Light beam tracing for multi-bounce specular and glossy transport paths

Abstract

Light beam tracing is an e cient rendering algorithm for simulating caustics, the envelopes of light that are scattered from shiny curved surfaces and focussed into lines or spots of concentrated light. Light beam tracing is e cient for rendering caustics because the algorithm is able to exploit the coherency of the transport paths within an envelope of light. However, light beam tracing rendering algorithms found in the literature only support mirror-like specular surface interactions. Therefore, there is motive for extending light beam tracing to include more realistic roughened specular and other glossy surfaces while maintaining the e ciency of the rendering algorithm. This thesis rst o ers a conjecture on how to extend light beam tracing to include glossy surface interactions. The glossy bidirectional re ectance distribution function (BRDF) that is required to support the conjecture is then derived and shown to be physically plausible. Following from the conjecture a new extension to light beam tracing that allows glossy surface interactions for more realistic rendering of caustics is formulated. Gauss' divergence theorem is used to replace the irradiance surface integral of the lighting equation with a more e cient boundary line integral. This solution is also shown to be reusable for all-frequency interactions although more work is required to complete the derivations. Finally, multi-bounce glossy light beam tracing is demonstrated which further extends the application domain of glossy light beam tracing. The new rendering algorithm is shown to be a good alternative for rendering single-bounce and multi-bounce caustics due to specular as well as glossy surfaces. The expectation is that the irradiance solution would also in future be useful for more general applications.