Hierarchical Solving of Symbolic Problems in Heterogeneous Geometry Environments

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Hierarchical Solving of Symbolic Problems in Heterogeneous Geometry EnvironmentsPI: Elaine Cohen, Co-PI Richard F. RiesenfeldSchool of Computing, University of UtahAbstractMany important types of problems can be posed in a mathematical form, yet many real-world applications do not provide data in a form that can be used by traditional mathematical solvers. For example, medical models may be made of a 3D volume of point samples rather than the smooth models needed by the mathematical solvers. This research involves unifying these multiple, important methods of representing real-world data with the power of mathematical solvers by using methods based on robust geometry to solve problems. The investigators will use these results in applications for computer prototyping of mechanical systems and for computer-based surgical training. This research should be able to provide such tools as virtual calipers for imaged tumors or force-feedback interaction with complex medical data in the medical realm, and checking the fit of a CAD modeled mechanical part with a laser-scanned real part in the engineering realm.This research proposes to use hierarchical, geometric representations to compute solutions of symbolic problems, thereby expanding the applicability of symbolic solvers to areas where the data may not be in the form of equations. Examples of such applications include real-world applications in engineering and medicine. Because this approach relies on bounds to intrinsic geometric properties, rather than manipulating only the underlying representations directly, the approach also will allow a single application problem to have several different model representations mixed together. This arises in complex problems where some data may be analytical, some acquired, and some just rough approximations.