3D Delaunay mesh generation coupled with an advancing-front approach

Frey, Pascal; Borouchaki, Houman; George, Paul‐Louis

doi:10.1016/s0045-7825(97)00222-3

Cited by 96 publications

(82 citation statements)

References 10 publications

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“…The octree technique recursively subdivides the cube containing the geometric model until the desired resolution is reached [39]. Advancing front methods start from a boundary and move a front from the boundary towards empty space within the domain [16] [29]. Delaunay refinement is used to refine triangles or tetrahedra locally by inserting new nodes to maintain the Delaunay criterion ('empty circum-sphere') [11].…”

Section: Mesh Generationmentioning

confidence: 99%

“…Here we choose the surface diffusion flow to smooth the molecular surface because it preserves volume, and it is especially suitable for biomoelcular meshes because it can also approximate spheres accurately if the initial mesh is embedded and close to a sphere. (16) where H is the mean curvature, n⃗ is the unit surface normal vector, and Δ is the Laplace-Beltrami operator. This flow is area shrinking and volume preserving.…”

Section: Improving the Aspect Ratio Of The Volumetric Mesh (Vertex Admentioning

confidence: 99%

“…In order to improve the aspect ratio, we need to add a tangent movement in Eqn. (16). Hence the flow becomes (17) where v(x) is the velocity in the tangent direction T ⃗ (x).…”

Section: Improving the Aspect Ratio Of The Volumetric Mesh (Vertex Admentioning

confidence: 99%

See 2 more Smart Citations

Quality meshing of implicit solvation models of biomolecular structures

Zhang

Bajaj

2006

Computer Aided Geometric Design

104

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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 binding rate constants.

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Section: Mesh Generationmentioning

confidence: 99%

Section: Improving the Aspect Ratio Of The Volumetric Mesh (Vertex Admentioning

confidence: 99%

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Quality meshing of implicit solvation models of biomolecular structures

Zhang

Bajaj

2006

Computer Aided Geometric Design

104

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“…In most cases a decomposition of the enclosed volume into discrete elements is neither obvious nor computationally simple to determine. Some volumetric meshing approaches rely on triangulating the CAD surface mesh first and computing a volumetric mesh through Delaunay tetrahedralization of the inner volume afterwards [12,30]. Nevertheless, in practice, using hexahedra as the discretization element of choice offers some important advantages, also see e.g.…”

Section: Introductionmentioning

confidence: 99%

Advanced Automatic Hexahedral Mesh Generation from Surface Quad Meshes

Kremer

Bommes

Lim

et al. 2014

Proceedings of the 22nd International Meshing Roundtable

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Summary. A purely topological approach for the generation of hexahedral meshes from quadrilateral surface meshes of genus zero has been proposed by M. Müller-Hannemann: in a first stage, the input surface mesh is reduced to a single hexahedron by successively eliminating loops from the dual graph of the quad mesh; in the second stage, the hexahedral mesh is constructed by extruding a layer of hexahedra for each dual loop from the first stage in reverse elimination order. In this paper, we introduce several techniques to extend the scope of target shapes of the approach and significantly improve the quality of the generated hexahedral meshes. While the original method can only handle "almost convex" objects and requires mesh surgery and remeshing in case of concave geometry, we propose a method to overcome this issue by introducing the notion of concave dual loops. Furthermore, we analyze and improve the heuristic to determine the elimination order for the dual loops such that the inordinate introduction of interior singular edges, i.e. edges of degree other than four in the hexahedral mesh, can be avoided in many cases.

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“…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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3D Delaunay mesh generation coupled with an advancing-front approach

Cited by 96 publications

References 10 publications

Quality meshing of implicit solvation models of biomolecular structures

Quality meshing of implicit solvation models of biomolecular structures

Advanced Automatic Hexahedral Mesh Generation from Surface Quad Meshes

Meshing Volumes Bounded by Smooth Surfaces

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