CAREER: Fast, Predictive Modeling and Simulation in Computer Graphics: Theoretical and Computational Foundations

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0133983Desbrun, MathieuU of Southern CaliforniaThe primary research objective in this project is to develop new mathematical and computational tools for irregular sampling in Computer Graphics. Digital geometry is rapidly emerging as a new ubiquitous medium, complementing the previous electronic datatypes for sound, images and movies. However, geometry requires to deal with irregular, non-uniform sampling living on curved manifolds, a radically different problematic that calls for novel, fundamental tools. Thus, this work is targeted towards a better understanding and handling of irregular sampling. Building on our theoretical results, we will develop new practical algorithms for fast and predictive modeling and/or simulation. We will establish a unified foundation for discrete/differential geometry, defining mimetic discretizations of the continuous case.This project will provide both theoretical foundations in the nascent field of Computational Differential Geometry, and robust, reliable tools that will advance the field of Computer Graphics. These foundations and computational tools will facilitate and accelerate the expansion of 3D models in our everyday life, be it in software products (ranging from games to computer-aided segmentation of MRI data), on the web for downloads, or even on small PDAs with 3D scanning abilities. The large number of immediate applications demonstrates the significance of this research:- Compression of 3D objects for optimal storage and transmission;- Modeling of 3D objects, including texturing, editing, smoothing;- Haptic rendering and sculpting of virtual objects;- Realtime virtual surgery training and planning.The educational aspect of the project includes initiatives designed to incorporate the project advancements in the graduate and undergraduate curriculum. The long-term impact of this work will likely be seen in fields that have significant geometric and computational components, such as biology, medicine, and geology.