Quality improvement of surface triangular mesh using a modified Laplacian smoothing approach avoiding intersection.

Tiantian Liu,Hongliang Li,Benzhuo Lu,Minxin Chen,Yu Song,Yongtang Shi

doi:10.1371/journal.pone.0184206

Abstract

We present a systematic procedure to improve the qualities of triangular molecular surface meshes and at the same time preserve the manifoldness. 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. This approach can be effectively applied to any manifold surface meshes with arbitrary complex geometry. In this paper, the tested meshes are biomolecular surface meshes exhibiting typically highly irregular geometry. The results show that the qualities of the surface meshes are greatly improved and the manifoldness of the surface meshes are preserved. 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 procedure has been incorporated into our triangular molecular surface mesh generator, TMSmesh 2.0. 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 package is downloadable at https://doi.org/10.6084/m9.figshare.5346169.v1 and can be run online at http://www.xyzgate.com.

Highlights

Surface mesh generation arises in many applications, such as numerical simulation, computer visualization and geometry processing
Some surface meshes generated by TMSmesh 2.0 can not be directly used to boundary element method (BEM) simulation or generation of body-fitted volume mesh due to singular triangles with tiny angles or very short edges
We test the initial and improved meshes in BEM computations of Poisson-Boltzmann (PB) electrostatics and generating corresponding surface conforming volume meshes that are required in finite element method (FEM) simulations

Summary

Introduction

Surface mesh generation arises in many applications, such as numerical simulation, computer visualization and geometry processing. Most computational applications involve triangulation of a complex surface geometry, especially in computational biology. Molecular surface plays an important role in computational biology, such as protein folding, structure prediction, docking and implicit solvent modeling. Recent developments in realistic mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling [1]. Many triangulated meshes are generated by scanning devices or by isosurfacing implicit representations. It is not easy to generate high-quality mesh for complex surface geometry in such

Methods

Results

Conclusion