Conditional Product Next Event Estimation for Gaussian Process Implicit Surfaces

Abstract

We propose a new next‐event estimation (NEE) technique for Gaussian Process Implicit Surfaces (GPISes). We show that the distribution of surface normals available for sampling at a GPIS hit point collapses from 2D to 1D as the GPIS realizations approach heightfields, causing existing NEE to fail entirely in this limit. We analyze this collapse and develop a new strategy that directly importance samples the resulting 1D arc of valid scattering directions restricted to the spherical cap towards a light source. Our technique enables NEE on heightfield GPISes for the first time and provides substantial variance reduction for highly anisotropic near‐heightfield configurations. We combine our strategy with existing techniques via multiple importance sampling for robust performance across all degrees of anisotropy, and support arbitrary emitter shapes via sphere proxies.