The.Algorithm.Design.Manual.Springer-Verlag.1998

Computational Geometry
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Computational Geometry
Computational geometry is the algorithmic study of geometric problems and objects. Compared to the
other topics in this book, computational geometry emerged as a field quite recently, with Shamos's Ph.D.
thesis [Sha78] typically cited as its founding event. Its emergence coincided with the explosion of
computer graphics and windowing systems, which directly or indirectly provide much of the motivation
for geometric computing. The past twenty years have seen enormous growth in computational geometry,
resulting in a significant body of useful algorithms, software, textbooks, and research results.
Good books on computational geometry include:
● Preparata and Shamos [PS85] - Although aging a bit, this book remains the best general
introduction to computational geometry, stressing algorithms for convex hulls, Voronoi diagrams,
and intersection detection.
● O'Rourke [O'R94] - Perhaps the best practical introduction to computational geometry. The
emphasis is on careful and correct implementation (in C language) of the fundamental algorithms
of computational geometry. These implementations are available from
http://grendel.csc.smith.edu/ orourke/.
● Edelsbrunner [Ede87] - This is the definitive book on arrangements, a topic that runs through
most of computational geometry. Although not appropriate for beginners, it provides an important
perspective for advanced geometers.
● Mulmuley [Mul94] - An approach to computational geometry through randomized incremental
algorithms. Very interesting, but likely too narrow to serve as a general introduction.
● Nievergelt and Hindrichs [NH93] - This idiosyncratic algorithms text focuses on problems in
graphics and geometry. Good coverage of line drawing, intersection algorithms, and spatial data
structures, but with too many topics touched on too lightly to serve as an effective reference.
The leading conference in computational geometry is the ACM Symposium on Computational Geometry,
held annually in late May or early June. Although the primary results presented at the conference are
theoretical, there has been a concerted effort on the part of the research community to increase the
presence of applied, experimental work through video reviews and poster sessions. The other major
annual conference is the Canadian Conference on Computational Geometry (CCCG), typically held in
early August. Useful literature surveys include [Yao90].
A unique source of computational geometry information is geom.bib, a community effort to maintain a
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