Computation of Irradiance from Triangles by Adaptive Sampling

Abstract

We introduce an algorithm for sample positioning in a planar triangle, which can be used to make numerical integration of an arbitrary function defined on it. This algorithm has some interesting properties which make it suitable for applications in the context of realistic rendering. We use an adaptive triangle partitioning procedure, driven by an appropriate measure of the error. The underlying variance is shown to be bounded, and in fact it can be controlled, so that it approaches the minimum possible value. We show results obtained when applying the method to irradiance computation, in the context of final-gather algorithms. We also describe a C++ class which offers all required functionality, and we made available its source code.