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Initially and still I'm not so sure how to get the color of the object behind the glass into the formulas. Normal, this was written with path / ray tracers in mind where that part is easy. Your idea of a cube map might be ok for some use cases (eg. reasonably rough surface for the distance to the surrounding objects). It is not a general solution however. ...


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The summation doesn't include the BxDF that was picked for sampling. Look again at this line: if (bxdfs[i] != bxdf && bxdfs[i]->MatchesFlags(type)) Here bxdf is the one that was sampled earlier, so when it iterates to that one it skips it.


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