Jaroslav Křivánek

Extended Path Integral Formulation for Volumetric Transport

Toshiya Hachisuka
The University of Tokyo
Iliyan Georgiev
Solid Angle
Wojciech Jarosz
Dartmouth College
Jaroslav Křivánek
Charles University, Prague
Derek Nowrouzezahrai
McGill University



We propose an extension of the path integral formulation amenable to the expression of volumetric light transport with photon beam estimates. Our main contribution is a generalization of Hachisuka et al.’s [2012] extended path space formulation to light transport in participating media. Our formulation supports various point- and beam-based volumetric density estimators, unifying them with path integration in the spirit of the work by Křivánek et al. [2014]. One unique and useful property of our formulation is that it recasts beam-based density estimation as Monte Carlo path vertex sampling in a higher-dimensional space, rather than beam merging in a lower-dimensional space, which enables a practical algorithm for beam estimators with 3D-blur kernels. We thus establish a complementary theoretical foundation for the development of rendering algorithms using points, beams, and paths in participating media.


Toshiya Hachisuka, Iliyan Georgiev, Wojciech Jarosz, Jaroslav Křivánek, Derek Nowrouzezahrai. Extended Path Integral Formulation for Volumetric Transport. Proceedings of EGSR (Experimental Ideas & Implementations), June 2017 ... DOI  |  BibTeX

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This work was partly supported by the Charles University grant SVV-2017-260452 and the Czech Science Foundation grant 16-18964S.