Approximate importance sampling of functions reconstructed from spherical harmonics

The ability to generate random samples that match a spherical PDF given in terms of spherical harmonic coefficients is very important in many fields of computer graphics. Recent work has shown that generating such samples can be done efficiently, but the published methods are not robust in the presence of reconstruction errors which manifest themselves as negative values of the PDF. In our paper, we extend the approach so that it can handle such errors, and generates uniform distribution of samples in the negative parts of the sampled function while preserving a distribution that matches the original function elsewhere. The overall distribution approximates the original function and guarantees that there are no parts of the spherical domain which remain unsampled. This property makes the scheme suitable for use in unbiased Monte Carlo rendering