Representing Spherical Functions with Rhombic Dodecahedron
In this thesis, we present a novel method to efficiently represent datasets over the 2D spherical domain based on rhombic dodecahedron. We propose a new subdivision strategy, a family of skew great circles, for parameterization of the spherical domain. The sampling pattern produced over the sphere surface does not only have low discrepancy, low stretch efficiency and low area standard deviation, but also allows fast location of sample points in real time. The data querying process of skew great circle subdivision strategy can be done through an analytical equation whereas recursive search is required for existing recursive subdivision strategy. This can speed up the data sampling and retrieval process. The effectiveness of this spherical data representation has been experimented with environment maps, shadow maps and high dynamic range data. The low discrepancy sampling pattern results in good rendering quality for environment mapping application and shadow mapping. The fast data query technique ensures real time environment mapping to be practical. The nice structure of the subdivision strategy allows the construction of spherical quadrilateral-based "quadtree", which is used for adaptive and deterministic sampling of static and dynamic sequence of high dynamic range environment maps.
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