Results 1 - 10
of
133
Meshing Piecewise Linear Complexes by Constrained Delaunay Tetrahedralizations
- In Proceedings of the 14th International Meshing Roundtable
, 2005
"... Summary. We present a method to decompose an arbitrary 3D piecewise linear complex (PLC) into a constrained Delaunay tetrahedralization (CDT). It successfully resolves the problem of non-existence of a CDT by updating the input PLC into another PLC which is topologically and geometrically equivalent ..."
Abstract
-
Cited by 65 (3 self)
- Add to MetaCart
(Show Context)
Summary. We present a method to decompose an arbitrary 3D piecewise linear complex (PLC) into a constrained Delaunay tetrahedralization (CDT). It successfully resolves the problem of non-existence of a CDT by updating the input PLC into another PLC which is topologically and geometrically equivalent to the original one and does have a CDT. Based on a strong CDT existence condition, the redefinition is done by a segment splitting and vertex perturbation. Once the CDT exists, a practically fast cavity retetrahedralization algorithm recovers the missing facets. This method has been implemented and tested through various examples. In practice, it behaves rather robust and efficient for relatively complicated 3D domains. 1
A crystalline, red green strategy for meshing highly deformable objects with tetrahedra
- In 12th Int. Meshing Roundtable
, 2003
"... Motivated by Lagrangian simulation of elastic deformation, we propose a new tetrahedral mesh generation algorithm that produces both high quality elements and a mesh that is well conditioned for subsequent large deformations. We use a signed distance function defined on a Cartesian grid in order to ..."
Abstract
-
Cited by 65 (13 self)
- Add to MetaCart
(Show Context)
Motivated by Lagrangian simulation of elastic deformation, we propose a new tetrahedral mesh generation algorithm that produces both high quality elements and a mesh that is well conditioned for subsequent large deformations. We use a signed distance function defined on a Cartesian grid in order to represent the object geometry. After tiling space with a uniform lattice based on crystallography, we use the signed distance function or other user defined criteria to guide a red green mesh subdivision algorithm that results in a candidate mesh with the appropriate level of detail. Then, we carefully select the final topology so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, we compress the mesh to tightly fit the object boundary using either masses and springs, the finite element method or an optimization approach to relax the positions of the nodes. The resulting mesh is well suited for simulation since it is highly structured, has robust topological connectivity in the face of large deformations, and is readily refined if deemed necessary during subsequent simulation.
Anisotropic Voronoi Diagrams and Guaranteed-Quality Anisotropic Mesh Generation
- in SCG ’03: Proceedings of the nineteenth annual symposium on Computational geometry
, 2003
"... We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteed-quality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of aniso ..."
Abstract
-
Cited by 60 (2 self)
- Add to MetaCart
We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteed-quality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of anisotropic Voronoi diagrams of arbitrary dimensionality---most notably circumstances in which a site can see its entire Voronoi cell. In two dimensions, the anisotropic Voronoi diagram dualizes to a triangulation under these same circumstances. We use these properties to develop an algorithm for anisotropic triangular mesh generation in which no triangle has an angle smaller than 20 # , as measured from the skewed perspective of any point in the triangle.
A Procedural Approach to Authoring Solid Models
, 2002
"... We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our fra ..."
Abstract
-
Cited by 51 (4 self)
- Add to MetaCart
We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our framework treats simulation as a modeling operator rather than simply as a tool for animation, thereby suggesting a new paradigm for modeling as well as a new level of abstraction for interacting with simulation environments.
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.
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 output-sensitive 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 ..."
Abstract
-
Cited by 42 (26 self)
- Add to MetaCart
(Show Context)
... a conformal Delaunay mesh in arbitrary dimension with guaranteed mesh size and quality. Our algorithm runs in output-sensitive 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 ..."
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
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
Sampling and meshing a surface with guaranteed topology and geometry
- Proc. 20th
, 2004
"... This paper presents an algorithm for sampling and triangulating a smooth surface Σ ⊂ R 3 where the triangulation is homeomorphic to Σ. The only assumption we make is that the input surface representation is amenable to certain types of computations, namely computations of the intersection points of ..."
Abstract
-
Cited by 35 (6 self)
- Add to MetaCart
(Show Context)
This paper presents an algorithm for sampling and triangulating a smooth surface Σ ⊂ R 3 where the triangulation is homeomorphic to Σ. The only assumption we make is that the input surface representation is amenable to certain types of computations, namely computations of the intersection points of a line with the surface, computations of the critical points of some height functions defined on the surface and its restriction to a plane, and computations of some silhouette points. The algorithm ensures bounded aspect ratio, size optimality, and smoothness of the output triangulation. Unlike previous algorithms, this algorithm does not need to compute the local feature size for generating the sample points which was a major bottleneck. Experiments show the usefulness of the algorithm in remeshing and meshing CAD surfaces that are piecewise smooth. 1
