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.

Combinatorial computational geometry[edit]

General-purpose textbooks[edit]

Specialized textbooks and monographs[edit]

References[edit]

  • Jacob E. Goodman and Joseph O'Rourke (editors) (2004) [1997]. Handbook of Discrete and Computational Geometry. North-Holland. 1st edition: ISBN 0-8493-8524-5, 2nd edition: ISBN 1-58488-301-4. 
    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]
  • Jörg-Rudiger Sack and Jorge Urrutia (1998). Handbook of Computational Geometry. North-Holland. 1st edition: ISBN 0-444-82537-1, 2nd edition (2000): 1-584-88301-4. 
    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.
  • Ding-Zhu Du and Frank Hwang (1995). Computing in Euclidean Geometry. Lectures Notes Series on Computing 4 (2nd ed.). World Scientific. ISBN 981-02-1876-1. 
    "This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry."[10] Its 11 chapters cover quantitative geometry, a history of computational geometry, mesh generation, automated generation of geometric proofs, randomized geometric algorithms, Steiner tree problems, Voronoi diagrams and Delaunay triangulations, constraint solving, spline surfaces, network design, and numerical primitives for geometric computing.

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

Monographs[edit]

Other[edit]

Conferences[edit]

The conferences below, of broad scope, published many seminal papers in the domain.

Paper collections[edit]

  • "Combinatorial and Computational Geometry", eds. Jacob E. Goodman, János Pach, Emo Welzl (MSRI Publications – Volume 52), 2005, ISBN 0-521-84862-8.
    • 32 papers, including surveys and research articles on geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their computational complexity, and the combinatorial complexity of geometric objects.
  • "Surveys on Discrete and Computational Geometry: Twenty Years Later" ("Contemporary Mathematics" series), American Mathematical Society, 2008, ISBN 0-8218-4239-0

See also[edit]

References[edit]

  1. ^ MR 0805539, MR 1004870
  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 MR 1211180 (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.
  10. ^ From the flyleaf of the book.

External links[edit]