Computer graphics draws on ideas from applied mathematics, differential geometry, and engineering to develop simple computational models for simulating the behavior and appearance of physical systems. With this in mind, I will present two significant contributions, Multiresolution Simulation and Discrete Models. Both demonstrate that simplicity in computational models often leads to more geometric insight, wider adoption and the opportunity to pursue more ambitious applications to mechanical engineering, medicine, biology, and computer graphics without sacrificing accuracy or performance.

Multiresolution Simulation promises superior scalability of simulators with respect to large datasets and high geometric complexity. Although adaptive solvers can significantly reduce the computational cost of simulations, building such solvers has been a daunting task. The framework I will present removes a number of implementation headaches associated with earlier approaches and is a general technique independent of domain dimension (e.g., 2D and 3D), element type (e.g., triangle, quad), and approximation order. I will demonstrate the versatility of this new approach via applications to medical imaging, surgical assistance, and mechanical engineering.

Discrete Models are geometric descriptions of physical phenomena distilled into a fundamentally discrete form. This exciting, emerging field promises to shed new geometric insight on well-studied physical phenomena. The model that I will present, Discrete Shells, reformulates the equations governing the behavior of thin, flexible objects as discrete operators over a triangle mesh. I will show novel animations of Discrete Shells, discuss the validity of our approach, and present plans for future endeavors.

Dr. Eitan Grinspun is a postdoctoral researcher at the Media Research Lab of the Courant Institute, NYU. In June 2003 he received a doctorate from Caltech for his contribution to the engineering and graphics communities, the Basis Refinement Method. During his graduate career, Eitan pursued a diverse range of research topics in simulation, modeling, GPU computation, as well as a Masters degree in asynchronous VLSI. He received an NVIDIA fellowship in 2001, and was chosen as an Everhart Distinguished Graduate Lecturer in 2003.