162 research outputs found
Consistently Orienting Facets in Polygon Meshes by Minimizing the Dirichlet Energy of Generalized Winding Numbers
Jacobson et al. [JKSH13] hypothesized that the local coherency of the
generalized winding number function could be used to correctly determine
consistent facet orientations in polygon meshes. We report on an approach to
consistently orienting facets in polygon meshes by minimizing the Dirichlet
energy of generalized winding numbers. While the energy can be concisely
formulated and efficiently computed, we found that this approach is
fundamentally flawed and is unfortunately not applicable for most handmade
meshes shared on popular mesh repositories such as Google 3D Warehouse.Comment: 6 pages, 4 figure
Robust Inside-Outside Segmentation Using Generalized Winding Numbers
Solid shapes in computer graphics are often represented with boundary descriptions, e.g. triangle meshes, but animation, physicallybased simulation, and geometry processing are more realistic and accurate when explicit volume representations are available. Tetrahedral meshes which exactly contain (interpolate) the input boundary description are desirable but difficult to construct for a large class of input meshes. Character meshes and CAD models are often composed of many connected components with numerous selfintersections, non-manifold pieces, and open boundaries, precluding existing meshing algorithms. We propose an automatic algorithm handling all of these issues, resulting in a compact discretization of the input’s inner volume. We only require reasonably consistent orientation of the input triangle mesh. By generalizing the winding number for arbitrary triangle meshes, we define a function that is a perfect segmentation for watertight input and is well-behaved otherwise. This function guides a graphcut segmentation of a constrained Delaunay tessellation (CDT), providing a minimal description that meets the boundary exactly and may be fed as input to existing tools to achieve element quality. We highlight our robustness on a number of examples and show applications of solving PDEs, volumetric texturing and elastic simulation
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