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Stratified sampling is expensive in higher dimensions. To reduce the cost, we can split dimensions into subsets and apply stratified sampling separately to each subset (in this case stratified sampling is applied separately to (p0, p1) and (p2, p3)). Then, we randomly associate a sample in one subset with one sample in another subset. In total we end up with n^s samples where s is the number of subsets and n is the number of strata per subset.


I've been reading through this article about stratified point sampling using a technique that begins with uniform sampling of a 3d mesh and placing a charged particle at each sampled position, while also incorporating octree voxelization of the model. Very interesting!