Handbook of Discrete and Computational Geometry (3rd Edition, 2016)

Handbook of Discrete and Computational Geometry
—Third Edition—
edited by Jacob E. Goodman, Joseph O’Rourke, and Csaba D. Tóth
CRC Press LLC, to appear (2016).

http://www.csun.edu/~ctoth/Handbook/HDCG3.html
Previous editions:

  1. Handbook of Discrete and Computational Geometry, First Edition
    J.E. Goodman and J. O’Rourke, editors,
    CRC Press LLC, Boca Raton, FL, 1997.
    ISBN 978-0849385247 (52 chapters, xiv + 991 pages).
  2. Handbook of Discrete and Computational Geometry, Second Edition
    J.E. Goodman and J. O’Rourke, editors,
    CRC Press LLC, Boca Raton, FL, 2004.
    ISBN 978-1584883012 (65 chapters, xvii + 1539 pages).


Tentative Contents of the Third Edition:

COMBINATORIAL AND DISCRETE GEOMETRY

  1. Finite point configurations (J. Pach) pdf
  2. Packing and covering (G. Fejes Tóth) pdf
  3. Tilings (E. Harriss, D. Schattschneider, and M. Senechal) pdf
  4. Helly-type theorems and geometric transversals (A. Holmsen and R. Wenger) pdf
  5. Pseudoline arrangements (S. Felsner and J.E. Goodman) pdf
  6. Oriented matroids (J. Richter-Gebert and G.M. Ziegler) pdf
  7. Lattice points and lattice polytopes (A. Barvinok) pdf
  8. Low-distortion embeddings of finite metric spaces (P. Indyk, J. Matoušek, and A. Sidiropoulos) pdf
  9. Geometry and topology of polygonal linkages (R. Connelly and E.D. Demaine) pdf
  10. Geometric graph theory (J. Pach) pdf
  11. Euclidean Ramsey theory (R.L. Graham) pdf
  12. Discrete aspects of stochastic geometry (R. Schneider) pdf
  13. Geometric discrepancy theory and uniform distribution (J.R. Alexander, J. Beck, and W.W.L. Chen) pdf
  14. Polyominoes (G. Barequet, S.W. Golomb, and D.A. Klarner) pdf

POLYTOPES AND POLYHEDRA

  1. Basic properties of convex polytopes (M. Henk, J. Richter-Gebert, and G.M. Ziegler) pdf
  2. Subdivisions and triangulations of polytopes (C.W. Lee and F. Santos) pdf
  3. Face numbers of polytopes and complexes (L.J. Billera and A. Björner) pdf
  4. Symmetry of polytopes and polyhedra (E. Schulte) pdf
  5. Polytope skeletons and paths (G. Kalai) pdf
  6. Polyhedral maps (U. Brehm and E. Schulte) pdf

COMBINATORIAL AND COMPUTATIONAL TOPOLOGY

  1. Topological methods in discrete geometry (R.T. Živaljević) pdf
  2. Random simplicial complexes (M. Kahle) pdf
  3. Computational topology of graphs on surfaces (É. Colin de Verdière) pdf
  4. Persistent homology (D. Morozov and H. Edelsbrunner) pdf
  5. High-dimensional topological data analysis (F. Chazal) pdf

ALGORITHMS AND COMPLEXITY OF FUNDAMENTAL GEOMETRIC OBJECTS

  1. Convex hull computations (R. Seidel) pdf
  2. Voronoi diagrams and Delaunay triangulations (S. Fortune) pdf
  3. Arrangements (D. Halperin and M. Sharir) pdf
  4. Triangulations and mesh generation (M. Bern, J. Shewchuk, and N. Amenta) pdf
  5. Polygons (J. O’Rourke, S. Suri, and C.D. Tóth) pdf
  6. Shortest paths and networks (J.S.B. Mitchell) pdf
  7. Proximity algorithms (J.S.B. Mitchell and W. Mulzer) pdf
  8. Visibility (J. O’Rourke) pdf
  9. Geometric reconstruction problems (Y. Disser and S.S. Skiena) pdf
  10. Curve and surface reconstruction (T.K. Dey) pdf
  11. Computational convexity (P. Gritzmann and V. Klee) pdf
  12. Computational and quantitative real algebraic geometry (S Basu and B. Mishra) pdf

GEOMETRIC DATA STRUCTURES AND SEARCHING

  1. Point location (J. Snoeyink)
  2. Collision and proximity queries (Y. Kim, M.C. Lin, and D. Manocha) pdf
  3. Range searching (P.K. Agarwal) pdf
  4. Ray shooting and lines in space (M. Pellegrini) pdf
  5. Geometric intersection (D.M. Mount) pdf
  6. Nearest neighbors in high-dimensional spaces (A. Andoni and P. Indyk) pdf

COMPUTATIONAL TECHNIQUES

  1. Randomizaton and derandomization (O. Cheong, K. Mulmuley, and E. Ramos) pdf
  2. Robust geometric computation (V. Sharma and C.K. Yap) pdf
  3. Parallel algorithms in geometry (N. Sitchinava and M.T. Goodrich) pdf
  4. Epsilon-nets and epsilon-approximations (N. Mustafa and K. Varadarajan) pdf
  5. Coresets and sketches (J. Phillips) pdf

APPLICATIONS OF DISCRETE AND COMPUTATIONAL GEOMETRY

  1. Linear programming (M. Dyer, B. Gartner, N. Megiddo, and E. Welzl) pdf
  2. Algorithmic motion planning (D. Halperin, O. Salzman, and M. Sharir) pdf
  3. Robotics (D. Halperin, L.E. Kavraki, and K. Solovey) pdf
  4. Computer graphics (D. Dobkin and S. Teller) pdf
  5. Modeling motion (L.J. Guibas and M. Roeloffzen) pdf
  6. Pattern recognition (J. O’Rourke and G.T. Toussaint) pdf
  7. Graph drawing (E. Di Giacomo, R. Tamassia, and G. Liotta) pdf
  8. Splines and geometric modeling (C.L. Bajaj) pdf
  9. Surface simplification and 3D geometry compression (J. Rossignac)
  10. Solid modeling (C.M. Hoffmann and V. Shapiro) pdf
  11. Computation of robust statistics: Depth, median, and related measures (M. Hubert and P.J. Rousseeuw) pdf
  12. Geographic information systems (M. van Kreveld) pdf
  13. Geometric applications of the Grassmann-Cayley algebra (N.L. White) pdf
  14. Rigidity and scene analysis (B. Schulze and W. Whiteley) pdf
  15. Rigidity of symmetric frameworks (B. Schulze and W. Whiteley) pdf
  16. Global rigidity (T. Jordan and W. Whiteley) pdf
  17. Crystals, periodic and aperiodic (M. Senechal) pdf
  18. Applications to structural molecular biology (H. Edelsbrunner and P. Koehl) pdf
  19. Geometry and topology of genomics (A.J. Blumberg and R. Rabadán) pdf

GEOMETRIC SOFTWARE

  1. Software (M. Joswig and B. Lorenz) pdf
  2. Two computational geometry libraries: LEDA and CGAL (M. Hoffmann, L. Kettner, and S. Näher) pdf

Index of cited authors
Index of defined terms

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