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Discrete and Computational Geometry

Edited by: Jacob E. Goodman , Joseph O’Rourke

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:

10.1201/9781420035315
 Cite  Marc Record

Book description

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

Chapter  1:  Finite Point Configurations Download PDF
Chapter  2:  Packing and Covering Download PDF
Chapter  3:  Tilings Download PDF
Chapter  4:  Helly-Type Theorems and Geometric Transversals Download PDF
Chapter  5:  Pseudoline Arrangements Download PDF
Chapter  6:  Oriented Matroids Download PDF
Chapter  7:  Lattice Points and Lattice Polytopes Download PDF
Chapter  8:  Low-Distortion Embeddings of Finite Metric Spaces Download PDF
Chapter  9:  Geometry and Topology of Polygonal Linkages Download PDF
Chapter  10:  Geometric Graph Theory Download PDF
Chapter  11:  Euclidean Ramsey Theory Download PDF
Chapter  12:  Discrete Aspects of Stochastic Geometry Download PDF
Chapter  13:  Geometric Discrepancy Theory and Uniform Distribution Download PDF
Chapter  14:  Topological Methods Download PDF
Chapter  15:  Polyominoes Download PDF
Chapter  16:  Basic Properties of Convex Polytopes Download PDF
Chapter  17:  Subdivisions and Triangulations of Polytopes Download PDF
Chapter  18:  Face Numbers of Polytopes and Complexes Download PDF
Chapter  19:  Symmetry of Polytopes and Polyhedra Download PDF
Chapter  20:  Polytope Skeletons and Paths Download PDF
Chapter  21:  Polyhedral Maps Download PDF
Chapter  22:  Convex Hull Computations Download PDF
Chapter  23:  Voronoi Diagrams and Delaunay Triangulations Download PDF
Chapter  24:  Arrangements Download PDF
Chapter  25:  Triangulations and Mesh Generation Download PDF
Chapter  26:  Polygons Download PDF
Chapter  27:  Shortest Paths and Networks Download PDF
Chapter  28:  Visibility Download PDF
Chapter  29:  Geometric Reconstruction Problems Download PDF
Chapter  30:  Curve and Surface Reconstruction Download PDF
Chapter  31:  Computational Convexity Download PDF
Chapter  32:  Computational Topology Download PDF
Chapter  33:  Computational Real Algebraic Geometry Download PDF
Chapter  34:  Point Location Download PDF
Chapter  35:  Collision and Proximity Queries Download PDF
Chapter  36:  Range Searching Download PDF
Chapter  37:  Ray Shooting and Lines in Space Download PDF
Chapter  38:  Geometric Intersection Download PDF
Chapter  39:  Nearest Neighbors in High-Dimensional Spaces Download PDF
Chapter  40:  Randomization and Derandomization Download PDF
Chapter  41:  Robust Geometric Computation Download PDF
Chapter  42:  Parallel Algorithms in Geometry Download PDF
Chapter  43:  Parametric Search Download PDF
Chapter  44:  The Discrepancy Method in Computational Geometry Download PDF
Chapter  45:  Linear Programming Download PDF
Chapter  46:  Mathematical Programming Download PDF
Chapter  47:  Algorithmic Motion Planning Download PDF
Chapter  48:  Robotics Download PDF
Chapter  49:  Computer Graphics Download PDF
Chapter  50:  Modeling Motion Download PDF
Chapter  51:  Pattern Recognition Download PDF
Chapter  52:  Graph Drawing Download PDF
Chapter  53:  Splines and Geometric Modeling Download PDF
Chapter  54:  Surface Simplification and 3D Geometry Compression Download PDF
Chapter  55:  Manufacturing Processes Download PDF
Chapter  56:  Solid Modeling Download PDF
Chapter  57:  Computation of Robust Statistics: Depth, Median, and Related Measures Download PDF
Chapter  58:  Geographic Information Systems Download PDF
Chapter  59:  Geometric Applications of The Grassmann-Cayley Algebra Download PDF
Chapter  60:  Rigidity and Scene Analysis Download PDF
Chapter  61:  Sphere Packing and Coding Theory Download PDF
Chapter  62:  Crystals and Quasicrystals Download PDF
Chapter  63:  Biological Applications of Computational Topology Download PDF
Chapter  64:  Software Download PDF
Chapter  65:  Two Computational Geometry Libraries: Leda and Cgal Download PDF
prelims Download PDF
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