Adaptive sampling for environment mapping

This paper proposes an adaptive sampling algorithm for environment mapping. Unlike importance sampling, adaptive sampling does not try to mimic the integrand with analytically integrable and invertible densities, but approximates the integrand with analytically integrable functions, thus it is more appropriate for complex integrands, which correspond to difficult lighting conditions and sophisticated BRDF models. We develop an adaptation scheme that is based on ray differentials and does not require neighbor finding and complex data structures in higher dimensions. As a side result of the adaptation criterion, the algorithm also provides error estimates, which are essential in predictive rendering applications.