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Now showing 1 - 10 of 10
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    Spherical Barycentric Coordinates
    (The Eurographics Association, 2006) Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter; Alla Sheffer and Konrad Polthier
    We 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.
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    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 Polthier
    We 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.
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    A Dynamic Surface Reconstruction Framework for Large Unstructured Point Sets
    (The Eurographics Association, 2006) Allègre, Rémi; Chaine, Raphaëlle; Akkouche, Samir; Mario Botsch and Baoquan Chen and Mark Pauly and Matthias Zwicker
    We present a method to reconstruct simplified mesh surfaces from large unstructured point sets, extending recent work on dynamic surface reconstruction. The method consists of two core components: an efficient selective reconstruction algorithm, based on geometric convection, that simplifies the input point set while reconstructing a surface, and a local update algorithm that dynamically refines or coarsens the reconstructed surface according to specific local sampling constraints. We introduce a new data-structure that significantly accelerates the original selective reconstruction algorithm and makes it possible to handle point set models with millions of sample points. Our data-structure mixes a kd-tree with the Delaunay triangulation of the selected points enriched with a sparse subset of landmark sample points. This design efficiently responds to the specific spatial location issues of the geometric convection algorithm. We also develop an out-of-core implementation of the method, that permits to seamlessly reconstruct and interactively update simplified mesh surfaces from point sets that do not fit into main memory.
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    Contour-Based Surface Reconstruction using Implicit Curve Fitting, and Distance Field Filtering and Interpolation
    (The Eurographics Association, 2006) Marker, Jeffrey; Braude, Ilya; Museth, Ken; Breen, David; Raghu Machiraju and Torsten Moeller
    This paper presents a volumetric approach to reconstructing a smooth surface from a sparse set of paral- lel binary contours, e.g. those produced via histologic imaging. It creates a volume dataset by interpolating 2D filtered distance fields. The zero isosurface embedded in the computed volume provides the desired result. MPU implicit functions are fit to the input contours, defined as binary images, to produce smooth curves with controllable error bounds. Full 2D Euclidean distance fields are then calculated from the implicit curves. A distance-dependent Gaussian filter is applied to the distance fields to smooth their medial axis discontinuities. Monotonicity-constraining cubic splines are used to construct smooth, blending slices between the input slices. A mesh that approximates the zero isosurface is then extracted from the resulting volume. The effectiveness of the approach is demonstrated on a number of complex, multi-component contour datasets.
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    Collision Detection for Deformable Objects using Octrees
    (The Eurographics Association, 2006) Madera, F. A.; Day, A. M.; Laycock, S. D.; Louise M. Lever and Mary McDerby
    We present an algorithm for collision detection between multiple deformable objects translating in a large environment. We use Spatial Partitioning to subdivide the scene and a Bounding Volume Hierarchy to decompose the objects, using octrees in both cases. The algorithm is divided in two parts, the Broad and Narrow Phases, with objects that can be rigid or deformable. In the Broad Phase, an octree is used to partition the scene and cull away the object s Bounding Volumes that are distant. In the Narrow Phase, a hierarchical decomposition of Axis Aligned Bounding Boxes or spheres is employed to reduce the number of primitives in the pairwise comparisons. In summary this work is a general-purpose collision detection technique for performing real time collision detection of deformable bodies in interactive 3D applications.
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    Real-Time Modelling of the Action of Wind on Liquid Surfaces
    (The Eurographics Association, 2006) Bristol, Amanda; Varsamidis, Thomas; Louise M. Lever and Mary McDerby
    This work in progress aims to model the appearance of the surface of various liquids, when force from a virtual wind is applied. The physical effects caused by a wind force include waves and spray. The appearance of these effects is dependent upon the physical characteristics of a liquid, such as viscosity and surface tension. Much of the realistic work carried out in this area has depended upon non real-time methods such as frame-by-frame rendering and animation. Alternatively, supercomputers have been used to process visualisation models which use large quantities of data. This study aims to produce realistic effects with an attractive appearance, in real time. Work will also be carried out to explore the possibilities of modelling breaking waves in real time.
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    Topological Descriptor for CAD Models with Inner Cavities
    (The Eurographics Association, 2006) Symonova, O.; Dao, M.-S.; Amicis, R. De; Ucelli, G.; S. Battiato and G. Gallo and F. Stanco
    The current work introduces an algorithm for constructing Reeb graph for CAD models and their inner cavities. The nodes of the graph represent areas of the manifold of the model where topological changes occur. Edges of the graph encode information about connections between such areas. The outline for the topological graph matching is given for detection of graph (sub)isomorphism. The proposed Reeb graph structure can be used as a descriptor of CAD models in the retrieval process.
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    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 Polthier
    Relating 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.
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    Data-driven Tetrahedral Mesh Subdivision
    (The Eurographics Association, 2006) Rodríguez, Lyudmila; Navazo, Isabel; Vinacua, Álvar; Pere Brunet and Nuno Correia and Gladimir Baranoski
    Given a tetrahedral mesh immersed in a voxel model, we present a method to refine the mesh to reduce the discrepancy between interpolated values based on either scheme at arbitrary locations. An advantage of the method presented is that it requires few subdivisions and all decisions are made locally at each tetrahedron. We discuss the algorithm s performance and applications.
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    Nonobtuse Remeshing and Mesh Decimation
    (The Eurographics Association, 2006) Li, J. Y. S.; Zhang, H.; Alla Sheffer and Konrad Polthier
    Quality 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.