Optimized Numerical Solvers for Calculating Radiative Transfer via a Feynman Path Integral Formulation

Abstract

The simulation of visible light propagation and interaction within virtual environments is particularly interesting in computer graphics. Volume rendering, a crucial technique, aims to simulate light transfer through scattering media accurately. While existing solutions provide reasonable results, they become computationally complex when multiple scattering events occur. This paper introduces a numerical solver based on the Feynman Path Integral designed to capture high orders of scattering events. While previous solvers of the FPI were computationally inefficient, we present novel numerical approaches for solving the FPI, which offer improved performance. The solvers are validated and applied to render volumetric environments, demonstrating their effectiveness. The proposed solutions hold promise for simulating radiative transfer in various disciplines and could serve as a benchmark for high-order scattering simulations.