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