Surface Smoothing and Quality Improvement of Quadrilateral/Hexahedral Meshes with Geometric Flow

Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.449-468, September 11-14 2005

MESHING
RESEARCH
CORNER

14th International Meshing Roundtable
San Diego, CA, USA
September 11-14, 2005

Yongjie Zhang
Computational Visualization Center, Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA.
jessica@ices.utexas.edu

Chandrajit Bajaj
Computational Visualization Center, Department of Computer Sciences and Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA.
bajaj@cs.utexas.edu

Guoliang Xu
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, China.
xuguo@lsec.cc.ac.cn

Abstract
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.

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