Efficient from-point visibility for global illumination in virtual scenes with participating media

Visibility determination is one of the fundamental building blocks of photorealistic image synthesis. Light reflected at a shading point depends on light reflected from the visible scene surfaces and on the visible light sources in the environment. However, computing visibility is computational highly demanding and global illumination algorithms, such as final gathering and bias compensation for instant radiosity spend most of their rendering time thereon. In this thesis we strive to improve the rendering performance of the aforementioned algorithms and propose methods that on the one hand compute and store visibility efficiently and on the other hand use feasible visibility approximations without introducing noticeable artifacts. Therefore we investigate a (hemi-)spherical parameterization based on the octahedron for efficient storage of visibility at arbitrary shading points. Having laid the groundwork, we then build on this foundation and formulate a point-based rendering technique that efficiently computes (hemi-)spherical visibility for final gathering. In the following, we show how the principles of epipolar geometry allow us to exploit visibility coherence, and we derive an optimized screen-space sampling strategy for single scattering from point light sources in homogeneous media. Combining single scattering from many (virtual) point light sources makes it possible to approximate global illumination with multiple scattering by instant radiosity complemented by bias compensation. Bias compensation corrects illumination errors that occur when radiative energy is eliminated over short distances by instant radiosity, leading to artificial darkening in the image. Bias compensation is computational highly demanding due to the high number of visibility evaluations required to evaluate the necessary correction term, and it easily outweighs illumination with (virtual) point lights only by magnitudes. To improve the efficiency of the compensation, we propose the usage of various visibility approximations in participating media and investigate several integration strategies for optimal results. Finally, we demonstrate that bias compensation on surfaces can be accurately approximated by a simple image-space post-process that does not require any visibility evaluations at all.