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Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation

机译：基于单元几何变形的平面网格曲面平滑算法

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摘要

Smoothing is one of the basic procedures for improvement of mesh quality. In this paper, a novel and efficient smoothing approach for planar and surface mesh based on element geometric deformation is developed. The presented approach involves two main stages. The first stage is geometric deformation of all the individual elements through a specially designed two-step stretching-shrinking operation (SSO), which is performed by moving the vertices of each element according to a certain rule in order to get better shape of the element. The second stage is to determine the position of each node of the mesh by a weighted average strategy according to quality changes of its adjacent elements. The suggested SSO-based smoothing algorithm works efficiently for triangular mesh and can be naturally expanded to quadrilateral mesh, arbitrary polygonal mesh, and mixed mesh. Combined with quadratic error metric (QEM), this approach may be also applied to improve the quality of surface mesh. The proposed method is simple to program and inherently very suitable for parallelization, especially on graphic processing unit (GPU). Results of numerical experiments demonstrate the effectiveness and potential of this method.
机译：平滑是改善网格质量的基本步骤之一。本文提出了一种基于单元几何变形的新颖有效的平面和表面网格平滑方法。所提出的方法涉及两个主要阶段。第一阶段是通过特殊设计的两步拉伸-收缩操作（SSO），对所有单个元素进行几何变形，该操作通过根据特定规则移动每个元素的顶点来执行，以便获得更好的元素形状。第二阶段是根据网格相邻节点的质量变化，通过加权平均策略确定网格每个节点的位置。所建议的基于SSO的平滑算法对于三角形网格有效，并且可以自然扩展到四边形网格，任意多边形网格和混合网格。结合二次误差度量（QEM），此方法也可用于提高表面网格的质量。所提出的方法易于编程，并且本质上非常适合并行化，尤其是在图形处理单元（GPU）上。数值实验结果证明了该方法的有效性和潜力。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第9期|435648.1-435648.9|共9页
  • 作者

    Sun Shuli; Zhang Minglei; Gou Zhihong;

  • 作者单位

    Peking Univ, Coll Engn, Dept Mech & Engn Sci, LTCS, Beijing 100871, Peoples R China.;

    Peking Univ, Coll Engn, Dept Mech & Engn Sci, LTCS, Beijing 100871, Peoples R China.;

    Peking Univ, Coll Engn, Dept Mech & Engn Sci, LTCS, Beijing 100871, Peoples R China.;

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