Cascaded Sobol' sampling

Rendering quality is largely influenced by the samplers used in Monte Carlo integration. Important factors include sample uniformity (e.g., low discrepancy) high-dimensional integration domain, lower-dimensional projections, and lack of dominant structures that could result aliasing artifacts. A widely successful construction Sobol' sequence guarantees good consequently results faster convergence quasi-Monte We show this exhibits low-dimensional projections. These impair context rendering, as they precisely occur 2-dimensional projections for sampling light sources, reflectance functions, or camera lens sensor. propose a new cascaded construction, which, despite dropping sequential aspect samples, produces point sets exhibiting provably perfect dyadic partitioning (and therefore, excellent uniformity) consecutive while preserving uniformity. By optimizing initialization parameters performing Owen scrambling at finer levels binary representations, we further improve over Sobol's rate. Our method does not incur any overhead compared to generation sequence, compatible with can be rendering applications.