The holes are filled in a careful manner to improve their valences as well as angle quality. For valence optimization, we remove the bad valence vertices with its neighbor triangle making regular holes in the mesh. In this paper, we present a novel method for valence optimization and angle improvement. The state-of-the-art mesh improvement methods often fail to deal with these issues. 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. Molecular surface mesh generation plays a vital role in molecular modeling and visualization. Numerical results are then reported to demonstrate the efficiency of the new numerical schemes and the quality of meshes generated by the new package for ion channel proteins with ion channel pores having different geometric complexities. To significantly improve its mesh quality and computer performance, in this paper, new numerical schemes for generating membrane and solvent meshes are presented and implemented in Python, resulting in a new ion channel mesh generation software package. Currently, an ion channel mesh generation software package developed in Lu's research group is one available in the public domain. However, generating these meshes is very difficult and highly technical due to the related three regions having very complex geometrical shapes. Ī finite element solution of an ion channel dielectric continuum model such as Poisson-Boltzmann equation (PBE) and a system of Poisson-Nernst-Planck equations (PNP) requires tetrahedral meshes for an ion channel protein region, a membrane region, and an ionic solvent region as well as an interface fitted irregular tetrahedral mesh of a simulation box domain. The package is downloadable at and can be run online at. It can be also used as a standalone program and works together with any other surface triangular mesh generator to obtain qualified manifold mesh. The procedure has been incorporated into our triangular molecular surface mesh generator, TMSmesh 2.0. Compared with the original meshes, these improved molecular surface meshes can be directly applied to boundary element simulations and generation of body-fitted volume meshes using Tetgen. The results show that the qualities of the surface meshes are greatly improved and the manifoldness of the surface meshes are preserved. In this paper, the tested meshes are biomolecular surface meshes exhibiting typically highly irregular geometry. This approach can be effectively applied to any manifold surface meshes with arbitrary complex geometry. ![]() ![]() The procedure utilizes an algorithm to remove redundant points having three or four valences and another algorithm to smooth the mesh using a modified version of Laplacian method without causing intersecting triangles. ![]() We present a systematic procedure to improve the qualities of triangular molecular surface meshes and at the same time preserve the manifoldness.
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