This paper describes an approach to smooth the surface and improve the quality of quadrilateral/hexahedral meshes with feature preserved using geometric flow. For quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent direction. For hexahedral meshes, besides the surface vertex movement in the normal and tangent directions, interior vertices are relocated to improve the aspect ratio. Our method has the properties of noise removal, feature preservation and quality improvement of quadrilateral/hexahedral meshes, and it is especially suitable for biomolecular meshes because the surface diffusion flow preserves sphere accurately if the initial surface is close to a sphere. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.
Figure 1: The comparison of mesh quality of Thermus Thermophilus small Ribosome 30S (1J5E) crystal subunit at the residual level. The pink color shows 16S rRNA and the remaining colors are proteins. (a) the original quadrilateral mesh (13705 vertices, 13762 quads); (b) the improved quadrilateral mesh; (c) the improved hexahedral mesh (40294 vertices, 33313 hexes).
Figure 2: The comparison of mesh quality of Haloarcula Marismortui large Ribosome 50S (1JJ2) crystal subunit at the residual level. The light yellow and the pink color show 5S and 23S rRNA respectively, the remaining colors are proteins. (a) the original quad mesh (17278 vertices, 17328 quads); (b) the improved quad mesh; (c) the improved hex mesh (57144 vertices, 48405 hexes).
Figure 3: Surface smoothing and quality improvement of the molecule consisting of three amino acids (ASN, THR and TYR) with 49 atoms at the atomic level. (a) and (c) - the original mesh (45534 vertices, 45538 quads); (b) and (d) - the improved mesh.
Figure 4: The quality of an adaptive quadrilateral mesh of a biomolecule mAChE is improved (26720 vertices, 26752 quads). (a) the original mesh; (b) after quality improvement.
Figure 5: Adaptive quadrilateral/hexadedral meshes of the human head. (a) the original quad mesh (1828 vertices, 1826 quads); (b) the improved quad mesh; (c) the improved hex mesh (4129 vertices, 3201 hexes), the right part of elements are removed to shown one cross section.
Figure 6: The comparison of mesh quality of the interior and exterior hexahedral meshes. (a) the original interior hex mesh (8128 vertices, 6587 hexes); (b) the improved interior hex mesh; (c) the improved exterior hex mesh (16521 vertices, 13552 hexes).
Figure 7: The comparison of mesh quality of the human knee and the Venus model. (a) the original hex mesh of the knee (2103 vertices, 1341 hexes); (b) the improved hex mesh of the knee; (c) the original hex mesh of Venus (2983 vertices, 2135 hexes); (d) the improved hex mesh of Venus.
Figure 8: The comparison of mesh quality of a bubble model. (a) a uniform quad mesh (828 vertices, 826 quads); (b) an adaptive quad mesh (5140 vertices, 5138 quads); (c) the improved adaptive quad mesh.