Non-Periodic Corner Tilingsin Computer Graphics
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Rendering computer-generated images is both memory and runtime intensive.This is particularly true in realtime computer graphics where large amounts ofcontent have to be produced very quickly and from limited data. Tile-basedmethods offer a solution to this problem by generating large portions of a specificcontent out of a much smaller data set of tiles.This dissertation investigates the use of corner tiles for this purpose unitsquare tiles with color-coded corners. They tile the plane by placing them withoutgaps or overlaps such that tiles have matching corner colors. We presentefficient algorithms to perform such a tiling that are both more flexible and lessprone to artifacts than existing algorithms. We also present solutions to combinatorialproblems that arise when using corner tiles, and introduce high-qualitymethods to perform the tile-based generation of two fundamental componentsof any rendering system: textures and two-dimensional sample point sets.The results of this dissertation are advantageous for both realtime and offlinerendering systems where they improve state-of-the-art results in texture synthesis,image plane sampling, and lighting computations based on numerical integration.