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Uniform random Voronoi meshes
 In 20th International Meshing Roundtable
, 2011
"... Summary. We generate Voronoi meshes over three dimensional domains with prescribed boundaries. Voronoi cells are clipped at onesided domain boundaries. The seeds of Voronoi cells are generated by maximal Poissondisk sampling. In contrast to centroidal Voronoi tessellations, our seed locations are ..."
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Cited by 12 (6 self)
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Summary. We generate Voronoi meshes over three dimensional domains with prescribed boundaries. Voronoi cells are clipped at onesided domain boundaries. The seeds of Voronoi cells are generated by maximal Poissondisk sampling. In contrast to centroidal Voronoi tessellations, our seed locations are unbiased. The exception is some bias near concave features of the boundary to ensure wellshaped cells. The method is extensible to generating Voronoi cells that agree on both sides of twosided internal boundaries. Maximal uniform sampling leads naturally to bounds on the aspect ratio and dihedral angles of the cells. Small cell edges are removed by collapsing them; some facets become slightly nonplanar. Voronoi meshes are preferred to tetrahedral or hexahedral meshes for some Lagrangian fracture simulations. We may generate an ensemble of random Voronoi meshes. Point location variability models some of the material strength variability observed in physical experiments. The ensemble of simulation results defines a spectrum of possible experimental results.
Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration
"... This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvatureadapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d ..."
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Cited by 6 (2 self)
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This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvatureadapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). In this high dimensional space, the mesh is optimized by computing a Centroidal Voronoi Tessellation (CVT), i.e. the minimizer of a C 2 objective function that depends on the coordinates at the vertices (quantization noise power). Optimizing this objective function requires to compute the intersection between the (higher dimensional) Voronoi cells and the surface (Restricted Voronoi Diagram). The method overcomes the dfactorial cost of computing a Voronoi diagram of dimension d by directly computing the restricted Voronoi cells with a new algorithm that can be easily parallelized (Vorpaline: Voronoi Parallel Linear Enumeration). The method is demonstrated with several examples comprising CAD and scanned meshes.
Robust modeling of constant mean curvature surfaces
 ACM Trans. Graph. (SIGGRAPH
, 2012
"... Copyright Notice Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profi t or direct commercial advantage and that copies show this notice on the fi rst page or initial scree ..."
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Cited by 4 (0 self)
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Copyright Notice Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profi t or direct commercial advantage and that copies show this notice on the fi rst page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specifi c permission and/or a fee. Permissions may be
Fast Updating of Delaunay Triangulation of Moving Points by Bicell Filtering
"... Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving thi ..."
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Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effective filtering technique that confirms most bicells whose Delaunay connectivities remain unchanged after the points are perturbed. Based on bicell flipping, we present an efficient algorithm for updating twodimensional and threedimensional Delaunay triangulations of dynamic point sets. Experimental results show that our algorithm outperforms previous methods.
paline: Voronoi Parallel Linear Enumeration). The method is demonstrated
"... This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvatureadapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d ..."
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This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvatureadapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). In this high dimensional space, the mesh is optimized by computing a Centroidal Voronoi Tessellation (CVT), i.e. the minimizer of a C2 objective function that depends on the coordinates at the vertices (quantization noise power). Optimizing this objective function requires to compute the intersection between the (higher dimensional) Voronoi cells and the surface (Restricted Voronoi Diagram). The method overcomes the dfactorial cost of computing a Voronoi diagram of dimension d by directly computing the restricted Voronoi cells with a new algorithm that can be easily parallelized (Vor
Discrete geodesics Exponential map Riemannian center
"... h i g h l i g h t s • We propose two intrinsic methods for computing centroidal Voronoi tessellation (CVT) on triangle meshes. • Thanks to their intrinsic nature, our methods compute CVT using metric only. • Our results are independent of the embedding space. a r t i c l e i n f o ..."
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h i g h l i g h t s • We propose two intrinsic methods for computing centroidal Voronoi tessellation (CVT) on triangle meshes. • Thanks to their intrinsic nature, our methods compute CVT using metric only. • Our results are independent of the embedding space. a r t i c l e i n f o