Handbook of Discrete and Computational Geometry / Edition 1

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Overview

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.

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Product Details

Table of Contents

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

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