Spherical harmonics scaling

In this paper, we present a new SH operation, called spherical harmonics scaling, to shrink or expand a spherical function in the frequency domain. We show that this problem can be elegantly formulated as a linear transformation of SH projections, which is efficient to compute and easy to implement on a GPU. Spherical harmonics scaling is particularly useful for extrapolating visibility and radiance functions at a sample point to points closer to or farther from an occluder or light source. With SH scaling, we present applications to low-frequency shadowing for general deformable object, and to efficient approximation of spherical irradiance functions within a mid-range illumination environment.