eBook

- 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

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

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

"[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…"