Automatic mesh generator with specified boundary

George, Paul‐Louis; Hecht, Frédéric; Saltel, Eric

doi:10.1016/0045-7825(91)90017-z

Cited by 231 publications

(130 citation statements)

References 6 publications

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“…• Valid volume: "yes" means that a volume mesh can be generated from the derived surface mesh with the surface constrained Delaunay mesher Tetmesh-GHS3D (see [6]). In this case, the surface mesh defines a volume and does not self-intersect.…”

Section: Applicationsmentioning

confidence: 99%

Automatic Non-manifold Topology Recovery and Geometry Noise Removal

Alleaume¹

2009

Proceedings of the 18th International Meshing Roundtable

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Abstract. This paper presents an effective method for automatic topology recovery of non-manifold geometries. Mixing topology recovery and geometry noise detection/removal allowed us to achieve effectively the automation and robustness required by such methods. We developped our method on CAD boundary representation (BREP) geometries in the context of surface mesh generation, but it could also be directly applied to discrete STL or mesh geometries. Its reliability and efficiency has been validated on a variety of complex manifold and non-manifold CAD geometries.

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Section: Applicationsmentioning

confidence: 99%

Automatic Non-manifold Topology Recovery and Geometry Noise Removal

Alleaume¹

2009

Proceedings of the 18th International Meshing Roundtable

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“…Computational methods for generating and refining triangular and tetrahedral finite element meshes in 2 and 3-dimensions can be roughly classified as Delaunay based methods, [6,19,7,17,50,47] and methods based on the partition of triangles and tetrahedra [39,33,34,28].…”

Section: Introductionmentioning

confidence: 99%

Multithread parallelization of Lepp-bisection algorithms

Rivara

Rodríguez

Montenegro

et al. 2012

Applied Numerical Mathematics

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Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained. Multithread parallelization of lepp-bisection algorithms AbstractLongest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained.

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“…The radius-radius ratios distribution of our algorithm (in medium grey) has been superimposed with those obtained by two other algorithms: the unit edge mesher of [GHS90,GHS91] (in dark grey), which priviledges the running time (approximately ten seconds for the skull model on a Pentium IV at 1.7 GHz), and the variational mesher of [ACSYD05] (in light grey), which priviledges the quality of the output. These two programs, run with our initial surface mesh D |∂O (P i ) as input, generated approximately the same number of vertices as our mesher.…”

Section: Implementation and Resultsmentioning

confidence: 99%

“…Then, the original boundary B is dropped away and replaced by its discretized version, P . On one hand, mesh generation algorithms based on advancing front methods [FBG96], as well as some Delaunay re nement techniques, like the unit edge mesher of [GHS90,GHS91], construct meshes that conform strictly to the discretized boundary P . On the other hand, Ruppertlike methods [She98] re ne the boundary mesh: whenever a point should be inserted on B, it is in fact inserted on P .…”

Section: Introductionmentioning

confidence: 99%

Meshing Volumes Bounded by Smooth Surfaces

Oudot

Rineau

Yvinec

Proceedings of the 14th International Meshing Roundtable

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This paper introduces a three-dimensional mesh generation algorithm for domains bounded by smooth surfaces. The algorithm combines a Delaunay-based surface mesher with a Ruppert-like volume mesher, to get a greedy algorithm that samples the interior and the boundary of the domain at once. The algorithm constructs provably-good meshes, it gives control on the size of the mesh elements through a user-de ned sizing eld, and it guarantees the accuracy of the approximation of the domain boundary. A noticeable feature is that the domain boundary has to be known only through an oracle that can tell whether a given point lies inside the object and whether a given line segment intersects the boundary. This makes the algorithm generic enough to be applied to a wide variety of objects, ranging from domains de ned by implicit surfaces to domains de ned by level-sets in 3D grey-scaled images or by point-set surfaces.

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Automatic mesh generator with specified boundary

Cited by 231 publications

References 6 publications

Automatic Non-manifold Topology Recovery and Geometry Noise Removal

Automatic Non-manifold Topology Recovery and Geometry Noise Removal

Multithread parallelization of Lepp-bisection algorithms

Meshing Volumes Bounded by Smooth Surfaces

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