Low-Error Reconstruction of Directional Functions With Spherical Harmonics

This paper proposes a novel approach for the low-error reconstruction of directional functions with spherical harmonics. We introduce a modified version of Spherical Gaussians with adaptive narrowness and amplitude to represent the input data in an intermediate form. This representation is then projected into spherical harmonics using a closed-form analytical solution. Because of the spectral properties of the proposed representation, the amount of ringing artifacts is reduced, and the overall precision of the reconstructed function is improved. The proposed method is more precise comparing to existing methods. The presented solution can be used in several graphical applications, as discussed in this paper. For example, the method is suitable for sparse models such as indirect illumination or reflectance functions.