ZH3: Quadratic Zonal Harmonics

Spherical Harmonics (SH) have been used widely to represent lighting in games and film. While the quadratic (SH3) and higher order spherical harmonics represent irradiance well, they are expensive to store and evaluate, requiring 27 coefficients per sample. Linear SH (SH2), requiring only 12 coefficients, are sometimes used, but they do not represent irradiance signals accurately and can have challenges with negative reconstruction. We introduce a new representation (ZH3) that augments linear SH with just the zonal coefficient of quadratic SH, yielding significant visual improvement with just 15 coefficients, and discuss how solving for a luminance zonal axis can significantly improve reconstruction accuracy and reduce color artifacts. We also discuss how, rather than storing the ZH3 coefficients explicitly, we can hallucinate them from the linear SH, improving reconstruction accuracy over linear SH at minimal extra cost.