Not to destroy anything, but at some point, there is no need to discuss the details of the 1988 paper. We can actually divide phi and theta however we like in the sum – we chose this as a reasonable compromise for the division cell aspect ratios, though it’s still pretty bad. (See Figure 12.7 from “Rendering with Radiance,” reproduced below.)
Likewise, we don’t use the split sphere estimate for calculation spacing anymore. We have supplanted this method in the current version with a more accurate Hessian calculation due to Schwarzhaupt, Wann Jensen and Jarosz:
“Practical Hessian-Based Error Control for Irradiance Caching”.
Jorge Schwarzhaupt, Henrik Wann Jensen, and Wojciech Jarosz
ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2012), Singapore, November 2012
They use the Shirley-Chiu hemisphere subdivision, which does a much better job and simplifies neighbor relationships. We also fixed an issue they had with locally shaded regions, as described in my 2014 workshop talk.
Cheers,
-Greg