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Now showing 1 - 3 of 3
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    Valence-Driven Connectivity Encoding for 3D Meshes
    (Blackwell Publishers Ltd and the Eurographics Association, 2001) Alliez, Pierre; Desbrun, Mathieu
    In this paper, we propose a valence-driven, single-resolution encoding technique for lossless compression of triangle mesh connectivity. Building upon a valence-based approach pioneered by Touma and Gotsman22 , we design a new valence-driven conquest for arbitrary meshes that always guarantees smaller compression rates than the original method. Furthermore, we provide a novel theoretical entropy study of our technique, hinting the optimality of the valence-driven approach. Finally, we demonstrate the practical efficiency of this approach (in agreement with the theoretical prediction) on a series of test meshes, resulting in the lowest compression ratios published so far, for both irregular and regular meshes, small or large.
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    Intrinsic Parameterizations of Surface Meshes
    (Blackwell Publishers, Inc and the Eurographics Association, 2002) Desbrun, Mathieu; Meyer, Mark; Alliez, Pierre
    Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.
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    Angle-Analyzer: A Triangle-Quad Mesh Codec
    (Blackwell Publishers, Inc and the Eurographics Association, 2002) Lee, Haeyoung; Alliez, Pierre; Desbrun, Mathieu