Abstract

Abstract Non-symmetric scattering is far more common in computer graphics thanis generally recognized, and can occur even when the underlying scattering model is physically correct. For example, we show that non-symmetry oc-curs whenever light is refracted, and also whenever shading normals are used (e.g. due to interpolation of normals in a triangle mesh, or bump mapping [5]).We examine the implications of non-symmetric scattering for light transport theory. We extend the work of Arvo et al. [4] into a complete frameworkfor light, importance, and particle transport with non-symmetric kernels. We show that physically valid scattering models are not always symmetric, andderive the condition for arbitrary models to obey Helmholtz reciprocity. By rewriting the transport operators in terms of optical invariants, we obtain anew framework where symmetry and reciprocity are the same. We also consider the practical consequences for global illumination al-gorithms. The problem is that many implementations indirectly assume symmetry, by using the same scattering rules for light and importance, or particlesand viewing rays. This can lead to incorrect results for physically valid models. It can also cause different rendering algorithms to converge to differentsolutions (whether the model is physically valid or not), and it can cause shading artifacts. If the non-symmetry is recognized and handled correctly, theseproblems can easily be avoided. 1 Introduction The equations governing the transport and measurement of light energy can be writ-ten in two equivalent forms, depending on whether we solve for radiance or importance. Most current global illumination algorithms take advantage of this duality.For example, importance is often used to guide mesh refinement in finite-element approaches, and traditional ray tracing is the dual of particle tracing, which simu-lates the emission and scattering of photons. 1

Citations

6	Theory of distributions, M - Al-Gwaiz - 1992
1	Factorization Calculus and Geometric Probability.Cambridge - AMBARTZUMIAN - 1990