A system and method for generating a set of samples stratified across two-dimensional elementary intervals of a two-dimensional space is disclosed within the application. A computer-implemented technique for generating the set of samples includes selecting an elementary interval associated with a stratification of the two-dimensional space, initializing at least one data structure that indicates valid regions within the elementary interface based on other samples previously placed within the two-dimensional space, and generating a sample in a valid region of the elementary interval utilizing the at least one data structure to identify the valid region prior to generating the sample. In some embodiments, the data structures comprise a pair of binary trees. The process can be repeated for each elementary interval of a selected stratification to generate the set of stratified two-dimensional samples.