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Real Time Visualization of Chaotic Functions
Teichmann, Antonín ; Elek, Oskár (advisor) ; Wilkie, Alexander (referee)
Fractals are a fundamental natural structure that has fascinated the sci- entific community for a long time. To allow for better understanding of fractals, visualization techniques can be used. The focus of this thesis is real-time rendering of fractals that are similar to the Mandelbrot set or the Newton fractal. Detailed exploration of these fractals is complicated due to their recursive-manner which leads to the fact that rendering them is com- putationally demanding. Existing solutions do not work in real-time or have low visual quality. We want to change that and allow high-quality real- time rendering. During our analysis of the problem, we generalize fractals to chaotic functions. To achieve high-quality rendering with low overhead, we introduce a method for adaptive super-sampling of chaotic functions. To achieve real-time performance, we show how to use sample reuse, foveated rendering, and other techniques. We implement a parallel, GPU-based, high- quality renderer that runs in real-time and produces visually-attractive views of given fractals. The program can visualize any given chaotic function. This way, we open the realm of real-time visualization of chaotic functions to the public and lay a basis for future research. 1
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Real-Time Light Transport in Analytically Integrable Participating Media
Iser, Tomáš ; Elek, Oskár (advisor) ; Horáček, Jan (referee)
The focus of this thesis is the real-time rendering of participating media, such as fog. This is an important problem, because such media significantly influence the appearance of the rendered scene. It is also a challenging one, because its physically correct solution involves a costly simulation of a very large number of light-particle interactions, especially when considering multiple scattering. The existing real-time approaches are mostly based on empirical or single-scattering approximations, or only consider homogeneous media. This work briefly examines the existing solutions and then presents an improved method for real-time multi- ple scattering in quasi-heterogeneous media. We use analytically integrable den- sity functions and efficient MIP map filtering with several techniques to minimize the inherent visual artifacts. The solution has been implemented and evaluated in a combined CPU/GPU prototype application. The resulting highly-parallel method achieves good visual fidelity and has a stable computation time of only a few milliseconds per frame.
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