Results 1  10
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339
Sliver Exudation
 ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 1999
"... A sliver is a tetrahedron whose four vertices lie close to a plane and whose orthogonal projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3dimensional Delaunay triangulations even for wellspaced point sets. We show that if the Delaunay triangu ..."
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Cited by 89 (11 self)
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A sliver is a tetrahedron whose four vertices lie close to a plane and whose orthogonal projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3dimensional Delaunay triangulations even for wellspaced point sets. We show that if the Delaunay
An Experimental Study of Sliver Exudation
, 2001
"... We present results on a twostep improvement of mesh quality in threedimensional Delaunay triangulations. The rst step re nes the triangulation by inserting sinks and eliminates tetrahedra with large circumradius over shortest edge length ratio. The second step assigns weights to the vertices to ..."
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Cited by 18 (0 self)
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to eliminate slivers. Our experimental ndings provide evidence for the practical eectiveness of sliver exudation.
Sliver Exudation \Lambda
"... Abstract A sliver is a tetrahedron whose four vertices lie close to a plane and whose orthogonal projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3dimensional Delaunay triangulations even for wellspaced point sets. We show that if the Delauna ..."
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Abstract A sliver is a tetrahedron whose four vertices lie close to a plane and whose orthogonal projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3dimensional Delaunay triangulations even for wellspaced point sets. We show
Quality Meshing with Weighted Delaunay Refinement
 SIAM J. Comput
, 2002
"... Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic ..."
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Cited by 42 (7 self)
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Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic
Perturbing Slivers in 3D Delaunay Meshes
 18TH INTERNATIONAL MESHING ROUNDTABLE (2009) 157173
, 2009
"... Isotropic tetrahedron meshes generated by Delaunay triangulations are known to contain a majority of wellshaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicit ..."
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Cited by 10 (1 self)
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Isotropic tetrahedron meshes generated by Delaunay triangulations are known to contain a majority of wellshaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay
Sliverfree Three Dimensional Delaunay Mesh Generation
 PH.D THESIS, UIUC
, 2000
"... A key step in the nite element method is to generate wellshaped meshes in 3D. A mesh is wellshaped if every tetrahedron element has a small aspect ratio. It is an old outstanding problem to generate wellshaped Delaunay meshes in three or more dimensions. Existing algorithms do not completely solv ..."
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Cited by 13 (5 self)
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solve this problem, primarily because they can not eliminate all slivers. A sliver is a tetrahedron whose vertices are almost coplanar and whose circumradius is not much larger than its shortest edge length. We present two new algorithms to generate sliverfree Delaunay meshes. The rst algorithm locally
Weighted Delaunay Refinement for Polyhedra with Small Angles
 the Proceeding of the Fourth International Meshing Roundtable
, 2005
"... Abstract Recently, a provable Delaunay meshing algorithm called QMesh has been proposed forpolyhedra that may have acute input angles. The algorithm guarantees bounded circumradius to shortest edge length ratio for all tetrahedra except the ones near small input angles. Thisguarantee eliminates or l ..."
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Cited by 6 (1 self)
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or limits the occurrences of all types of poorly shaped tetrahedra except slivers. A separate technique called weight pumping is known for sliver elimination. But,allowable input for the technique so far have been periodic point sets and piecewise linear complex with nonacute input angles. In this paper
3d finite element meshing from imaging data
, 2005
"... This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the finite element method (FEM). A topdown octree subdivision coupled with a dual contouring method is used to r ..."
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Cited by 44 (19 self)
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This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the finite element method (FEM). A topdown octree subdivision coupled with a dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve mesh quality. The main contribution is extending the dual contouring method to crackfree interval volume 3D meshing with boundary feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing quality meshes for finite element calculations.
A geometric convection approach of 3D reconstruction
 EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING (2003)
, 2003
"... This paper introduces a fast and efficient algorithm for surface reconstruction. As many algorithms of this kind, it produces a piecewise linear approximation of a surface S from a finite, sufficiently dense, subset of its points. Originally, the starting point of this work does not come from the co ..."
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Cited by 48 (6 self)
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This paper introduces a fast and efficient algorithm for surface reconstruction. As many algorithms of this kind, it produces a piecewise linear approximation of a surface S from a finite, sufficiently dense, subset of its points. Originally, the starting point of this work does not come from the computational geometry field. It is inspired by an existing numerical scheme of surface convection developed by Zhao, Osher and Fedkiw. We have translated this scheme to make it depend on the geometry of the input data set only, and not on the precision of some grid around the surface. Our algorithm deforms a closed oriented pseudosurface embedded in the 3D Delaunay triangulation of the sampled points, and the reconstructed surface consists of a set of oriented facets located in this 3D Delaunay triangulation. This paper provides an appropriate data structure to represent a pseudosurface, together with operations that manage deformations and topological changes. The algorithm can handle surfaces with boundaries, surfaces of high genus and, unlike most of the other existing schemes, it does not involve a global heuristic. Its complexity is that of the 3D Delaunay triangulation of the points. We present some results of the method, which turns out to be efficient even on noisy input data.
Manifold reconstruction in arbitrary dimensions using witness complexes
 In Proc. 23rd ACM Sympos. on Comput. Geom
, 2007
"... It is a wellestablished fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, und ..."
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Cited by 39 (11 self)
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It is a wellestablished fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling assumptions. Unfortunately, these results do not extend to higherdimensional manifolds, even under stronger sampling conditions. In this paper, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between both complexes still hold on higherdimensional manifolds. We also use our structural results to devise an algorithm that reconstructs manifolds of any arbitrary dimension or codimension at different scales. The algorithm combines a farthestpoint refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample W to be sparse. Its time complexity is bounded by c(d)W  2, where c(d) is a constant depending solely on the dimension d of the ambient space. 1
Results 1  10
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339