Efficient methods for physically-based rendering of participating media

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This thesis proposes several novel methods for realistic synthesis of images containing participating media. This is a challenging problem, due to the multitude and complexity of ways how light interacts with participating media, but also an important one, since such media are ubiquitous in our environment and therefore are one of the main constituents of its appearance. The main paradigm we follow is designing efficient methods that provide their user with an interactive feedback, but are still physically plausible. The presented contributions have varying degrees of specialisation and, in a loose connection to that, their resulting efficiency. First, the screen-space scattering algorithm simulates scattering in homogeneous media, such as fog and water, as a fast image filtering process. Next, the amortised photon mapping method focuses on rendering clouds as arguably one of the most difficult media due to their high scattering anisotropy. Here, interactivity is achieved through adapting to certain conditions specific to clouds. A generalisation of this approach is principal-ordinates propagation, which tackles a much wider class of heterogeneous media. The resulting method can handle almost arbitrary optical properties in such media, thanks to a custom finite-element propagation scheme. Finally, spectral ray differentials aim at an efficient reconstruction of chromatic dispersion phenomena, which occur in transparent media such as water, glass and gemstones. This method is based on analytical ray differentiation and as such can be incorporated to any ray-based rendering framework, increasing the efficiency of reproducing dispersion by about an order of magnitude. All four proposed methods achieve efficiency primarily by utilising high-level mathematical abstractions, building on the understanding of the underlying physical principles that guide light transport. The methods have also been designed around simple data structures, allowing high execution parallelism and removing the need to rely on any sort of preprocessing. Thanks to these properties, the presented work is not only suitable for interactively computing light transport in participating media, but also allows dynamic changes to the simulated environment, all while maintaining high levels of visual realism.