The mesh size is related to the complexity of the mesh. In some numerical analysis, such as finite element analysis, regular or qualified mesh is always required. The quality of triangles in surface mesh is crucial for robustness of boundary element method (BEM) and finite element method (FEM) computations. Uniformness includes the triangle shape, regularity, complexity and so on. It is an important issue that preserving the manifoldness of the original surface meshes in the process of improvements of mesh qualities. One of the typical non-manifold errors in surface meshes is intersecting triangles. Non-manifold surface mesh brings difficulties in generating corresponding surface conforming volume mesh that is an essential prerequisite for successful finite element method computations. Manifoldness of a surface mesh means that each point on the surface has a neighborhood which is homeomorphic to a disk in a real plane. Faithfulness related to the accuracy of the numerical simulation and geometry processing. Faithfulness is measured by how accurately the surface mesh preserves the original geometry and topology, such as surface area, volume and curvature of the referenced surface. Mesh quality refers to the faithfulness, manifoldness and uniformness. In this case, it is desirable to build high-quality meshes from those low-quality meshes before performing any numerical simulation. Low-quality triangular meshes can undermine the order of accuracy or even cause non-convergence in numerical computations. ![]() However, it is not easy to generate high-quality mesh for complex surface geometry in such processes, especially if automated. Many triangulated meshes are generated by scanning devices or by isosurfacing implicit representations. 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. Molecular surface plays an important role in computational biology, such as protein folding, structure prediction, docking and implicit solvent modeling. Most computational applications involve triangulation of a complex surface geometry, especially in computational biology. Surface mesh generation arises in many applications, such as numerical simulation, computer visualization and geometry processing. 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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