SWEPT VOLUMES FROM THE COMPUTATIONAL TOPOLOGY VIEWPOINT

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MAE/AMAE GRADUATE SEMINAR SERIES April 22, 2004
330 p.m. 430 p.m. Room 107C Mechanical
Engineering Annex
SWEPT VOLUMES FROM THE COMPUTATIONAL TOPOLOGY
VIEWPOINT
Dr. Denis Blackmore Professor of Mathematical
Sciences New Jersey Institute of Technology
Newark, New Jersey
Abstract
When an object moves or is swept through space,
the totality of points that it traverses is
called its swept volume. In this talk, the
computer-aided analysis and representation of
swept volumes is studied through the lens of
computational topology - an exciting new field
that blends computer-aided geometric design with
deep concepts from geometry and topology. The
definition of a swept volume is used as a
paradigm to illustrate some fundamental questions
in computational topology related to shape,
stability and consistency of algorithms, and
effective computability of topological
invariants. It will be shown that a rigorous
mathematical approach to swept volumes yields a
number of somewhat unexpected benefits in
applications ranging from virtual sculpting to
the modeling of heterogeneous structures such as
those arising in tissue engineering. The work
reported on is part of a multidisciplinary
project being carried out in collaboration with
Ming Leu at UMR, and Bill Regli and Wei Sun at
Drexel. _________________________________________
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Department of Mechanical Aerospace Engineering
Dr. Denis Blackmore has been a Professor of
Mathematical Sciences at the New Jersey Institute
of Technology (NJIT) since 1982. Previously, he
taught at the Polytechnic University of New York,
where he earned his Ph.D. in Mathematics in 1971.
He is and has been engaged in research and
teaching in several areas embracing mathematics
and its applications such as computer-aided
geometric design, computational topology,
dynamical systems, and fluid mechanics. Over the
years, he has participated in a variety of
multidisciplinary research projects, and he
received the Harlan J. Perlis Research Award from
NJIT in 1993 for his efforts. At present, much of
his attention is devoted to a project in
computational topology in collaboration with
researchers at UMR and Drexel University.
(Refreshments Served at 315 p.m.)