Computational Geometry
Books

In the future, this page may include short reviews of each book. If you are familiar with any of these books and would like to contribute a review, please send me email. I would especially like to hear from anyone who has used any of these books as textbooks, either as students or teachers.

Michel Pocchiola also has several web pages listing computational geometry books, collections, and monographs, and a few books on polytopes.

Computational Geometry Textbooks

• Computational Geometry, Algorithms and Applications
  by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf
  Springer­Verlag, 1997.
  • Table of contents
  • Other recommended textbooks
  • Ordering information from Springer

• Algorithmic Geometry (also here and here)
  by Jean-Daniel Boissonnat and Mariette Yvinec, translated by Hervé Brönnimann
  Cambridge University Press, 1998.

• Géométrie Algorithmique (en français)
  by Jean-Daniel Boissonnat and Mariette Yvinec
  Ediscience International, 1995

• Algorithms in Combinatorial Geometry
  by Herbert Edelsbrunner
  EATCS Monographs in Computer Science 10, Springer­Verlag, 1987

• Algorithmische Geometrie (auf deutsch)
  by Rolf Klein
  Addison-Wesley, 1996

• Computational Geometry and Computer Graphics in C++
  by Michael J. Laszlo (Nova Southeastern University)
  Prentice-Hall, 1996.
  Not recommended.

• Data Structures and Efficient Algorithms 3: Multi-dimensional Searching and Computational Geometry
  by Kurt Mehlhorn
  EATCS Monographs in Computer Science 3, Springer­Verlag, 1984
  Out of print.

• Computational Geometry: An Introduction Through Randomized Algorithms
  by Ketan Mulmuley
  Prentice-Hall, 1994

• Computational Geometry in C
  by Joseph O'Rourke
  Cambridge University Press, second edition, 1998
  • Source code (in both C and Java) and errata
  • Computational Geometry applet illustrating several pieces of code from the book
  • Information about the first edition is still available.

• Computational Geometry: An Introduction
  by Franco P. Preparata and Michael Ian Shamos
  Springer­Verlag, 1985

• Einführung in graphisch-geometrische Algorithmen (auf deutsch)
  by Alfred Schmitt, Oliver Deussen, and Marion Kreeb
  B. G. Teubner, 1996
  [Has anyone actually seen this book? -Jeff]

Surveys and Collections

• Keisankikagaku Risankagaku (Computational and Discrete Geometry)
  by David Avis and Hiroshi Imai
  Asakura, Tokyo, 1994. In Japanese, 150pp.

• Advances in Discrete and Computational Geometry
  Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference "Discrete & Computational Geometry: Ten Years Later", July 1996.
  Edited by Bernard Chazelle, Jacob E. Goodman, and Richard Pollack,
  Contemporary Mathematics series
  Americal Mathematical Society, Providence, in preparation.

• Computational Geometry
  Edited by Godfried T. Toussaint
  North-Holland, Amsterdam, 1985
  Out of print.

• Computational Morphology
  Edited by Godfried T. Toussaint
  North-Holland, Amsterdam, 1988
  Out of print.

• Computing in Euclidean Geometry (2nd edition)
  Edited by Ding-Zhu Du and Frank Hwang
  Lectures Notes Series on Computing 4
  World Scientific, Singapore, 1995

• Algorithmic Foundations of Robotics
  Edited by Ken Goldberg, Dan Halperin, Jean-Claude Latombe, and Randall Wilson
  A K Peters, Ltd., 1995

• Handbook of Discrete and Computational Geometry
  Edited by Jacob E. Goodman and Joseph O'Rourke
  CRC Press, 1997.

• Discrete and Computational Geometry: Papers from the DIMACS Special Year
  Edited by Jacob E. Goodman, Richard Pollack, and William Steiger
  DIMACS Series in Discrete Mathematics and Computer Science 6
  American Mathematical Society, 1992

• Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift
  Edited by Peter Gritzmann and Bernd Sturmfels
  DIMACS Series in Discrete Mathematics and Computer Science 4
  American Mathematical Society, 1991

• Directions in Geometric Computing
  Edited by Ralph Martin
  Information Geometers Ltd, 1993

• New Trends in Discrete and Computational Geometry
  Edited by János Pach
  Algorithms and Combinatorics 10
  Springer­Verlag, 1995.

• Fundamentos de Geometria Computacional (em Português)
  by Pedro J. de Resende and Jorge Stolfi
  Preparado para a IX Escola de Computação (Recife, Brasil, 1994)
  Departmento de Informatica da Universidade Federal de Pernambuco, Brasil, 1994

• Handbook for Computational Geometry
  Edited by Jorge Urrutia and Jörg-Rudiger Sack
  North-Holland, in preparation.

Specialized and Related Topics

• Parallel Computational Geometry
  by Selim G. Akl and Kelly A. Lyons
  Prentice-Hall, 1993

• Oriented Matroids
  by Anders Björner, Michel Las Vergnas, Bernd Sturmfels, Neil White, and Günter Ziegler
  Encyclopedia of Mathematics and its Applications 46
  Cambridge University Press, 1993
  • For updates and corrections, see Ziegler's ``Oriented Matroids Today'', a dynamic survey of the Electronic Journal of Combinatorics.

• Algebraic Complexity Theory (also here)
  by Peter Bürgisser, Michael Clausen, and Amin Shokrollati
  Grundlehren der mathematischen Wissenschaften 315, Springer­Verlag, 1996

• The Discrepancy Method
  by Bernard Chazelle
  In preparation, 1998.

• Graph Drawing: Algorithms for the Visualization of Graphs
  by Giuseppe Di Battista Peter Eades, Roberto Tamassia, and Ioannis G. Tollis
  Prentice-Hall, 1998.

• An Introduction to Computational Geometry for Curves and Surfaces
  by Alan Davies and Philip Samuels
  Oxford University Press, 1996.
  [This is the British use of the phrase ``computational geometry''; Americans would call it ``computer­aided geometric design''.]

• Triangulation de Delaunay et maillage: applications aux éléments finis (en français)
  by Paul-Louis George and Houman Bourachaki
  Editions Hermes, 1997
  English translation: Delaunay Triangulation and Meshing: Application to Finite Elements, 1998.

• Geometric Discrepancy: An Illustrated Guide
  by Jirí Matousek
  Springer-Verlag, 1998.

• Randomized Algorithms
  by Rajeev Motwani and Prakhabar Raghavan
  Cambridge University Press, 1995

• Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
  by Atsuyuki Okabe, Barry Boots, and Kokichi Sugihara
  John Wiley & Sons, 1992
  Table of Contents from GIS World

• Art Gallery Theorems and Algorithms
  by Joseph O'Rourke
  Oxford University Press, 1987

• Combinatorial Geometry
  by János Pach and Pankaj K. Agarwal
  John Wiley & Sons, 1995

• Applications of Spatial Data Structures
  by Hanan Samet
  Addison-Wesley, Reading, MA, 1990
  Table of Contents from GIS World

• The Design and Analysis of Spatial Data Structures
  by Hanan Samet
  Addison-Wesley, Reading, MA, 1990
  Table of Contents from GIS World

• Davenport-Schinzel Sequences and Their Geometric Applications
  by Micha Sharir and Pankaj K. Agarwal
  Cambridge University Press, 1995.

• The Algorithm Design Manual
  by Steven S. Skeina
  TELOS/Springer­Verlag, 1997
  Code from the book is collected at the The Stony Brook Algorithms Repository.

• Contouring: A Guide to the Analysis and Display of Spatial Data
  by David Watson
  Pergamon Press, 1992.

• Lectures on Polytopes
  by Günter Ziegler
  Graduate Texts in Mathamatics 152
  Springer­Verlag, 1995. Corrected 2nd printing, 1997.
  • "Updates, Corrections, and More!"
  • Convex hull code

Publishers

• Academic Press: US or UK
• ACM
• Addison-Wesley
• AMS
• Cambridge University Press: New York or Cambridge
• Elsevier Science (Amsterdam)
• Information Geometers Ltd.
• Kluwer: US or Netherlands
• MIT Press
• SIAM
• Springer­Verlag: TELOS, Berlin/Heidelberg, London, or New York
• World Scientific (Singapore)
• John Wiley & Sons