Model Reducing Radiosity and Fluids of Deformable Scenes

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.


"Non-Polynomial Galerkin Projection on Deforming Meshes"
Matt Stanton, Yu Sheng, Martin Wicke, Federico Perazzi, Amos Yuen, Srinivasa G. Narasimhan, Adrien Treuille
ACM Transactions on Graphics 32(4) (SIGGRAPH 2013),
July 2013.


The scene consists of two rooms, a brightly-lit living room with light colored walls linked by a door to a dimmer bedroom with darker-colored walls. The scene is illuminated by an overcast sky through two windows and a skylight. The scene mesh consists of 5012 faces, and the sizes of the skylights, windows, and doors can be changed interactively. In addition, the living room ceiling can be tilted. [left] Ground truth rendering of using classical radiosity. [right] Simulation result using our non-polynomial Galerkin projection technique.
The global illumination computed by full space radiosity and our model reduction method. The exposure is increased for better visualization.


SIGGRAPH 2013 Video (with narration)
The archictectural scene rendered by full space radiosity The same scene rendered with our model reduction method
The archictectural scene rendered by full space radiosity, at a different viewpoint The same scene rendered with our model reduction method