Valence optimization and angle improvement for molecular surface remeshing
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ORIGINAL ARTICLE
Valence optimization and angle improvement for molecular surface remeshing Dawar Khan1 · Alexander Plopski2 · Yuichiro Fujimoto1 · Masayuki Kanbara1 · Zhanglin Cheng3 · Hirokazu Kato1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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, selfintersections, 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◦ 120◦ ] but also improves the vertices’ regularity, reduces the ratio of obtuse triangles, preserves the area and volume, and always succeeds with downstream applications. Keywords Molecular surface remeshing · Mesh quality · Valence optimization · Molecular modeling
1 Introduction Molecular surface meshing and molecular modeling are an interesting research direction used in many fields including computer graphics, mathematics, molecular biology, biophysics, and chemistry. It plays a vital role in various phenomena such as protein folding, docking, implicit-solvent modeling, structure prediction, interaction of molecules, and measuring their areas/volumes [1,2]. However, meshes generated directly from molecular data have several defects including self-intersections, small and large angles, and redundant and irregular vertices. There are several methods to improve the mesh quality prior to its use in the downstream
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Dawar Khan [email protected]
1
Interactive Media Design Lab, Nara Institute of Science and Technology, Nara 630-0192, Japan
2
Department of Information Science, University of Otago, Dunedin, New Zealand
3
Shenzhen VisuCA Key Lab, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
applications. Some of these defects such as self-intersections have been addressed in SMOPT [3]. However, SMOPT fails in maximal and minimal angle improvements. Similarly, small and large angles have been improved up to an acceptable level by a recently proposed cut-and-fill (CAF) method [1]. However, CAF fails to achieve a considerable improvement in valence optimization. Figure 1 shows the main steps in molecular surface remeshing. Protein Data Bank (PDB) files are downloadable from their online repository
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