While books and journals of high quality have proliferated in discrete and compu-
tational geometry during recent years, there has been to date no single reference
work fully accessible to the nonspecialist as well as to the specialist, covering all
the major aspects of both fields. The Handbook of Discrete and Computational
Geometry is intended to do exactly that: to make the most important results and
methods in these areas of geometry readily accessible to those who use them in
their everyday work, both in the academic world—as researchers in mathematics
and computer science—and in the professional world—as practitioners in fields as
diverse as operations research, molecular biology, and robotics.
A significant part of the growth that discrete mathematics as a whole has
experienced in recent years has consisted of a substantial development in discrete
geometry. This has been fueled partly by the advent of powerful computers and
by the recent explosion of activity in the relatively young field of computational
geometry. This synthesis between discrete and computational geometry, in which
the methods and insights of each field have stimulated new understanding of the
other, lies at the heart of this Handbook.
The phrase "discrete geometry," which at one time stood mainly for the areas
of packing, covering, and tiling, has gradually grown to include in addition such
areas as combinatorial geometry, convex polytopes, and arrangements of points,
lines, planes, circles, and other geometric objects in the plane and in higher dimen-
sions. Similarly, "computational geometry," which referred not long ago to simply
the design and analysis of geometric algorithms, has in recent years broadened its
scope, and now means the study of geometric problems from a computational point
of view, including also computational convexity, computational topology, and ques-
tions involving the combinatorial complexity of arrangements and polyhedra. It
is clear from this that there is now a significant overlap between these two fields,
and in fact this overlap has become one of practice as well, as mathematicians and
computer scientists have found themselves working on the same geometric problems
and have forged successful collaborations as a result.
At the same time, a growing list of areas in which the results of this work are
applicable has been developing. It includes areas as widely divergent as engineer-
ing, crystallography, computer-aided design, manufacturing, operations research,
geographic information systems, robotics, error-correcting codes, tomography, geo-
metric modeling, computer graphics, combinatorial optimization, computer vision,
pattern recognition, and solid modeling.
