Molecular surface mesh generation plays a vital role in molecular modeling and visualization. However, meshes extracted directly from Protein Data Bank files have several issues such as small and large triangles, redundant elements, self-intersections, and irregular vertices. The state-of-the-art mesh improvement methods often fail to deal with these issues. In this paper, we present a novel method for valence optimization and angle improvement. For valence optimization, we remove the bad valence vertices with its neighbor triangle making regular holes in the mesh. The holes are filled in a careful manner to improve their valences as well as angle quality. We also use a segmentation-based surface remeshing which segments the mesh into random segments and then each segment is independently remeshed. In addition, a point insertion scheme is applied to minimize the ratio of obtuse triangles. Experimental results show that our method not only improves the maximal and minimal angles to an angle bound of $$[30^{\circ }\;120^{\circ }]$$ but also improves the vertices’ regularity, reduces the ratio of obtuse triangles, preserves the area and volume, and always succeeds with downstream applications.

中文翻译：

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分子表面重新网格化的价态优化和角度改进

分子表面网格生成在分子建模和可视化中起着至关重要的作用。然而，直接从蛋白质数据库文件中提取的网格有几个问题，例如小三角形和大三角形、冗余元素、自相交和不规则顶点。最先进的网格改进方法通常无法解决这些问题。在本文中，我们提出了一种用于价态优化和角度改进的新方法。对于价优化，我们移除坏价顶点及其相邻三角形在网格中形成规则孔。这些孔以仔细的方式填充，以提高它们的价数和角度质量。我们还使用基于分割的表面重新划分网格，将网格划分为随机段，然后每个段独立地重新划分网格。此外，应用点插入方案来最小化钝角三角形的比率。实验结果表明，我们的方法不仅将最大和最小角度提高到 $$[30^{\circ }\;120^{\circ }]$$ 的角度界限，而且还提高了顶点的规则性，降低了比率钝角三角形，保留面积和体积，并且总是在下游应用中取得成功。