Guaranteed-quality anisotropic mesh generation for domains with curved boundaries

Yokosuka, Yusuke; Imai, Keisuke

doi:10.1016/j.cad.2008.08.010

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…This algorithm is extended in 3D by [30,31] and to domains with curves by [294]. This pseudo-geodesic distanced has also been applied to image sampling [115] and surface remeshing [279].…”

Section: Geodesic Delaunay Refinementmentioning

confidence: 99%

Geodesic Methods in Computer Vision and Graphics

Peyré¹

2009

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This paper reviews both the theory and practice of the numerical computation of geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows one to define a local metric (a symmetric positive tensor field) that encodes the information about the problem one wishes to solve. This takes into account a local isotropic cost (whether some point should be avoided or not) and a local anisotropy (which direction should be preferred). Using this local tensor field, the geodesic distance is used to solve many problems of practical interest such as segmentation using geodesic balls and Voronoi regions, sampling points at regular geodesic distance or meshing a domain with geodesic Delaunay triangles. The shortest paths for this Riemannian distance, the so-called geodesics, are also important because they follow salient curvilinear structures in the domain. We show several applications of the numerical computation of geodesic distances and shortest paths to problems in surface and shape processing, in particular segmentation, sampling, meshing and comparison of shapes.

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“…This algorithm is extended in 3D by [30,31] and to domains with curves by [294]. This pseudo-geodesic distanced has also been applied to image sampling [115] and surface remeshing [279].…”

Section: Geodesic Delaunay Refinementmentioning

confidence: 99%

Geodesic Methods in Computer Vision and Graphics

Peyré¹

2009

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“…This latter approach is used in conjunction with Ruppert's Delaunay refinement algorithm to provide anisotropic triangulation with guaranties on the aspect ratio of the triangles. This algorithm is extended to domains with curves by [23], and an alternative construction of the anisotropic Voronoi diagram is proposed in [24]. The simplified distance has been applied to image sampling [25], optimal samples placement with centroidal tessellations [26] and surface remeshing [27].…”

Section: Application To Meshing Of Planar Domainsmentioning

confidence: 99%

Anisotropic Geodesics for Perceptual Grouping and Domain Meshing

Bougleux

Peyré

Cohen

2008

Lecture Notes in Computer Science

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Abstract. This paper shows how Voronoi diagrams and their dual Delaunay complexes, defined with geodesic distances over 2D Reimannian manifolds, can be used to solve two important problems encountered in computer vision and graphics. The first problem studied is perceptual grouping which is a curve reconstruction problem where one should complete in a meaningful way a sparse set of noisy curves. From this latter curves, our grouping algorithm first designs an anisotropic tensor field that corresponds to a Reimannian metric. Then, according to this metric, the Delaunay graph is constructed and pruned in order to correctly link together salient features. The second problem studied is planar domain meshing, where one should build a good quality triangulation of a given domain. Our meshing algorithm is a geodesic Delaunay refinement method that exploits an anisotropic tensor field in order to locally impose the orientation and aspect ratio of the created triangles.

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A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics

Keskin

Peiró

2014

Journal of Computing and Information Science in Engineering

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A Voronoi region can be interpreted as the shape achieved by a crystal that grows from a seed and stops growing when it reaches either the domain boundary or another crystal. This analogy is exploited here to devise a method for the generation of anisotropic boundary-conforming Voronoi regions for a set of points. This is achieved by simulating the propagation of crystals as evolving fronts modeled by a level set method. The techniques to detect the collision of fronts (crystals), formation of interfaces between seeds, and treatment of boundaries as additional (inner or outer) restricting seeds are described in detail. The generation of anisotropic Voronoi regions consistent with a user-prescribed Riemannian metric is achieved by re-interpreting the metric tensor in terms of the speed of propagation normal to the boundary of the crystal. This re-interpretation offers a better means of restricting metric fields for mesh generation.

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Guaranteed-quality anisotropic mesh generation for domains with curved boundaries

Cited by 3 publications

References 9 publications

Geodesic Methods in Computer Vision and Graphics

Geodesic Methods in Computer Vision and Graphics

Anisotropic Geodesics for Perceptual Grouping and Domain Meshing

A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics

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