### Unbiased way to independently find SDS paths

Posted:

**Mon Apr 13, 2015 9:06 pm**The idea i am presenting is to use some form of vertex merging to provide an initial guess which is then iteratively corrected into an unbiased path using manifold(Manifold Exploration) or half vector space perturbations(The Natural-Constraint Representation of the Path Space for Efficient Light Transport Simulation) until the result is unbiased within machine precision. In theory algorithms like path tracing and MLT unbiased, however in practice due to lack of infinite precision all rendering is biased and inconsistent. This method can used to find SDS paths from point lights, without adding bias, as well as reducing the amount of error in brightness when used in conjunction with MLT. A potential problem of this method is that the correction could be expensive, which could be amortized by using MLT with the aforementioned perturbations to mutate the path.

**update**: I went through the hlst paper and found out that the perturbation first perturbs the half vectors of the path then iteratively corrects the path to satisfy the new half vector constraints.