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Extracting multiple lights from Spherical Harmonics

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I've read Stupid Spherical harmonic tricks: http://www.ppsloan.org/publications/StupidSH36.pdf

It describes techniques to extract conventional lights from a SH coefficient vector. I understand the math behind extracting a single directional light, but I get quite lost in the section where he discusses extracting multiple lights.

The basic idea seems to be using numerical optimization techniques to find the required N directions, and then use the equations provided in order to calculate the light intensity for each direction. The paper goes into some amount of detail with several different techniques that seem to solve different portions of this problem, but I'm having trouble seeing how they all fit together.

I was wondering if anyone has any experience using this in practice and can maybe provide some pointers or additional resources.

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