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首页> 外文会议>Visualization, Image-Guided Procedures pt.2; Progress in Biomedical Optics and Imaging; vol.8 no.28; Proceedings of SPIE-The International Society for Optical Engineering; vol.6509 pt.2 >Quality improvement of tetrahedral meshes by optimizing the minimum local angle
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Quality improvement of tetrahedral meshes by optimizing the minimum local angle

机译：通过优化最小局部角度来改善四面体网格的质量

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摘要

Mesh quality is an important factor for stable, repeatable numerical simulations. The Delaunay method is widely used for creation of 3D tetrahedral meshes. Two-dimensional triangulation via Delaunay exhibits the mathematical property of maximizing the minimum interior angle. This feature provides excellent quality meshes for a given node deployment. However, the 3D equivalent of this property, i.e. to maximize the minimum solid angle, is not assured with 3D Delaunay. The tetrahedron's interior solid angle is directly related to mesh quality, but it is independent of the Delaunay process. Consequently, sliver elements and poor quality meshes can be created via Delaunay tetrahedral formation. In this paper, we describe a method for maximizing the minimum solid angle of tetrahedral meshes by changing the locations of non-boundary nodes. The displacement of nodes uses a gradient-based approach. The process is iterative and terminates when the mesh quality exceeds a user specified quality or convergence criterion. The technique is robust. The relocation of vertices is local which avoids significant deformation of the mesh. The results show considerable improvements in mesh quality. Using a 3D human brain mesh (27,000+ elements), our algorithm reduced the number of ill-formed elements three fold. We are extending this approach to allow tangential motion along the boundary surfaces. Currently all boundary nodes are fixed which constrains some of the element qualities.
机译：网格质量是稳定，可重复的数值模拟的重要因素。 Delaunay方法被广泛用于创建3D四面体网格。通过Delaunay进行的二维三角剖分显示出最大化最小内角的数学特性。对于给定的节点部署，此功能可提供出色的网格质量。但是，使用3D Delaunay不能确保此属性的3D等效值，即最大化最小立体角。四面体的内部立体角与网格质量直接相关，但与Delaunay过程无关。因此，通过Delaunay四面体形成会产生条子元素和劣质的网格。在本文中，我们描述了一种通过更改非边界节点的位置来最大化四面体网格的最小立体角的方法。节点的位移使用基于梯度的方法。该过程是迭代的，并在网格质量超过用户指定的质量或收敛标准时终止。该技术是鲁棒的。顶点的重定位是局部的，这避免了网格的明显变形。结果显示出网格质量的显着改善。使用3D人脑网格（27,000多个元素），我们的算法将不合格元素的数量减少了三倍。我们正在扩展这种方法，以允许沿边界表面的切线运动。当前，所有边界节点都是固定的，这限制了某些元素的质量。

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