EXPLORING COMPUTATIONAL TOPOLOGY
Denis Blackmore, PhD, professor of mathematical sciences, works in the new and expanding field of computational topology, the study of basic and subtle aspects of the shapes of objects created by algorithmic means with the help of a computer. He is one of only a handful of experts nationally to win grant support from the joint NSF/DARPA initiative on Computational and Algorithmic Representations of Geometric Objects (CARGO). His team will study configurations generated by sweeping objects along a path through space, with the goal of developing new virtual reality systems for design and manufacturing and devising novel methods for modeling biological materials.
Computational topology involves a combination of techniques from computer aided geometric design, computer science, differential geometry, differential topology, and dynamical systems theory aimed at producing accurate and efficient computer programs, that include effectively computable criteria for analyzing shape characteristics, for representing geometric objects.
Dr. Blackmore has assembled an interdisciplinary team of researchers, comprised of Ming Leu, (manufacturing engineering, University of Missouri-Rolla, and William Regli and Wei Sun, computer science and information systems, Drexel University, to study configurations generated by sweeping objects along a path in space. Their goal for this CARGO project is to make some fundamental theoretical contributions in the field of computational topology that will be translated into useful algorithms, and to explore applications of the results to modeling heterogeneous biological materials, such as bones, and in the development of new virtual reality systems for design and manufacturing.