Langevin dynamics in stochastic ray tracing: computing the preconditioning matrix according to restrictions and choice of time step

The main computationally extensive task of realistic computer graphics is the calculation of global illumination. The work investigates the speed of the convergence of lighting simulation using Monte Carlo integration based on the Langevin equation. The paper presents the first part of the work, which provides a detailed overview of the problem, examines the influence of the divergent term, the choice of the integration step, and derives formulae for calculating the preconditioning matrix. It is shown how these aspects affect convergence.