Handbook of Discrete and Computational Geometry, Second Edition

Handbook of Discrete and Computational Geometry, Second Edition

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$179.95
ISBN 9781584883012
Cat# C3014
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ISBN 9781420035315
Cat# CE3014
 

Features

  • Provides a one-stop reference both for researchers in geometry and geometric computing and for professionals who use geometric tools in their work
  • Covers a broad range of topics in discrete and computational geometry as well as numerous applications
  • Presents results in the forms of theorems, algorithms, and tables
  • Addresses many important new developments in the field, including solution of the Kepler conjecture, results on the 2-center problem, new bounds on k-sets and geometric permutations, and new art gallery theorems
  • Includes nearly 300 illustrations, almost 200 tables, and glossaries that provide clear definitions of more than 4000 terms

Summary

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date.

Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications.

Highlights of the Second Edition:

  • Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory
  • Thorough revisions of all remaining chapters
  • Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software
  • Two indices: An Index of Defined Terms and an Index of Cited Authors
  • Greatly expanded bibliographies

Table of Contents

COMBINATORIAL AND DISCRETE GEOMETRY
Finite Point Configurations, J. Pach
Packing and Covering, G. Fejes Tóth
Tilings, D. Schattschneider and M. Senechal
Helly-Type Theorems and Geometric Transversals, R. Wenger
Pseudoline Arrangements, J.E. Goodman
Oriented Matroids, J. Richter-Gebert and G.M. Ziegler
Lattice Points and Lattice Polytopes, A. Barvinok
New! Low-Distortion Embeddings of Finite Metric Spaces, P. Indyk and J. Matousek
New! Geometry and Topology of Polygonal Linkages, R. Connelly and E.D. Demaine
New! Geometric Graph Theory, J. Pach
Euclidean Ramsey Theory, R.L. Graham
Discrete Aspects of Stochastic Geometry, R. Schneider
Geometric Discrepancy Theory and Uniform Distribution, J.R. Alexander, J. Beck, and W.W.L. Chen
Topological Methods, R.T. Zivaljevic
Polyominoes, S.W. Golomb and D.A. Klarner

POLYTOPES AND POLYHEDRA
Basic Properties of Convex Polytopes, M. Henk, J. Richter-Gebert, and G.M. Ziegler
Subdivisions and Triangulations of Polytopes, C.W. Lee
Face Numbers of Polytopes and Complexes, L.J. Billera and A. Björner
Symmetry of Polytopes and Polyhedra, E. Schulte
Polytope Skeletons and Paths, G. Kalai
Polyhedral Maps, U. Brehm and E. Schulte

ALGORITHMS AND COMPLEXITY OF FUNDAMENTAL GEOMETRIC OBJECTS
Convex Hull Computations, R. Seidel
Voronoi Diagrams and Delaunay Triangulations, S. Fortune
Arrangements, D. Halperin
Triangulations and Mesh Generation, M. Bern
Polygons, J. O'Rourke and S. Suri
Shortest Paths and Networks, J.S.B. Mitchell
Visibility, J. O'Rourke
Geometric Reconstruction Problems, S.S. Skiena
New! Curve and Surface Reconstruction, T.K. Dey
Computational Convexity, P. Gritzmann and V. Klee
Computational Topology, G. Vegter
Computational Real Algebraic Geometry, B. Mishra

GEOMETRIC DATA STRUCTURES AND SEARCHING
Point Location, J. Snoeyink
New! Collision and Proximity Queries, M.C. Lin and D. Manocha
Range Searching, P.K. Agarwal
Ray Shooting and Lines in Space, M. Pellegrini
Geometric Intersection, D.M. Mount
New! Nearest Neighbors in High-Dimensional Spaces, P. Indyk

COMPUTATIONAL TECHNIQUES
Randomization and Derandomization, O. Cheong, K. Mulmuley, and E. Ramos
Robust Geometric Computation, C.K. Yap
Parallel Algorithms in Geometry, M.T. Goodrich
Parametric Search, J.S. Salowe
New! The Discrepancy Method in Computational Geometry, B. Chazelle

APPLICATIONS OF DISCRETE AND COMPUTATIONAL GEOMETRY
Linear Programming, M. Dyer, N. Megiddo, and E. Welzl
Mathematical Programming, M.H. Todd
Algorithmic Motion Planning, M. Sharir
Robotics, D. Halperin, L.E. Kavraki, and J.-C. Latombe
Computer Graphics, D. Dobkin and S. Teller
New! Modeling Motion, L.J. Guibas
Pattern Recognition, J. O'Rourke and G.T. Toussaint
Graph Drawing, R. Tamassia and G. Liotta
Splines and Geometric Modeling, C.L. Bajaj
New! Surface Simplification and 3D Geometry Compression, J. Rossignac
Manufacturing Processes, R. Janardan and T.C. Woo
Solid Modeling, C.M. Hoffmann
New! Computation of Robust Statistics: Depth, Median, and Related Measures, P.J. Rousseeuw and A. Struyf
New! Geographic Information Systems, M. van Kreveld
Geometric Application of the Grassmann-Cayley Algebra, N.L. White
Rigidity and Scene Analysis, W. Whiteley
Sphere Packing and Coding Theory, G.A. Kabatiansky and J.A. Rush
Crystals and Quasicrystals, M. Senechal
New! Biological Applications of Computational Topology, H. Edelsbrunner

New! GEOMETRIC SOFTWARE
Software, J. Joswig
Two Computation Geometry Libraries: LEDA and CGAL, L. Kettner and S. Näher

Index of Defined Terms
New! Index of Cited Authors

Editorial Reviews

"[T]his book puts together under one cover more and broader information on discrete (= combinatorial) and computational geometry than any other book in existence. Better yet, chapters of the book have been written by some of the best informed in their subject matter …[A]ctive mathematicians and scientists in many … fields - such as computer science, physics, biology, chemistry, etc. - will browse this volume profitably in search for tools that can aid them in their creative endeavors. This is the second edition … . It is therefore fair to ask, should those who [bought] the first edition buy this edition as well? I think so, for it offers 500 additional pages, thoroughly revised old chapters, and 14 new chapters."
- Geombinatorics XIV(3), January 2005

"The second edition of this remarkable handbook is 50% larger than the first…clearly written and well-organized..this handbook should be available in research and academic libraries as well as mathematics department libraries."
E-Streams, 2005

"This laptop of a handbook is a tremendous collection of 65 articles on discrete and computational geometry. The organization of this book is superb. The work's breadth and the wealth of its scope make in an invaluable resource…"
laptop of a handbook is a tremendous collection of 65 articles on discrete and computational geometry. The organization of this book is superb. The work's breadth and the wealth of its scope make in an invaluable resource…"

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