Deringing spherical harmonics

Spherical Harmonics (SH) are a convenient basis for representing various signals in computer graphics, with lighting and visibility being the most common. While the inputs tend to be strictly positive, after projection the reconstructed function can be negative. The projection can also exhibit "ringing" artifacts, oscillations that are common with least squares. This paper presents an algorithm to efficiently and conservatively solve for a windowing function that results in a strictly positive function by minimizing a univariate polynomial that works well for irradiance signals in video games.