:
  • LCSH : Combinatorial geometry -- Handbooks, manuals, etc
  • LCSH : Geometry -- Data processing -- Handbooks, manuals, etc
• 親書誌ID:
  • BA25247299