Quality Tetrahedral Mesh Generation for Macromolecules

This paper presents an algorithm to generate quality tetrahedral meshes for the volumes bounded by the molecular skin model defined by Edelsbrunner. The algorithm applies the Delaunay refinement to the tetrahedral meshes bounded by quality surface meshes. In particular, we iteratively insert the circumcenters of bad shape tetrahedra with a priority parameterized by its distance from the surface. We achieve a bounded radius-edge ratio for the tetrahedral mesh after the refinement. Finally, we apply the sliver exudation algorithm to remove ‘slivers'. The algorithm terminates with guarantees on the tetrahedral quality and an accurate approximation of the original surface boundary.

[1]  Herbert Edelsbrunner,et al.  Sliver exudation , 1999, SCG '99.

[2]  Herbert Edelsbrunner,et al.  An Experimental Study of Sliver Exudation , 2002, Engineering with Computers.

[3]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.

[4]  Ho-Lun Cheng,et al.  Dynamic Skin Triangulation , 2001, SODA '01.

[5]  Steve Oudot,et al.  Provably Good Surface Sampling and Approximation , 2003, Symposium on Geometry Processing.

[6]  Tamal K. Dey,et al.  Quality meshing for polyhedra with small angles , 2004, SCG '04.

[7]  Tamal K. Dey,et al.  Quality meshing with weighted Delaunay refinement , 2002, SODA '02.

[8]  Tamal K. Dey,et al.  Weighted Delaunay Refinement for Polyhedra with Small Angles , 2005, IMR.

[9]  Herbert Edelsbrunner,et al.  Sink-insertion for mesh improvement , 2001, SCG '01.

[10]  Emil Alexov,et al.  Rapid grid‐based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects , 2002, J. Comput. Chem..

[11]  Michael T. Goodrich,et al.  Drawing planar graphs with circular arcs , 2001, Discret. Comput. Geom..

[12]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

[13]  Tamal K. Dey,et al.  Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction , 2005, Symposium on Computational Geometry.

[14]  Tamal K. Dey,et al.  Sampling and meshing a surface with guaranteed topology and geometry , 2004, SCG '04.

[15]  Xiang-Yang Li,et al.  Smoothing and cleaning up slivers , 2000, STOC '00.