Our paper is devoted to the study of the Monte Carlo method based on the Langevin equation as applied to Monte Carlo rendering. We describe a simplified scene with a complex and discountinious density of contribution function, in which we evaluate the influence of the preconditioning matrix in the Langevin equation. Such a scene allows us to obtain explainable and interpretable results, which is difficult in real scenes encountered in Monte Carlo rendering. Test results demonstrate that a properly selected way to build preconditioning matrix can significantly reduce the number of steps of the Monte Carlo method, necessary to achieve the specified accuracy.

global illumination, stochastic ray tracing, Markov chain, Langevin equation

Mathematical modelling in actual problems of science and technics

Nikolaev Alexander Alekseevich,  ,  orcid.org/0009-0005-3840-7038,  Lomonosov Moscow State University

Ershov Sergey Valentinovich,  ,  orcid.org/0000-0002-5493-1076,  KIAM RAS

Frolov Vladimir Alexandrovich,  ,  orcid.org/0000-0001-8829-9884,  KIAM RAS