Geometric Skeletons for Topologically Evolving Domains

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The objective of this award is to develop a fundamentally new approach to construct families of geometric skeletons for 2- and 3-dimensional geometric shapes that can be either rigid or undergoing drastic topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations, can generate novel, more stable skeletons, and intrinsically supports localized and parallel skeleton computations for domains with rigid or evolving boundaries. The goals of the research program are to develop new theoretical foundations for geometric skeletons as geometric and topological descriptors of shape, as well as a computational framework capable of efficiently computing local changes to the skeleton induced by local changes to the boundary of the domain.If successful, this research will lead to powerful generic algorithms for computing families of geometric skeletons for complex spatial environments. This, in turn, could transform all geometrically intensive areas of science, including almost all engineering disciplines, by providing access to new and potent descriptors of shape. Applications that would benefit from the new approach include geometric modeling of engineering artifacts, fully automated mesh generation for engineering analysis, feature recognition and defeaturing of engineering models, and real-time trajectory planning of autonomous vehicles and machine tools with adaptive geometric constraints. Furthermore, this new framework will stimulate critical new avenues of interdisciplinary research involving engineering, biology, computer science, and human-computer interaction. This program will perform targeted outreach to K-12 students, teachers and local school district serving groups that have traditionally been underrepresented in the engineering disciplines via several University of Connecticut outreach programs. The integration of geometric reasoning and algorithmic design into the engineering curriculum will help develop a new generation of engineers that will be able to exploit the capabilities of modern geometric algorithms in conjunction with traditional mechanical engineering knowledge.