Recent development in Graphics Processing Units (GPUs) has enabled inexpensive high-performance computing for general-purpose applications. The K-Nearest Neighbors problem is widely used in applications ranging from classification to gathering of photons in the Photon Mapping algorithm. Using the euclidean distance measure when gathering photons can cause false bleeding of colors between surfaces. Ellipsoidical search boundaries for photon gathering are shown to reduce artifacts due to this false bleeding. Shifted Sorting has been found to yield high performance on GPUs while simultaneously retaining a high approximation rate. This study presents an algorithm for approximatively solving the K-Nearest Neighbors problem modified to use a distance measure creating an ellipsoidical search boundary. The ellipsoidical search boundary is used to alleviate the issue of false bleeding of colors between surfaces in Photon Mapping. The Approximative K-Nearest Neighbors algorithm presented is a modification of the Shifted Sorting algorithm. The algorithm is found to be highly parallelizable and performs to a factor of 86% queries processed per millisecond compared to a reference implementation using spherical search boundaries implied by the euclidean distance. The rate of compression from spherical to ellipsoidical search boundary is appropriately chosen in the range 3.0 to 7.0. The algorithm is found to scale well in respect to increases in both number of data points and number of query points. / Grafikprocessorer (GPU-er) har på senare tid möjliggjort högprestandaberäkningar till låga kostnader för generella applikationer. K-Nearest Neighbors problemet har vida applikationsområden, från klassifikation inom maskininlärning till insamlande av fotoner i Photon Mapping för rendering av tredimensionella scener. Användning av euklidiska avstånd vid insamling av fotoner kan leda till en felaktig bladning av färger mellan ytor. Ellipsoidiska sökområden vid fotoninsamling har visats reducera artefakter oraskade av denna typ av felaktiga färgutblandning. Shifted Sorting har visats ge hög prestanda på GPU-er utan att förlora kvalitet av approximationsgrad. Denna rapport undersöker hur den approximativa varianten av K-Nearest Neighborsalgoritmen med Shifted Sorting presterar på GPU-er med avståndsmåttet modifierat sådant att ett ellipsoidiskt sökområde bildas. Algoritmen används för att reduceras problemet av felaktig blanding av färg i Photon Mapping. Algoritmen visas vara mycket parallelliserbar och presterar till en grad av 86% behandlade sökpunkter per millisekund i jämförelse med en referensimplementation som använder sfäriska sökområden. Kompressionsgraden längs sökpunktens ytnormal väljs fördelaktligen till ett värde i intervallet 3,0 till 7,0. Algoritmen visas skala väl med avseende på både ökningar i antal data punkter och antal sökpunkter.

For photographers to capture good pictures of their subjects, the lighting conditions must be taken into account and adjusted for accordingly. The same holds true for a satellite attempting to photograph another object in space: it must know the lighting conditions to adjust camera settings and position itself properly to take the best photograph. This thesis presents a photon mapping based algorithm to compute a physically accurate representation of the illumination of objects in orbit around the Earth, taking into account the effects that cause refraction in the atmosphere. I also discuss the assumptions that I have made to utilize the algorithm in an interactive 3D visualization tool, which I implemented to view the illumination on objects at arbitrary positions in space. Finally, I show that the photon mapping method offers improvements over simpler methods of computing illumination.

The rendering of participating media is an interesting and important problem without a simple solution. Yet even among the wide variety of participating media the clouds stand out as an especially difficult case, because of their properties that make their simulation even harder. The work presented in this thesis attempts to provide a solution to this problem, and moreover, to make the proposed method to work in interactive rendering speeds. The main design criteria in designing this method were its physical plausibility and maximal utilization of specific cloud properties which would help to balance the complex nature of clouds. As a result the proposed method builds on the well known photon mapping algorithm, but modifies it in several ways to obtain interactive and temporarily coherent results. This is further helped by designing the method in such a way which allows its implementation on contemporary GPUs, taking advantage of their massively parallel sheer computational power. We implement a prototype of the method in an application that renders a single realistic cloud in interactive framerates, and discuss possible extensions of the proposed technique that would allow its use in various practical industrial applications.

This thesis deals with practical implementation of photon mapping algorithm. To achieve better results some basic and some more advanced methods of global illumination has been examined. These time demanding algorithms are often practically unusable and their further optimization is necessary. Optimized ray tracer is essential for practical implementation. Computing diffuse interreflection by Monte Carlo sampling is also very time demanding operation. Therefore it is appropriate to use it along with proper interpolation.

Subject of this thesis is acceleration of the photon mapping method on a graphic card. The photon mapping is a method for computing almost realistic global illumination of the scene. The computation itself is relatively time-consuming, so the acceleration of it is a hot issue in the field of computer graphics. The photon mapping is described in detail from photon tracing to rendering of the scene. The thesis is then focused on spatial subdivision structures, especially to the uniform grid. The design and the implementation of the application computing the photon mapping on GPU, which is achieved by OpenGL and CUDA interoperability, is described in the next part of the thesis. Lastly, the application is tested properly. The achieved results are reviewed in the conclusion of the thesis.

Raytracing is a basic technique for displaying 3D objects. The goal of this thesis is to demonstrate the possibility of implementing raytracer using a programmable GPU. The algorithm and its modified version, implemented using "C for CUDA" language, are described. The raytracer is focused on displaying dynamic scenes. For this purpose the KD tree structure, bounding volume hierarchies and PBO transfer are used. To achieve realistic output, photon mapping was implemented.

This thesis deals with the techniques of global illumination of the scene. The theoretical part discusses various techniques, focusing on processing in real-time using various optimization methods. It focuses to the technology of photon splatting using view sample cluster hierarchy. The main part is analysis, implenetation and measurement of mentioned method.