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Isosurface stuffing: Fast tetrahedral meshes with good dihedral angles
 Special issue on Proceedings of SIGGRAPH 2007
, 2007
"... org/10.1145/1239451.1239508. 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 ..."
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Cited by 59 (3 self)
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org/10.1145/1239451.1239508. 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
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 46 (20 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.
Sparse Voronoi Refinement
 IN PROCEEDINGS OF THE 15TH INTERNATIONAL MESHING ROUNDTABLE
, 2006
"... ... a conformal Delaunay mesh in arbitrary dimension with guaranteed mesh size and quality. Our algorithm runs in outputsensitive time O(nlog(L/s) + m), with constants depending only on dimension and on prescribed element shape quality bounds. For a large class of inputs, including integer coordina ..."
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Cited by 42 (26 self)
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... a conformal Delaunay mesh in arbitrary dimension with guaranteed mesh size and quality. Our algorithm runs in outputsensitive time O(nlog(L/s) + m), with constants depending only on dimension and on prescribed element shape quality bounds. For a large class of inputs, including integer coordinates, this matches the optimal time bound of Θ(n log n + m). Our new technique uses interleaving: we maintain a sparse mesh as we mix the recovery of input features with the addition of Steiner vertices for quality improvement.
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 40 (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 point sets, but not with boundaries. Recently a randomized pointplacement strategy has been proposed to remove slivers while conforming to a given boundary. In this paper we present a deterministic algorithm for generating a weighted Delaunay mesh which respects the input boundary and has no poor quality tetrahedron including slivers. This success is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation. We show that an incremental weight pumping can be mixed seamlessly with vertex insertions in our weighted Delaunay refinement paradigm. 1
Adaptive and Quality 3D Meshing from Imaging Data
 SM'03
, 2003
"... This paper presents an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging dataprimarily Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). The extracted tetrahedral and hexahedral meshes are extensively used in finite element simulations. Our comprehe ..."
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Cited by 32 (11 self)
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This paper presents an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging dataprimarily Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). The extracted tetrahedral and hexahedral meshes are extensively used in finite element simulations. Our comprehensive approach combines bilateral and anisotropic (feature specific) diffusion filtering, with contour spectrum based, isosurface and interval volume selection. Next, a topdown octree subdivision coupled with the dual contouring method is used to rapidly extract adaptive 3D finite element meshes from volumetric imaging data. The main contributions are extending the dual contouring method to crack free interval volume tetrahedralization and hexahedralization with feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates better quality adaptive 3D meshes without hanging nodes. Our method has the properties of crack prevention and feature sensitivity.
Quality Meshing for Polyhedra with Small Angles
, 2004
"... We present an algorithm to compute a Delaunay mesh conforming to a polyhedron possibly with small input angles. The radiusedge ratio of most output tetrahedra are bounded by a constant, except possibly those that are provably close to small angles. Furthermore, the mesh is not unnecessarily dense i ..."
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Cited by 32 (8 self)
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We present an algorithm to compute a Delaunay mesh conforming to a polyhedron possibly with small input angles. The radiusedge ratio of most output tetrahedra are bounded by a constant, except possibly those that are provably close to small angles. Furthermore, the mesh is not unnecessarily dense in the sense that the edge lengths are at least a constant fraction of the local feature sizes at the edge endpoints. This algorithm is simple to implement as it eliminates most of the computation of local feature sizes and explicit protective zones. Our experimental results validate that few skinny tetrahedra remain and they lie close to small acute input angles. 1
Solving elliptic finite element systems in nearlinear time with support preconditioners
 Manuscript, Sandia National
"... Abstract. We show in this note how support preconditioners can be applied to a class of linear systems arising from use of the finite element method to solve linear elliptic problems. Our technique reduces the problem, which is symmetric and positive definite, to a symmetric positive definite diagon ..."
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Cited by 32 (1 self)
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Abstract. We show in this note how support preconditioners can be applied to a class of linear systems arising from use of the finite element method to solve linear elliptic problems. Our technique reduces the problem, which is symmetric and positive definite, to a symmetric positive definite diagonally dominant problem. Significant theory has already been developed for preconditioners in the diagonally dominant case. We show that the degradation in the quality of the preconditioner using our technique is only a small constant factor. 1. Introduction. Finite
ThreeDimensional Delaunay Mesh Generation
 Discrete and Computational Geometry
, 2004
"... We propose an algorithm to compute a conforming Delaunay mesh of a bounded domain specified by a piecewise linear complex. Arbitrarily small input angles are allowed, and the input complex is not required to be a manifold. ..."
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Cited by 28 (5 self)
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We propose an algorithm to compute a conforming Delaunay mesh of a bounded domain specified by a piecewise linear complex. Arbitrarily small input angles are allowed, and the input complex is not required to be a manifold.
A TimeOptimal Delaunay Refinement Algorithm in Two Dimensions
 In Symposium on Computational Geometry
, 2005
"... We propose a new refinement algorithm to generate sizeoptimal qualityguaranteed Delaunay triangulations in the plane. The algorithm takes O(n log n + m) time, where n is the input size and m is the output size. This is the first timeoptimal Delaunay refinement algorithm. 1 ..."
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Cited by 24 (3 self)
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We propose a new refinement algorithm to generate sizeoptimal qualityguaranteed Delaunay triangulations in the plane. The algorithm takes O(n log n + m) time, where n is the input size and m is the output size. This is the first timeoptimal Delaunay refinement algorithm. 1
Graded Conforming Delaunay Tetrahedralization with Bounded RadiusEdge Ratio
 Proceedings of the Fourteenth Annual ACMSIAM Symposium on Discrete Algorithms
, 2002
"... We propose an algorithm to compute a conforming Delaunay mesh of a polyhedral domain in three dimensions. Arbitrarily small input angles are allowed. The output mesh is graded and has bounded radiusedge ratio everywhere. 1 ..."
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Cited by 22 (1 self)
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We propose an algorithm to compute a conforming Delaunay mesh of a polyhedral domain in three dimensions. Arbitrarily small input angles are allowed. The output mesh is graded and has bounded radiusedge ratio everywhere. 1