Results 1 - 10
of
88
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 ..."
Abstract
-
Cited by 59 (3 self)
- Add to MetaCart
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 top-down octree subdivision coupled with a dual contouring method is used to r ..."
Abstract
-
Cited by 46 (20 self)
- Add to MetaCart
(Show Context)
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 top-down 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 crack-free 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.
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 ..."
Abstract
-
Cited by 40 (7 self)
- Add to MetaCart
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 point-placement 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
Tetrahedral mesh generation and optimization based on centroidal Voronoi tesselations
- INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
, 2003
"... ..."
Manifold reconstruction in arbitrary dimensions using witness complexes
- In Proc. 23rd ACM Sympos. on Comput. Geom
, 2007
"... It is a well-established 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 ..."
Abstract
-
Cited by 39 (11 self)
- Add to MetaCart
(Show Context)
It is a well-established 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 higher-dimensional 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 higher-dimensional 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 farthest-point 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
Aggressive Tetrahedral Mesh Improvement
- In Proc. of the 16th Int. Meshing Roundtable
, 2007
"... Summary. We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or “mesh clean-up. ” Our goal is to aggressively optimize the worst t ..."
Abstract
-
Cited by 39 (4 self)
- Add to MetaCart
(Show Context)
Summary. We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or “mesh clean-up. ” Our goal is to aggressively optimize the worst tetrahedra, with speed a secondary consideration. Mesh optimization methods often get stuck in bad local optima (poor-quality meshes) because their repertoire of mesh transformations is weak. We employ a broader palette of operations than any previous mesh improvement software. Alongside the best traditional topological and smoothing operations, we introduce a topological transformation that inserts a new vertex (sometimes deleting others at the same time). We describe a schedule for applying and composing these operations that rarely gets stuck in a bad optimum. We demonstrate that all three techniques—smoothing, vertex insertion, and traditional transformations—are substantially more effective than any two alone. Our implementation usually improves meshes so that all dihedral angles are between 31 ◦ and 149 ◦ , or (with a different objective function) between 23 ◦ and 136 ◦. 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 data-primarily Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). The extracted tetrahedral and hexahedral meshes are extensively used in finite element simulations. Our comprehe ..."
Abstract
-
Cited by 32 (11 self)
- Add to MetaCart
This paper presents an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data-primarily 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 top-down 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 of implicit solvation models of biomolecular structures
- COMPUT. AIDED GEOM. DES
, 2006
"... This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gauss ..."
Abstract
-
Cited by 32 (9 self)
- Add to MetaCart
(Show Context)
This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gaussian isotropic kernel functions and a two-level clustering technique. This enables the selection of a smooth implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flow techniques are used to improve the surface and volume mesh quality. Several examples are presented, including generated meshes for biomolecules that have been successfully used in finite element simulations involving solvation energetics and rate binding constants.
