Handbook of Discrete and Computational Geometry / Edition 2

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More About This Textbook


The second edition of the Handbook of Discrete and Computational Geometry is a thoroughly revised version of the bestselling first edition. With the addition of 500 pages and 14 new chapters covering topics such as geometric graphs, collision detection, clustering, applications of computational geometry, and statistical applications, this is a significant update. This edition includes expanded coverage on the topics of mesh generation in two and three dimensions, aspect graphs, center points, and probabilistic roadmap algorithms. It also features new results on solutions of the Kepler conjecture, and honeycomb conjecture, new bounds on K sets, and new results on face numbers of polytopes.

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Product Details

  • ISBN-13: 9781584883012
  • Publisher: Taylor & Francis
  • Publication date: 2/15/2004
  • Series: Discrete and Combinatorial Mathematics Series
  • Edition description: REV
  • Edition number: 2
  • Pages: 1560
  • Product dimensions: 7.40 (w) x 10.30 (h) x 3.15 (d)

Table of Contents

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

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

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

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

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

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

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

Index of Defined Terms
New! Index of Cited Authors

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