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SWEPT VOLUMES FROM THE COMPUTATIONAL TOPOLOGY VIEWPOINT

MAE/AMAE GRADUATE SEMINAR SERIES April 22, 2004 3:30 p.m. – 4:30 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.

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SWEPT VOLUMES FROM THE COMPUTATIONAL TOPOLOGY VIEWPOINT

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  1. MAE/AMAE GRADUATE SEMINAR SERIES April 22, 2004 3:30 p.m. – 4:30 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. _______________________________________________________________________ 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 3:15 p.m.)

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