This paper extends Galerkin projection to a large class of non-polynomial functions typically encountered in graphics. We demonstrate the broad applicability of our approach by applying it to two strikingly different problems: fluid simulation and radiosity rendering, both using deforming meshes. Standard Galerkin projection cannot efficiently approximate these phenomena. Our approach, by contrast, enables the compact representation and approximation of these complex non-polynomial systems, including quotients and roots of polynomials. We rely on representing each function to be model-reduced as a composition of tensor products, matrix inversions, and matrix roots. Once a function has been represented in this form, it can be easily model-reduced, and its reduced form can be evaluated with time and memory costs dependent only on the dimension of the reduced space.
Matt Stanton
Yu Sheng
Martin Wicke
Federico Perazzi
Amos Yuen
Srinivasa Narasimhan
Adrien Treuille
|
Non-Polynomial Galerkin Projection on Deforming Meshes
Stanton, M. Sheng, Y. Wicke, M. Perazzi, F. Yuen, A. Narasimhan, S. Treuille, A. ACM Transactions on Graphics 32(4) (SIGGRAPH 2013) [Paper (6.0 MB)] |
|
SIGGRAPH video (6 mins)
[Movie (145 MB)] |
This material is based upon work supported by:
National Science Foundation Grants GRFP-0946825, IIS-0953985, IIP-1127777, and IIS-0964562
Office of Naval Research Grant N00014-11-1-0295
Google
Qualcomm
Adobe
Intel
The Okawa Foundation
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.