•   When: Monday, November 27, 2023 from 01:00 PM to 03:00 PM
•   Speakers: Josef Graus
•   Location: ENGR 1602
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Shape similarity is a fundamental problem in geometry processing, enabling applications such as surface correspondence, segmentation, and edit propagation. Commensurable shape signatures ideally emit unique measures of surface features at multiple scales around a point. However, the computational cost of metrics that are well behaved and sufficiently describe complex geometries is prohibitively high. Furthermore, purely geometric descriptions do not sufficiently address modeling intentions of human operators. Compounding these issues, mesh creation user applications must contend with supplying realtime feedback for editing tools routinely posed as numerical optimization problems. There is a significant amount of redundant processing in recomputing configuration space minima/maxima. While comprehensively mapping objective function energy basins can quickly become intractable, there is unused information uncovered by user interaction to infer structure about function energy landscapes. This dissertation explores shape signatures and proposes Smoothed Shape Diameter Signature (SSDS) as a superior replacement for mesh comparability. It also addresses inefficiencies in gradient-descent numerical optimization when employed in realtime user editing applications by examining objective function surfaces and sparse hyperspace solver solution trajectories.