An original motivation for algebraic geometry was to understand
curves and surfaces in three dimensions. Recent theoretical and
technological advances in areas such as robotics, computer vision,
computer-aided geometric design and molecular biology, together
with the increased availability of computational resources, have
brought these original questions once more into the forefront of
research. One particular challenge is to combine applicable methods
from algebraic geometry with proven techniques from
piecewise-linear computational geometry (such as Voronoi diagrams
and hyperplane arrangements) to develop tools for treating curved
objects. These research efforts may be summarized under the term
nonlinear computational geometry. This volume grew out of an IMA
workshop on Nonlinear Computational Geometry in May/June 2007
(organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald)
which gathered leading experts in this emerging field. The research
and expository articles in the volume are intended to provide an
overview of nonlinear computational geometry. Since the topic
involves computational geometry, algebraic geometry, and geometric
modeling, the volume has contributions from all of these areas. By
addressing a broad range of issues from purely theoretical and
algorithmic problems, to implementation and practical applications
this volume conveys the spirit of the IMA workshop.
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