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Advanced Global Illumination, 2nd Edition by Kavita Bala, Philippe Bekaert, Philip Dutre

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Appendix C

Theoretical Analysis of Stochastic Relaxation Radiosity

In this appendix, we show how the variance of the incremental shooting iterative algorithm of Section 6.3 can be analyzed, and demonstrate how a number of practical results can be derived from it. The analysis of the other algorithms is very similar and is a recommended exercise for the interested reader.

We start with the derivation of the variance of the incremental shooting iterative algorithm. The first thing to point out is that the resulting radiosities are obtained as the sum of increments computed in several iteration steps. We first derive the variance of a single iteration and next show how the variance on the converged results is composed from the single-iteration variances. ...

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