An adaptive method for the automatic triangulation of 3D parametric surfaces

Cuillière, Jean-Christophe

doi:10.1016/s0010-4485(97)00085-7

Cited by 85 publications

(59 citation statements)

References 22 publications

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“…Cuillire et al [5] introduces a analytic expression about the distortion level of mapping by parameter equation of curved surface, then the subdivision is carried out using AFT, finally mapped them onto curved surface to obtain meshes. The algorithm can measure the degree of distortion more accurately, but it doesn't apply to every situation.…”

Section: Related Workmentioning

confidence: 99%

“…Several commercial FEM software packages are available and widely used in the practical for industrial engineering design and analysis, such as ABAQUS, ANSYS. The typical approach could be divided into several categories: Octree [1], Delaunay triangulation [2][3][4] and advancing front technology (AFT) [5][6][7][8].In this paper an fast and accurate approach is proposed, which combine the Octree and AFT method.…”

Section: Introductionmentioning

confidence: 99%

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3D Mesh Generation Based on Improved Advancing Front Method

Xie¹,

Geng²

2017

Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)

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Abstract-Being able to generate 3D meshes automatically is an important issue in the domain of finite element analysis. A novel algorithm of 3D finite element mesh generation is proposed. The algorithm combines the Octree and advancing front technology to create meshes which have significantly higher quality and lower computational cost than single method. The key step and the main contribution of this work are to apply background grid to control the density and size of mesh, simultaneously reduce the intersection computation costs when internal units are generated. First the background grid is constructed using the Octree, and then the model surface is triangulated according to background grid. After that 3D entity unit is constructed and the whole mesh is optimized finally. The experiments results indicate that, compared with advancing front technology, the increment for its efficiency is about 20%, which reduce the time complexity.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

3D Mesh Generation Based on Improved Advancing Front Method

Xie¹,

Geng²

2017

Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)

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“…For the front/segment whose end points are N D 1 , N D 2 in the parametric space of a closed surface, there is a reference point outside the front/segment (as shown in Figure 17), named as N D 3 . The front/segment's end points are in the state of Section 4.3.1, and then the shift operator of front is described as follows.…”

Section: Shift Operator Of Frontsmentioning

confidence: 99%

“…Many efforts have been devoted to find robust and efficient methods for 3D surface mesh generation, in which two techniques, advancing front technique (AFT) [1][2][3][4][5][6] and Delaunay triangulation (DT) [7][8][9][10], are widely adopted.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage of this method is that the surface derivatives can be easily computed from NURBS surface. In the methods proposed by Lee [5], Cuilliere [3], and Tristano [2], a general anisotropic metric derived from the surface curvatures was used during surface meshing in the parametric space. The metric can be represented by a 2×2 matrix to transform the vectors and distances in the parametric space.…”

Section: Introductionmentioning

confidence: 99%

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An extended advancing front technique for closed surfaces mesh generation

Guan

Shan

Zheng

et al. 2007

Numerical Meth Engineering

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SUMMARYAn extended advancing front technique (AFT) with shift operations and Riemann metric named as shifting-AFT is presented for finite element mesh generation on 3D surfaces, especially 3D closed surfaces. Riemann metric is used to govern the size and shape of the triangles in the parametric space. The shift operators are employed to insert a floating space between real space and parametric space during the 2D parametric space mesh generation. In the previous work of closed surface mesh generation, the virtual boundaries are adopted when mapping the closed surfaces into 2D open parametric domains. However, it may cause the mesh quality-worsening problem. In order to overcome this problem, the AFT kernel is combined with the shift operator in this paper. The shifting-AFT can generate high-quality meshes and guarantee convergence in both open and closed surfaces. For the shifting-AFT, it is not necessary to introduce virtual boundaries while meshing a closed surface; hence, the boundary discretization procedure is largely simplified, and moreover, better-shaped triangles will be generated because there are no additional interior constraints yielded by virtual boundaries. Comparing with direct methods, the shifting-AFT avoids costly and unstable 3D geometrical computations in the real space. Some examples presented in this paper have demonstrated the advantages of shift-AFT in 3D surface mesh generation, especially for the closed surfaces.

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2001

Building and Solving Mathematical Programming Models in Engineering and Science

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An adaptive method for the automatic triangulation of 3D parametric surfaces

Cited by 85 publications

References 22 publications

3D Mesh Generation Based on Improved Advancing Front Method

3D Mesh Generation Based on Improved Advancing Front Method

An extended advancing front technique for closed surfaces mesh generation

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