Importance sampling of partitioned domains, where a probability is known for each set of the partition, is used for Monte Carlo and quasi-Monte Carlo methods. Monte Carlo methods are a class of algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used when simulating physical and mathematical systems. Quasi-Monte Carlo methods are similar to Monte Carlo methods, however, instead deterministic samples are used, which can result in an improved convergence.
Quite often, a function is at least in part defined by some discrete energy density, such as a textured light source in computer graphics. To date, the sampling speed for importance sampling of partitioned (or discretized) domains has not been fully optimized. There is thus a need for addressing these and/or other issues.