Handbook of Discrete and Computational Geometry, Second Edition (Google eBook)

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Csaba D. Toth, Joseph O'Rourke, Jacob E. Goodman
CRC Press, Apr 13, 2004 - Mathematics - 1560 pages
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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
  

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Contents

FINITE POINT CONFIGURATIONS
3
PACKING AND COVERING
25
TILINGS
53
HELLYTYPE THEOREMS AND GEOMETRIC TRANSVERSALS
73
PSEUDOLINE ARRANGEMENTS
97
ORIENTED MATROIDS
129
LATTICE POINTS AND LATTICE POLYTOPES
153
LOWDISTORTION EMBEDDINGS OF FINITE METRIC SPACES
177
COLLISION AND PROXIMITY QUERIES
787
RANGE SEARCHING
809
RAY SHOOTING AND LINES IN SPACE
839
GEOMETRIC INTERSECTION
857
NEAREST NEIGHBORS IN HIGHDIMENSIONAL SPACES
877
RANDOMIZATION AND DERANDOMIZATION
895
ROBUST GEOMETRIC COMPUTATION
927
PARALLEL ALGORITHMS IN GEOMETRY
953

GEOMETRY AND TOPOLOGY OF POLYGONAL LINKAGES
197
GEOMETRIC GRAPH THEORY
219
EUCLIDEAN RAMSEY THEORY
239
DISCRETE ASPECTS OF STOCHASTIC GEOMETRY
255
GEOMETRIC DISCREPANCY THEORY AND UNIFORM DISTRIBUTION
279
TOPOLOGICAL METHODS
305
POLYOMINOES
331
POLYTOPES AND POLYHEDRA
353
BASIC PROPERTIES OF CONVEX POLYTOPES
355
SUBDIVISIONS AND TRIANGULATIONS OF POLYTOPES
383
FACE NUMBERS OF POLYTOPES AND COMPLEXES
407
SYMMETRY OF POLYTOPES AND POLYHEDRA
431
POLYTOPE SKELETONS AND PATHS
455
POLYHEDRAL MAPS
477
CONVEX HULL COMPUTATIONS
495
VORONOI DIAGRAMS AND DELAUNAY TRIANGULATIONS
513
ARRANGEMENTS
529
TRIANGULATIONS AND MESH GENERATION
563
POLYGONS
583
SHORTEST PATHS AND NETWORKS
607
VISIBILITY
643
GEOMETRIC RECONSTRUCTION PROBLEMS
665
CURVE AND SURFACE RECONSTRUCTION
677
COMPUTATIONAL CONVEXITY
693
COMPUTATIONAL TOPOLOGY
719
COMPUTATIONAL REAL ALGEBRAIC GEOMETRY
743
GEOMETRIC DATA STRUCTURES AND SEARCHING
765
POINT LOCATION
767
PARAMETRIC SEARCH
969
THE DISCREPANCY METHOD IN COMPUTATIONAL GEOMETRY
983
LINEAR PROGRAMMING
999
MATHEMATICAL PROGRAMMING
1015
ALGORITHMIC MOTION PLANNING
1037
ROBOTICS
1065
COMPUTER GRAPHICS
1095
MODELING MOTION
1117
PATTERN RECOGNITION
1135
GRAPH DRAWING
1163
SPLINES AND GEOMETRIC MODELING
1187
SURFACE SIMPLIFICATION AND 3D GEOMETRY COMPRESSION
1209
MANUFACTURING PROCESSES
1241
SOLID MODELING
1257
COMPUTATION OF ROBUST STATISTICS DEPTH MEDIAN AND RELATED MEASURES
1279
GEOGRAPHIC INFORMATION SYSTEMS
1293
GEOMETRIC APPLICATIONS OF THE GRASSMANNCAYLEY ALGEBRA
1315
RIGIDITY AND SCENE ANALYSIS
1327
SPHERE PACKING AND CODING THEORY
1355
CRYSTALS AND QUASICRYSTALS
1377
BIOLOGICAL APPLICATIONS OF COMPUTATIONAL TOPOLOGY
1395
GEOMETRIC SOFTWARE
1413
SOFTWARE
1415
TWO COMPUTATIONAL GEOMETRY LIBRARIES LEDA AND CGAL
1435
INDEX OF CITED AUTHORS
1465
INDEX OF DEFINED TERMS
1497
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