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68U: Computer graphics and computational geometry


Introduction

At present there is really nothing here regarding computer graphics per se; this is primarily focused on computational geometry.

In keeping with the general pattern of use of the Mathematics Subject Classifications, computational topics primarily focused on geometry are classified in sections 51: Geometry and 52: Convex Geometry and their subareas such as 52B: Polygons and polyhedra. This classification is intended for topics whose geometric aspects are fairly straightforward, but for which the main questions involve efficient, accurate computation.

Many geometric questions arise involving large sets of points (e.g. which of these points are closest together?) which are arguably combinatorics or statistics, but we have included them here.

History

Applications and related fields

Some problems (e.g. finding the best circle passing through some points) are considered Statistics.

Subfields

Parent field: 68U - Computing methodologies. But there is not yet a page for that; see its parent page, Computer Science.


Textbooks, reference works, and tutorials

Matousek, Jirí: "Mathematical snapshots from the computational geometry landscape", Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Doc. Math. 1998, Extra Vol. III, 365--375 (electronic). CMP1648170

Many of these questions arise in the USENET newsgroup comp.graphics.algorithms. Fortunately, that group has a nice FAQ file, the latest version of which may be found at the MIT USENET FAQ site. (The latest copy resides at rtfm.mit.edu:/usenet/comp.graphics.algorithms) There is also a moderated newsgroup comp.graphics.research .

Here is a list of books in computational geometry.

The book by de Berg, Mark; van Kreveld, Marc; Overmars, Mark; Schwarzkopf, Otfried: "Computational geometry, Algorithms and applications", Springer-Verlag, Berlin, 1997. 365 pp. ISBN 3-540-61270-X, appears to be a nice textbook [not reviewed].

Book announcement: The Handbook Of Discrete And Computational Geometry, J. E. Goodman and J. O'Rourke, editors. (Intended for applications, not development of the theory.)

Software and tables

GAMS Computational geometry and Graphics software.

Computational Geometry package for Mathematica

LEDA is designed for computational geometry and combinatorics.

Other web sites with this focus

Selected topics at this site


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Last modified 2000/08/14 by Dave Rusin. Mail: