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
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.