CAREER: Multiresolution Foundations for Physics-Based Computer Animation and Interactive Engineering Design

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Multiresolution Foundations for Physics-Based Computer Animation and Interactive Engineering DesignPI: Eitan Grinspun, Columbia UniversityPhysical simulations enable scientists and engineers to study complex systems for which direct, controlled experimentation is costly, dangerous, or intractable. Exploratory studies enable engineers to gather qualitative intuition, or feel for the subject system, which in turn leads to the posing of new hypotheses and directions for experimentation. While exploratory processes are inherently interactive, today's computational barriers limit the exploration of important systems to non-interactive modalities. This research seeks to overcome these obstacles with novel methods that quickly but coarsely resolve the physics, skipping over irrelevant data to capture only the coarse variables that drive design decisions. The investigators develop simulation techniques that address the vision of a rapid, interactive design cycle, with a specific focus on the physical simulation of thin shells flexible surfaces such as air bags, biological membranes, and textiles, with pervasive applications in automotive design, biomedical device optimization, and feature film production. In a synergistic pedagogical thrust, this project trains young scientists with a deep understanding of computation, mathematics, and application domain areas despite being in high demand, this combination of skills remains rare.The investigators are developing a principled, methodical approach to coarsening an existing discrete geometric model of a mechanical system, using adaptive, multi-resolution decompositions. Whereas adaptivity is commonly studied in the context of error estimators for mesh refinement, interactivity suggests a focus on how best to give up precision in a simulation. Therefore, this research (i) builds on early work in the field of discrete differential geometry to formulate coarse geometric representations of physical systems that preserve key geometric and physical invariants, (ii) investigates the convergence, resolution- and meshing-dependence of discrete differential operators, and (iii) contributes toward a software platform for interactive design space exploration with concrete applications in automotive, biomedical, and feature-film engineering.