Sampling Algorithms

Jittering, motion blurring, area light sources, and the depth-of-field lens shader are based on multiple sampling that is based on varying the sample locations in time, 2D or 3D space. mental ray offers a proprietary implementation of the Quasi-Monte Carlo method for achieving these variations. Sample locations in time, 2D and 3D space are deterministically chosen on fixed points that ensure optimal coverage of the sample space. The algorithm is similar to fixed-raster algorithms, but avoids the regular lattice appearance of such algorithms. The resulting images are identical if the scene is re-rendered with the same options due to the deterministic nature of the algorithm.

Quasi-Monte Carlo methods can be succinctly described as strictly deterministic sampling methods. Determinism enters in two ways, namely, by working with deterministic points rather than random samples and by the availability of deterministic error bounds (Niederreiter92).