List of books in computational geometry

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This is a list of books in computational geometry. There are two major, largely nonoverlapping categories:

  • Combinatorial computational geometry, which deals with collections of discrete objects or defined in discrete terms: points, lines, polygons, polytopes, etc., and algorithms of discrete/combinatorial character are used
  • Numerical computational geometry, also known as geometric modeling and computer-aided geometric design (CAGD), which deals with modelling of shapes of real-life objects in terms of curves and surfaces with algebraic representation.

Contents

[edit] Combinatorial computational geometry

[edit] Textbooks and monographs

  • Franco P. Preparata and Michael Ian Shamos (1985). Computational Geometry - An Introduction. Springer-Verlag. 1st edition: ISBN 0-387-96131-3; 2nd printing, corrected and expanded, 1988: ISBN 3-540-96131-3; Russian translation, 1989: ISBN 5-03-001041-6. 
    The book is the first comprehensive monograph on the level of a graduate textbook to systematically cover the fundamental aspects of the emerging discipline of computational geometry. It is written by founders of the field and the first edition covered all major developments in the preceding 10 years. In the aspect of comprehensiveness it was preceded only by the 1984 survey paper, Lee, D, T., Preparata, F. P. : "Computational geometry - a survey". IEEE Trans. on Computers. Vol. 33, No. 12, pp. 1072-1101 (1984). It is focused on two-dimensional problems, but also has digressions into higher dimensions.[1] [2]
    The initial core of the book was M.I.Shamos' doctoral disserttion, which was suggested to turn into a book by a yet another pioneer in the field, Ronald Graham.
    The introduction covers the history of the field, basic data structures, and necessary notions from the theory of computation and geometry.
    The subsequent sections cover geometric searching (point location, range searching), convex hull computation, proximity-related problems (closest points, computation and applications of theVoronoi diagram, Euclidean minimum spanning tree, triangulations, etc.), geometric intersection problems, algorithms for sets of isothetic rectangles
  • Herbert Edelsbrunner (1987). Algorithms in Combinatorial Geometry. Springer-Verlag. ISBN 0-89791-517-8. 
    The monograph is a rather advanced exposition of problems and approaches in computational geometry focused on the role of hyperplane arrangements, which are shown to constitute a basic underlying combinatorial-geometric structure in certain areas of the field. The primary target audience are active theoretical researchers in the field, rather than application developers. Unlike most of books in computational geometry focussed on 2- and 3-dimensional problems (where most applications of computational geometry are), the book aims to treat its subject in the general multi-dimensional setting. [3]
  • Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000). Computational Geometry, 2nd revised edition, Springer-Verlag. ISBN 3-540-65620-0, 1st edition (1987): ISBN 3-540-61270-X. 
    The textbook provides an introduction to computation geometry from the point of view of practical applications. Starting with an introducion chapter, each of the 15 remaining ones formulates a real application problem, formulates an underlying geometrical problem, and discusses techniques of computational geometry useful for its solution, with algorithms provided in pseudocode. The book treats mostly 2- and 3-dimensional geometry. The goal of the book is to provide a comprehensive introduction into methods and approached, rather than the cutting edge of the research in the field: the presented algorithms provide transparent and reasonably efficient solutions based on fundamental "building blocks" of computational geometry. [4][5]
    The book consists of the following chapters (which provide both solutions for the topic of the title and its appilications): "Computational Geometry (Introduction)" "Line Segment Intersection", "Polygon Triangulation", "Linear Programming", "Orthogonal Range Searching", "Point Location", "Voronoi Diagrams", "Arrangements and Duality", "Delaunay Triangulations", "More Geometric Data Structures", "Convex Hulls", "Binary Space Partitions", "Robot Motion Planning", "Quadtrees", "Visibility Graphs", "Simplex Range Searching".
  • Jean-Daniel Boissonnat, Mariette Yvinec (1998). Algorithmic Geometry, Translation of a 1995 French edition, Cambridge University Press. ISBN 0-521-56529-4. 
  • Kurt Mehlhorn (1984). Data Structures and Efficient Algorithms 3: Multi-dimensional Searching and Computational Geometry. Springer-Verlag. 
  • Ketan Mulmuley (1994). Computational Geometry: An Introduction Through Randomized Algorithms. Prentice-Hall. ISBN 0-13-336363-5. 
  • Joseph O'Rourke (1998). Computational Geometry in C, 2nd edition, Cambridge University Press. ISBN 0-521-64976-5. 
  • Janos Pach and Pankaj K. Agarwal (1995). Combinatorial Geometry. John Wiley and Sons. ISBN 0-471-58890-3. 
  • Micha Sharir and Pankaj K. Agarwal (1995). Davenport-Schinzel Sequences and Their Geometric Applications. Cambridge University Press. ISBN 0-521-47025-0. 
  • Kurt Mehlhorn and Stefan Naeher (1999). LEDA, A Platform for Combinatorial and Geometric Computing. Cambridge University Press. ISBN 0-521-56329-1. 
  • Jörg-Rudiger Sack and Jorge Urrutia (1998). Handbook for Computational Geometry. North-Holland. 1st edition: ISBN 0-444-82537-1, 2nd edition: 1-584-88301-4. 
  • Selim G. Akl and Kelly A. Lyons (1993). Parallel Computational Geometry. Prentice-Hall. ISBN 0-13-652017-0. 
    The books discusses parallel algorithms for basic problems in computational geometry in various models of parallel computation. [6]
  • Joseph O'Rourke (1987). Art Gallery Theorems and Algorithms. Oxford University Press. 
  • Hanan Samet (1990). The Design and Analysis of Spatial Data Structures. Addison-Wesley. 
  • Clara I. Grima and Alberto Márquez (1990). Computational Geometry on Surfaces: Performing Computational Geometry on the Cylinder, the Sphere, the Torus, and the Cone. Kluwer Academic Publishers. 1402002025. 
    The book shows how classical problems of computational geometry and algorithms for their solutions may be adapted or redesigned to work on surfaces other than plane. After defining notations and ways of positioning on these surfaces, the book considers the problems of the construction of convex hulls, Voronoi diagrams, and triangulations, proximity problems, and visibility problems.
  • Ghosh, Subir Kumar (2007). Visibility Algorithms in the Plane. Cambridge University Press. ISBN 0521875749. 
    Contents: Preface; 1. Background; 2. Point visibility; 3. Weak visibility and shortest paths; 4. L-R visibility and shortest paths; 5. Visibility graphs; 6. Visibility graph theory; 7. Visibility and link paths; 8. Visibility and path queries[7]
  • Giri Narasimhan, Michiel Smid (2007). Geometric Spanner Networks. Cambridge University Press. ISBN 0521815134. 
    Contents:[8]
    • Part I. Introduction: 1. Introduction; 2. Algorithms and graphs; 3. The algebraic computation-tree model;
    • Part II. Spanners Based on Simplical Cones: 4. Spanners based on the Q-graph; 5. Cones in higher dimensional space and Q-graphs; 6. Geometric analysis: the gap property; 7. The gap-greedy algorithm; 8. Enumerating distances using spanners of bounded degree;
    • Part III. The Well Separated Pair Decomposition and its Applications: 9. The well-separated pair decomposition; 10. Applications of well-separated pairs; 11. The Dumbbell theorem; 12. Shortcutting trees and spanners with low spanner diameter; 13. Approximating the stretch factor of Euclidean graphs;
    • Part IV. The Path Greedy Algorithm: 14. Geometric analysis: the leapfrog property; 15. The path-greedy algorithm; Part V. Further Results and Applications: 16. The distance range hierarchy; 17. Approximating shortest paths in spanners; 18. Fault-tolerant spanners; 19. Designing approximation algorithms with spanners; 20. Further results and open problems.

[edit] References

  • Jacob E.Goodman and Joseph O'Rourke (editors) (1997, 2004). Handbook for Computational Geometry. North-Holland. 1st edition: ISBN 0-8493-8524-5, 2nd edition: ISBN 1-584-88301-4. 
    In its organization, the book resembles the classical handbook in algorithms, Introduction to Algorithms, in its comprehensiveness, only restricted to discrete and computational geometry, computational topology, as well as a broad range of their applications. The second edition expands the book by half, with 14 chapters added and old chapters brought up to date. Its 65 chapters (in over 1,500 pages) are written by a large team of active researchers in the field. [9]
  • J. R. Sack and J. Urrutia (eds.) (2000). Handbook of Computational Geometry. North Holland. ISBN 0-44482-537-1. 
    The handbook contains survey chapters in classical and new studies in geometric algorithms: hyperplane arrangements, Voronoi diagrams, geometric and spatial data structures, polygon decomposition, randomized algorithms, derandomization, parallel computational geometry (deterministic and randomized), visibility, Art Gallery and Illumination Problems, closest point problems, link distance problems, similarity of geometric objects, Davenport-Schinzel sequences, spanning trees and spanners for geometric graphs, robustness and numerical issues for geometric algorithms, animation, and graph drawing.
    In addition, the book surveys applications of geometric algorithms in such areas as geographic information systems, geometric shortest path and network optimization and mesh generation.

[edit] Numerical computational geometry (geometric modelling, computer-aided geometric design)

[edit] Monographs

[edit] Other

[edit] Conferences

  • Annnual Symposium on Computational Geometry
  • Canadian Conference on Computational Geometry (CCCG)
  • Japanese Conference on Discrete and Computational Geometry (JCDCG)
  • The conferences below, of broad scope, published many seminal papers in the domain
    • Annual ACM Symposium on Theory of Computing (STOC)
    • Annual IEEE Symposium on Foundations of Computer Science (FOCS)
    • Annual Allerton Conference on Communications, Control and Computing (ACCC)

[edit] References

  1. ^ MR0805539, MR1004870
  2. ^ Zbl 0575.68037, Zbl 0575.68059
  3. ^ A review of Edelsbrunner's book in Zbl 0634.52001
  4. ^ Reviews in Zbl 0877.68001 (1st ed.), Zbl 0939.68134 (2nd ed.)
  5. ^ About the book by de Berg, van Kreveld, Overmars, and Schwarzkopf
  6. ^ A review of the Akl-Lyons book in MR1211180 (94c:68192)
  7. ^ "Visibility Algorithms in the Plane", from the Cambridge University Press catalogue
  8. ^ "Geometric Spanner Networks", from the Cambridge University Press catalogue
  9. ^ A review of the Handbook for Computational Geometry in Geombinatorics, January 2005.