Description
Taylor & Francis Handbook of Discrete and Computational Geometry 1997 Edition by Csaba D. Toth, Joseph O'Rourke, Jacob E. Goodman
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 handbookfor 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. Table of Contents : Finite point configurationsPacking and coveringTilingsHelly-type theorems and geometric transversalsPseudoline arrangementsOriented matroidsLattice points and lattice polytopesEuclidean Ramsey theoryDiscrete aspects of stochastic geometryGeometric discrepancy theory and uniform distributionTopological methodsPolyominoesBasic properties of convex polytopesSubdivisions and triangulations of polytopesFace numbers of polytopes and complexesSymmetry of polytopes and polyhedraPolytope skeletons and pathsPolyhedral maps Convex hull computationsVoronoi diagrams and Delaunay triangulationsArrangementsTriangulationsPolygonsShortest paths and networksVisibilityGeometric reconstruction problemsComputational convexityComputational topologyComputational real algebraic geometryPoint locationRange searchingRay shooting and lines in spaceGeometric intersectionRandomized algorithmsRobust geometric computationParallel algorithms in geometryParametric searchLinear programming in low dimensionsMathematical programmingAlgorithmic motion planningRoboticsComputer graphicsPattern recognitionGraph drawingSplines and geometric modelingManufacturing processesSolid modelingGeometric applications of the Grassmann-Cayley algebraRigidity and scene analysisSphere packing and coding theoryCrystals and quasicrystalsComputational geometry software