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Trends in automatic three-dimensional mesh generation

Profile image of Will SchroederWill Schroeder

1988, Computers & Structures

https://doi.org/10.1016/0045-7949(88)90248-9
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Abstract

Some recent efforts on the development of methods to ensun the robustness of automatic thracdimensional mesh generation techniques arc discuss& The topic arcas considered arc mesh entity classification, finite octrcc cell triangulation, and coarse mesh generation by element removal.

FAQs

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What are the key advantages of using octree structures for mesh generation?add

The study reveals that octree structures provide linear growth rates and regular discretization, enhancing computational efficiency for complex geometries. For instance, they simplify adaptive analysis by enabling local control over mesh generation.

How does mesh classification impact the accuracy of finite element meshes?add

The paper demonstrates that accurate mesh classification ensures topology compatibility, which prevents topological holes in finite element meshes. It finds that inferior classification can lead to invalid mesh representations, particularly in complex geometries.

What challenges arise when applying Delaunay triangulation for 3D mesh generation?add

The research notes difficulties in achieving topological compatibility due to reliance solely on point data, leading to potential 'holes' in mesh topology. Furthermore, these challenges are exacerbated by insufficient point distributions, as shown in practical case studies.

What are the methodologies explored for integrating geometric and finite element modeling?add

The methods discussed include leveraging topological data structures to interlink geometric models and finite element mesh data. The paper also outlines geometric operators necessary for dynamic interactions between modeling systems and mesh generation.

How does the element removal procedure enhance mesh generation in complex objects?add

This procedure allows for generating large coarse meshes by strategically removing vertices, edges, and faces, providing controlled geometric modeling interactions. The study exemplifies its effectiveness in creating valid tetrahedral elements while maintaining shape integrity.

Figures (5)
Fig. 1. Finite octree mesh example. The complexity of procedures required to decom- One approach to fully automatic three-dimensional mesh generation is based on spatial decomposition followed by subdomain meshing. In this approach, the object of interest is first decomposed into a number of regular disjoint cells. The cells are further decomposed into the individual finite elements. This approach, typically based on quadtree structures in two dimensions [7, 8] and octree structures in three dimensions [9, 10] (Fig. 1), has the advantage of being computationally efficient with a linear growth rate and provides a regular discretization structure that can be taken advantage of in adaptive analysis. However, it is important to point out that the octree-based decomposition used for mesh generation represent a form of discretization of the domain in which individual cells can be quite complex. Figure 2 demonstrates this for a simple example. Figure 2(a) shows just the surface information in the finite octree for an object. The octant at the intersection of three primitives has been drawn in dashed lines. Figure 2(b) shows a close-up of this single octant indicating the discrete geometric information contained within it. It is clear that the decomposition of the geometric information in the individual cells to produce a finite element mesh requires additional specific consideration.
Fig. 1. Finite octree mesh example. The complexity of procedures required to decom- One approach to fully automatic three-dimensional mesh generation is based on spatial decomposition followed by subdomain meshing. In this approach, the object of interest is first decomposed into a number of regular disjoint cells. The cells are further decomposed into the individual finite elements. This approach, typically based on quadtree structures in two dimensions [7, 8] and octree structures in three dimensions [9, 10] (Fig. 1), has the advantage of being computationally efficient with a linear growth rate and provides a regular discretization structure that can be taken advantage of in adaptive analysis. However, it is important to point out that the octree-based decomposition used for mesh generation represent a form of discretization of the domain in which individual cells can be quite complex. Figure 2 demonstrates this for a simple example. Figure 2(a) shows just the surface information in the finite octree for an object. The octant at the intersection of three primitives has been drawn in dashed lines. Figure 2(b) shows a close-up of this single octant indicating the discrete geometric information contained within it. It is clear that the decomposition of the geometric information in the individual cells to produce a finite element mesh requires additional specific consideration.
Fig. 2. Finite octree for simple example. (a) Surface entities in finite octree; (b) discrete geometry in single octant. Trends in automatic three-dimensional mesh generation
Fig. 2. Finite octree for simple example. (a) Surface entities in finite octree; (b) discrete geometry in single octant. Trends in automatic three-dimensional mesh generation
Fig. 3. Element removal meshing in finite octree cell. (a) Geometry in cell; (b) mesh for geometry in cell.. Figure 3 demonstrates the application of this procedure to an example boundary octant. Figure 3(a) shows the discrete geometry in the octant and
Fig. 3. Element removal meshing in finite octree cell. (a) Geometry in cell; (b) mesh for geometry in cell.. Figure 3 demonstrates the application of this procedure to an example boundary octant. Figure 3(a) shows the discrete geometry in the octant and
This paper has focused on two of the areas important to providing robust fully automatic three- dimensional mesh generating capabilities. Emphasis has been placed on the importance of properly classifying the finite element entities against the geometric model as well as supporting the geometric modeling needs of these mesh generators. It is important to realize that the satisfactory solution to these two needs relates to some of the important current issues in computational geometry. However, the development of satisfactory solution to these geometry related problems is necessary before robust automated analysis procedures for complex problems, including those with evolving problems, can be developed.
This paper has focused on two of the areas important to providing robust fully automatic three- dimensional mesh generating capabilities. Emphasis has been placed on the importance of properly classifying the finite element entities against the geometric model as well as supporting the geometric modeling needs of these mesh generators. It is important to realize that the satisfactory solution to these two needs relates to some of the important current issues in computational geometry. However, the development of satisfactory solution to these geometry related problems is necessary before robust automated analysis procedures for complex problems, including those with evolving problems, can be developed.

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References (20)

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