Open Access. Powered by Scholars. Published by Universities.®
Graphics and Human Computer Interfaces Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Graphics and Human Computer Interfaces
A Bidirectional Formulation For Walk On Spheres, Yang Qi
A Bidirectional Formulation For Walk On Spheres, Yang Qi
Dartmouth College Master’s Theses
Poisson’s equations and Laplace’s equations are important linear partial differential equations (PDEs)
widely used in many applications. Conventional methods for solving PDEs numerically often need to
discretize the space first, making them less efficient for complex shapes. The random walk on spheres
method (WoS) is a grid-free Monte-Carlo method for solving PDEs that does not need to discrete the
space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS
algorithm is conceptually identical to forward path tracing.
We show that solving the Poisson’s equation is equivalent to solving the Green’s function for every
pair of …