ITR/AP: Interactive Spatial Physics: Computational Foundations and Systems

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The goal of this project is to develop an interactive geometric approach to creating, editing, transforming, and computing with models of spatially distributed physical phenomena. The funded effort will involve fleshing out sound theoretical foundations, developing appropriate data structures and algorithms, as well as implementing a prototype system for interactive physical modeling. At the heart of the proposal is a novel use of tools from algebraic topology and geometric algebra to describe, classify, and unify physical phenomena. The prototype system will allow users to create models of physical phenomena through an interactive geometric interface designed in terms of familiar and intuitive control elements. The created models may be interactively transformed, modified, combined, visualized, and instantiated. The successful outcome of the proposed research should have broad technological, economic, educational, and social impact. The physics editor will allow users to create, visualize, test, and experiment with new models of physical phenomena quickly and effortlessly. It could greatly enhance the ability to efficiently create and modify scientific software that is modular, reusable, and consistent across the disciplinary boundaries. Engineers may discover a practical tool that will allow them to communicate with computer-aided design systems in a visual intuitive language that does not require deep mathematical knowledge and unifies a multitude of theories and special cases. And perhaps most importantly, the proposed research could open doors of computational sciences to college and high school students and others who may have been discouraged or intimidated by traditional methods of mathematical physics and scientific computing.