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Deterministic Monte Carlo sampling uses a pre-defined set of random samples, which allows producing the exact same result when re-rendering an image. The difference with pure Monte Carlo sampling is that Monte Carlo uses pseudo-random numbers which are different for every evaluation and so re-rendering a single image will always produce slightly different results in the noise. By default, the Deterministic Monte Carlo method used by V-Ray is a modification of Schlick sampling, introduced by Christophe Schlick.

V-Ray is an adaptive sampling engine. This means that whenever V-Ray needs to compute a value, like the color of a pixel, or the light reflected from a surface, V-Ray will take a varying number of samples for that value, depending on the context. The adaptive algorithm that V-Ray uses is very straightforward: for any effect that requires several samples, V-Ray first computes a small amount of samples, and then, if the variance of the samples is too big, it continues to take more samples until the result is good enough.

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 More information on deterministic Monte Carlo sampling for computer graphics can be found from the sources listed below. 

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  • C. Schlick, An Adaptive Sampling Technique for Multidimensional Integration by Ray Tracing, in Second Eurographics Workshop on Rendering (Spain), 1991, pp. 48-56
    Describes deterministic MC sampling for antialiasing, motion blur, depth of field, area light sampling and glossy reflections.

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  • K. Chiu, P. Shirley and C. Wang,

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  • Multi-Jittered Sampling, in Graphics Gems IV, 1994
    Describes a combination of jittered and N-rooks sampling for the purposes of computer graphics.

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  • Masaki Aono and Ryutarou Ohbuchi, Quasi-Monte Carlo Rendering with Adaptive Sampling, IBM Tokyo Research Laboratory Technical Report RT0167, November 25, 1996, pp.1-5
    An online version can be found at
    http://www.kki.yamanashi.ac.jp/~ohbuchi/online_pubs/eg96_html/eg96.htm
    Describes an application of low discrepancy sequences to area light sampling and the global illumination problem.

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  • M. Fajardo, Monte Carlo Raytracing in Action, in State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis, SIGGRAPH 2001 Course 21, pp. 151-162;
    An online version can be found at
    http://cseweb.ucsd.edu/~viscomp/classes/cse274/wi18/readings/course29sig01.pdf
    Describes the ARNOLD renderer employing randomized quasi-Monte Carlo sampling using low discrepancy sequences for pixel sampling, global illumination, area light sampling, motion blur, depth of field, etc.

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  • E. Veach, December, Robust Monte Carlo Methods for Light Transport Simulation, Ph. D. dissertation for Stanford University, 1997, pp. 58-65
    An online version can be found at  http://graphics.stanford.edu/papers/veach_thesis/
    Includes a description of low discrepancy sequences, quasi-Monte Carlo sampling and its application to solving the global illumination problem.

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  • L. Szirmay-Kalos, Importance Driven Quasi-Monte Carlo Walk Solution of the Rendering Equation, Winter School of Computer Graphics Conf., 1998
    An online version can be found at https://www.sciencedirect.com/science/article/abs/pii/S0097849399000308 (This page is no longer available)
    Describes a two-pass method for solving the global illumination problem employing quasi-Monte Carlo sampling, as well as importance sampling using low discrepancy sequences.