The Meccano Method for Automatic Three-Dimensional Triangulation and Volume Parametrization of Complex Solids

Montenegro, R.; Cascón, J.M.; Rodríguez, Eduardo; Escobar, J. M.; Montero, G.

doi:10.4203/csets.26.2

Cited by 11 publications

(20 citation statements)

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“…Our procedure has been specifically developed for genus-zero solids, but it can be generalized to arbitrary objects, as it is explained in subsection 4.3. The key lies on having a volumetric parameterization of the solid following the mecano method described in [27,28]. In this method the surface parameterization must be explicitly given, but we think that this handicap could be overcome by applying a technique similar to PolyCubeMaps [24,34,36].…”

Section: Conclusion and Challengesmentioning

confidence: 99%

“…To do that, the given surface triangulation of the solid, T S , is divided in six patches or connected subtriangulations, T i S (i = 1, 2,...,6), having the same connectivities as the cube faces. Specifically, if we consider that each subtriangulation corresponds to a vertex of a graph and two vertices of the graph are connected if their corresponding subtriangulations have at least a common edge, then, the graphs corresponding to the solid and the graph of the cube must be isomorphic (see [8,28] for details).…”

Section: Boundary Mappingmentioning

confidence: 99%

“…Secondly, a mapping from the meccano boundary to the solid surface is required. Then, the meccano method [7,8,27,28] automatically produces the volumetric parameterization.…”

Section: Solid With Surface Of Genus Greater Than Zeromentioning

confidence: 99%

“…In the next section we describe the main steps to parameterize a genus-zero solid onto a cube. Some parts of this section are taken from our previous works on mesh untangling and smoothing and the meccano method [7,8,11,27,28], but they have been adapted to the requirements of the present work. The representation of the solid by means of trivariate T-splines is developed in section 3.…”

Section: Introductionmentioning

confidence: 99%

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The meccano method for isogeometric solid modeling and applications

Escobar

Montenegro

Rodríguez

et al. 2012

Engineering with Computers

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We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation. We present some results of the application of isogeometric analysis with T-splines to the resolution of Poisson equation in solids parameterized with this technique.

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Section: Conclusion and Challengesmentioning

confidence: 99%

Section: Boundary Mappingmentioning

confidence: 99%

“…Secondly, a mapping from the meccano boundary to the solid surface is required. Then, the meccano method [7,8,27,28] automatically produces the volumetric parameterization.…”

Section: Solid With Surface Of Genus Greater Than Zeromentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The meccano method for isogeometric solid modeling and applications

Escobar

Montenegro

Rodríguez

et al. 2012

Engineering with Computers

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“…The average mesh quality is obtained by summing the quality of all valid tetrahedra and dividing the sum by the number of valid and inverted tetrahedra. All these tetrahedral meshes were constructed with a tool that applies an automatic strategy for adaptive tetrahedral mesh generation based on the meccano method [6,7,28,29]. Some of them were generated using, as input data, the surface triangulations obtained from different Internet repositories [30].…”

mentioning

confidence: 99%

Performance Evaluation of a Parallel Algorithm for Simultaneous Untangling and Smoothing of Tetrahedral Meshes

Benítez

Rodríguez

Escobar

et al. 2014

Proceedings of the 22nd International Meshing Roundtable

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Abstract.A new parallel algorithm for simultaneous untangling and smoothing of tetrahedral meshes is proposed in this paper. We provide a detailed analysis of its performance on shared-memory many-core computer architectures. This performance analysis includes the evaluation of execution time, parallel scalability, load balancing, and parallelism bottlenecks. Additionally, we compare the impact of three previously published graph coloring procedures on the performance of our parallel algorithm. We use six benchmark meshes with a wide range of sizes. Using these experimental data sets, we describe the behavior of the parallel algorithm for different data sizes. We demonstrate that this algorithm is highly scalable when it runs on two different high-performance many-core computers with up to 128 processors. However, some parallel deterioration is observed. Here, we analyze the main causes of this parallel deterioration.

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Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Ruiz‐Gironés

Oliver

Socorro-Marrero

et al. 2017

Numerical Meth Engineering

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This is the peer reviewed version of the following article: Ruiz Gironès , E., Oliver , A., Socorro, G., Cascón, J., Escobar, J.M., Montenegro, R., Sarrate, J. Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures. "International journal for numerical methods in engineering", 2018, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5706/pdf. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.Peer ReviewedPostprint (author's final draft

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The Meccano Method for Automatic Three-Dimensional Triangulation and Volume Parametrization of Complex Solids

Cited by 11 publications

References 0 publications

The meccano method for isogeometric solid modeling and applications

The meccano method for isogeometric solid modeling and applications

Performance Evaluation of a Parallel Algorithm for Simultaneous Untangling and Smoothing of Tetrahedral Meshes

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

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