SGP06: Eurographics Symposium on Geometry Processing
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Browsing SGP06: 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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Item Nonobtuse Remeshing and Mesh Decimation(The Eurographics Association, 2006) Li, J. Y. S.; Zhang, H.; Alla Sheffer and Konrad PolthierQuality meshing in 2D and 3D domains is an important problem in geometric modeling and scientific computing. We are concerned with triangle meshes having only nonobtuse angles. Specifically, we propose a solution for guaranteed nonobtuse remeshing and nonobtuse mesh decimation. Our strategy for the remeshing problem is to first convert an input mesh, using a modified Marching Cubes algorithm, into a rough approximate mesh that is guaranteed to be nonobtuse. We then apply iterative "deform-to-fit" via constrained optimization to obtain a high-quality approximation, where the search space is restricted to be the set of nonobtuse meshes having a fixed connectivity. With a detailed nonobtuse mesh in hand, we apply constrained optimization again, driven by a quadric-based error, to obtain a hierarchy of nonobtuse meshes via mesh decimation.Item A Quadratic Bending Model for Inextensible Surfaces(The Eurographics Association, 2006) Bergou, Miklos; Wardetzky, Max; Harmon, David; Zorin, Denis; Grinspun, Eitan; Alla Sheffer and Konrad PolthierRelating the intrinsic Laplacian to the mean curvature normal, we arrive at a model for bending of inextensible surfaces. Due to its constant Hessian, our isometric bending model reduces cloth simulation times up to three-fold.Item Robust Reconstruction of Watertight 3D Models from Non-uniformly Sampled Point Clouds Without Normal Information(The Eurographics Association, 2006) Hornung, Alexander; Kobbelt, Leif; Alla Sheffer and Konrad PolthierWe present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero level-set of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laser-scanned data, image-based 3D reconstruction, and mesh repair.Item Spherical Barycentric Coordinates(The Eurographics Association, 2006) Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter; Alla Sheffer and Konrad PolthierWe develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the positions of points on a sphere with respect to the vertices of a given spherical polygon. In particular, we introduce spherical mean value coordinates that inherit many good properties of their planar counterparts. Furthermore, we present a construction that gives a simple and intuitive geometric interpretation for classical barycentric coordinates, like Wachspress coordinates, mean value coordinates, and discrete harmonic coordinates. One of the most interesting consequences is the possibility to construct mean value coordinates for arbitrary polygonal meshes. So far, this was only possible for triangular meshes. Furthermore, spherical barycentric coordinates can be used for all applications where only planar barycentric coordinates were available up to now. They include Bézier surfaces, parameterization, free-form deformations, and interpolation of rotations.