System and method for rendering images using a strictly-deterministic methodology for generating a coarse sequence of sample points

Abstract

A system and method for generating sample points that can generate the sample points in parallel. The sample points can be used in processing in parallel, with the results subsequently collected and used as necessary in subsequent rendering operations. Sample points are generated using a coarse Halton sequence, which makes use of coarse radical inverse values Φ(j) as follows:Φ()=Φ()where base 'b' is preferably a prime number, but not a divisor of 'M,' and “i” is an integer. Using this definition, the s-dimensional coarse Halton sequence U, which may be used to define sample points for use in evaluating integrals, is defined as=(Φ(), . . . , Φ))where b, . . . , bare the first “s” prime numbers that are not divisors of “M.” Each value of “i” defines a subsequence that is a low-discrepancy sequence, and so can be used in connection with processing. Similarly, the union of all subsequences for all values of “i” between “zero” and “M−1” is also a low-discrepancy sequence, so results of processing using the coarse Halton sequences for all such values of “i” can be collected together and used in the same manner as if the results had been generated using a Halton sequence to define the sample points.