Goodman J.E., O'Rourke J. Handbook of Discrete and Computational Geometry

2nd edition. — Chapman and Hall/CRC, 2004. — 1558 p.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.
While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discre 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.PrefacesCombinatorial and Discrete Geometry
Fiite point collfigurations ( J. Pach)
Packing and covering ( G. Fejes Tth)
Tilings ( D. Schattschneider and М. Senechal)
Helly-type theorems and geometric transversals (R. Wenger)
Pseudoline arrangements ( J.E. Goodman)
Oriented шat·oids (J. Ricliter-GeЬert and G.M. Ziegler)
Lattice points and lattice polytopes (А. BanJinok)
Low-distortioп embeddings of finite metric spaces
( Р. Indyk and J. М atousek)
Geometry and topology of polygonal linkages
(R. Connelly and E.D. Demaine)
Geometric graph theory (J. Pach)
Euclidean Ramsey theory ( R. L. Graham)
Discrete aspects of stoclastic geometry (R. Schneider)
Geoшetric discrepancy theory and unifo" distribution
(J.R. Alexander, J. Beck, and W. W.L. Chen)
Topological methods (R. Т. Zivaljevic)
Polyominoes (S. W. GolomЬ and .D.A. Кlarner)Polytopes and Polyhedra
Basic properties of covex polytopes
(М. Henk, J. Richter-GeЬert, and G.M. Ziegler)
Subdivisions and triangulations of polytopes (С. W. Lee)
Face numbers of polytopes and complexes (L.J. Billera and А. Bjiirner)
Symmetry of polytopes and polyhedra (Е. Schulte)
Polytope skeletons and patls ( G. Kalai)
Polyhedral maps ( U. Brehm and Е. Schulte)Algorithms and Complexiтy of Fundamental Geometric Objects
Convex hнll cornputations ( R. Seidel)
Vo·onoi diagrams and Delaunay triangulations (S. Fortune)
Arrangements (D. Halperin)
Тriangulations and rnesh generation (М. Bern)
Polygons ( J. О 'Rourke and S. Suri)
Shortest paths and networks (J.S.B. Mitchell)
Visibllity (J. O'Rourke)
Geometric reconstruction p·Ыems (S.S. Skiena)
Curve and surface reconstruction ( Т.К. Dey)
Computational convexity (Р. Gritzmann and V. Кlее)
Computational topology ( G. Vegter)
Computational real algebraic geometry (В. Mishra)Geometric Data Structures and Searching
Point location (J. Snoeyink)
Collision and proximity queries (М.С. Lin and D. Manocha)
Range searching ( Р.К. Aganoal)
Ray shooting and lines in space (М. Pellegrini)
Geometric intersection (D.M. Mount)
Neai·est neighbш·s i blgh-dimesional spaces (Р. lndyk)Computational Techniques
Randomizaton and derandomization
(О. Cheong, К. Mulmuley, and Е. Ramos)
Robust geometric comp\tation (С.К. Уар)
Parallel algorithms in geomet-y ( М. Т. Goodrich)
Parametric search (J.S. Salowe)
The discrepancy method in computational geometry (В. Chazelle)Applications of Discrete and Computational Geometry
Lineai· programming (М. Dyer, N. Megiddo, and Е. Welzl)
:Мathematical p·ogramming (M.J. Todd)
Algoithmic motion planning (М. Sharir)
Robotics (D. Halperin, L.E. Kavraki, and J.-C. LatomЬe)
Computer graphics (D. Dobkin and S. Teller)
Modeling motion (L.J. GuiЬas)
Pattern recognition (J. O'Rourke and G.T. Toussaint)
Graph drawing (R. Tamassia and G. Liotta)
Splines and geometric modeling ( C.L. Bajaj)
Surface simplification and D geometry compression (J. Rossignac)
Man\facturing processes (R. Janardan and Т.С. Woo)
Solid modeling ( С.М. Hoffmann)
Computation of robust statistics: Depth, median, and related measui·es
(P.J. Roшseeuw and А. Struyf)
Geographic info"Пlation systems (М. van Kreveld)
Geometric applications of the Grassmann-Cayley algebra (N.L. White)
Rigidity and scene analysis ( W. Whiteley)
Sphere packing and coding theory ( G.A. Kabatiansk"J and J.A. Rush)
Crystals and quasicrystals (М. Senechal)
Biological applications of computational topology (Н. Edelsbrnnner)Geometric Software
Software (М. Joswig)
Two computational geometry libraries: Leda and Cgal
(l. Kettner and S. Niiher)Jndex of Cited Аuthors
lndex of Defined Terns