Method and Apparatus for Converting Spherical Harmonics Representations of Functions into Multi-Resolution Representations

An analytical method to efficiently convert a function that is stored in spherical harmonics into a function that is stored in a wavelet or mip map representation enables a variety of computer graphics functions to be efficiently performed. A function may be stored as a spherical harmonic representation and rotated in the spherical harmonic domain; the function can then be converted to a wavelet representation. The conversion method may be used to convert a spherical harmonic function to wavelets, and then an importance sampling technique may be applied to the wavelet representation to generate a set of importance samples for the function. The conversion method may be applied to convert a spherical harmonic representation into the wavelet domain, and an importance sampling technique may then be applied which samples the product of the function and another function in the wavelet domain.