Handbook of Discrete and Computational Geometry / Edition 1

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While much information can be found on discrete and computational geom etry, it is scattered among many sources, and individual books and art icles are often narrowly focused. Handbook of Discrete and Computation al Geometry brings together, for the first time, all of the major resu lts in both these fields into one volume. Thousands of results - theor ems, algorithms, and tables - throughout the volume definitively cover the field, while numerous applications from many different fields dem onstrate practical usage. The material is presented clearly enough to assist the novice, but in enough depth to appeal to the specialist. Ev ery technical term is clearly defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples.

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Table of Contents

Finite point configurations
Packing and covering
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

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
Shortest paths and networks
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
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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