40-Issue 5
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Browsing 40-Issue 5 by Author "Alliez, Pierre"
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Item Delaunay Meshing and Repairing of NURBS Models(The Eurographics Association and John Wiley & Sons Ltd., 2021) Xiao, Xiao; Alliez, Pierre; Busé, Laurent; Rineau, Laurent; Digne, Julie and Crane, KeenanCAD models represented by NURBS surface patches are often hampered with defects due to inaccurate representations of trimming curves. Such defects make these models unsuitable to the direct generation of valid volume meshes, and often require trial-and-error processes to fix them. We propose a fully automated Delaunay-based meshing approach which can mesh and repair simultaneously, while being independent of the input NURBS patch layout. Our approach proceeds by Delaunay filtering and refinement, in which trimmed areas are repaired through implicit surfaces. Beyond repair, we demonstrate its capability to smooth out sharp features, defeature small details, and mesh multiple domains in contact.Item Progressive Discrete Domains for Implicit Surface Reconstruction(The Eurographics Association and John Wiley & Sons Ltd., 2021) Zhao, Tong; Alliez, Pierre; Boubekeur, Tamy; Busé, Laurent; Thiery, Jean-Marc; Digne, Julie and Crane, KeenanMany global implicit surface reconstruction algorithms formulate the problem as a volumetric energy minimization, trading data fitting for geometric regularization. As a result, the output surfaces may be located arbitrarily far away from the input samples. This is amplified when considering i) strong regularization terms, ii) sparsely distributed samples or iii) missing data. This breaks the strong assumption commonly used by popular octree-based and triangulation-based approaches that the output surface should be located near the input samples. As these approaches refine during a pre-process, their cells near the input samples, the implicit solver deals with a domain discretization not fully adapted to the final isosurface. We relax this assumption and propose a progressive coarse-to-fine approach that jointly refines the implicit function and its representation domain, through iterating solver, optimization and refinement steps applied to a 3D Delaunay triangulation. There are several advantages to this approach: the discretized domain is adapted near the isosurface and optimized to improve both the solver conditioning and the quality of the output surface mesh contoured via marching tetrahedra.