Paper Info
Title
Monte Carlo geometry processing: a grid-free approach to PDE-based methods on volumetric domains
Abstract
AbstractThis paper explores how core problems in PDE-based geometry processing can be efficiently and reliably solved via grid-free Monte Carlo methods. Modern geometric algorithms often need to solve Poisson-like equations on geometrically intricate domains. Conventional methods most often mesh the domain, which is both challenging and expensive for geometry with fine details or imperfections (holes, self-intersections, etc.). In contrast, grid-free Monte Carlo methods avoid mesh generation entirely, and instead just evaluate closest point queries. They hence do not discretize space, time, nor even function spaces, and provide the exact solution (in expectation) even on extremely challenging models. More broadly, they share many benefits with Monte Carlo methods from photorealistic rendering: excellent scaling, trivial parallel implementation, view-dependent evaluation, and the ability to work with any kind of geometry (including implicit or procedural descriptions). We develop a complete "black box" solver that encompasses integration, variance reduction, and visualization, and explore how it can be used for various geometry processing tasks. In particular, we consider several fundamental linear elliptic PDEs with constant coefficients on solid regions of Rn. Overall we find that Monte Carlo methods significantly broaden the horizons of geometry processing, since they easily handle problems of size and complexity that are essentially hopeless for conventional methods.
Year
DOI
Venue
2020
10.1145/3386569.3392374
ACM Transactions on Graphics
Keywords
DocType
Volume
numerical methods, stochastic solvers
Journal
39
Issue
ISSN
Citations 
4
0730-0301
1
PageRank 
References 
Authors
0.35
0
2
Name
Order
Citations
PageRank
Rohan Sawhney151.09
Keenan Crane258629.28