SGP03: Eurographics Symposium on Geometry Processing

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https://diglib.eg.org/handle/10.2312/444

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Browsing SGP03: Eurographics Symposium on Geometry Processing by Subject "Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling"

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    Explicit Surface Remeshing
    (The Eurographics Association, 2003) Surazhsky, Vitaly; Gotsman, Craig; Leif Kobbelt and Peter Schroeder and Hugues Hoppe
    We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an areabased smoothing technique. Area-based smoothing allows the control of both triangle quality and vertex sampling over the mesh, as a function of some criteria, e.g. the mesh curvature. To perform local modifications of arbitrary genus meshes we use dynamic patch-wise parameterization. The parameterization is constructed and updated onthe- fly as the algorithm progresses with local updates. As a post-processing stage, we introduce a new algorithm to improve the regularity of the mesh connectivity. The algorithm is able to create an unstructured mesh with a very small number of irregular vertices. Our remeshing scheme is robust, runs at interactive speeds and can be applied to arbitrary complex meshes.
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    A Geometric Convection Approach of 3-D Reconstruction
    (The Eurographics Association, 2003) Chaine, Raphaƫlle; Leif Kobbelt and Peter Schroeder and Hugues Hoppe
    This paper introduces a fast and efficient algorithm for surface reconstruction. As many algorithms of this kind, it produces a piecewise linear approximation of a surface S from a finite, sufficiently dense, subset of its points. Originally, the starting point of this work does not come from the computational geometry field. It is inspired by an existing numerical scheme of surface convection developed by Zhao, Osher and Fedkiw. We have translated this scheme to make it depend on the geometry of the input data set only, and not on the precision of some grid around the surface. Our algorithm deforms a closed oriented pseudo-surface embedded in the 3D Delaunay triangulation of the sampled points, and the reconstructed surface consists of a set of oriented facets located in this 3D Delaunay triangulation. This paper provides an appropriate data structure to represent a pseudo-surface, together with operations that manage deformations and topological changes. The algorithm can handle surfaces with boundaries, surfaces of high genus and, unlike most of the other existing schemes, it does not involve a global heuristic. Its complexity is that of the 3D Delaunay triangulation of the points. We present some results of the method, which turns out to be efficient even on noisy input data.