Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baker, N.A., McCammon, J.A.: Structural Bioinformatics. Wiley-Liss, Inc., Chichester (2003)
Bloomenthal, J.: An Implicit Surface Polygonizer. Academic Press, Boston (1994)
Boissonnat, J.D., Oudot, S.: Provably good surface sampling and approximation. In: Proceedings of the Eurographics/ACM SIGGRAPH symposium on Geometry processing, pp. 9–18. Eurographics Association (2003)
Cheng, H., Dey, T.K., Edelsbrunner, H., Sullivan, J.: Dynamic Skin Triangulation. Discrete Comput. Geom. 25, 525–568 (2001)
Cheng, H.-L., Shi, X.: Quality mesh generation for molecular skin surfaces using restricted union of balls. In: Proceedings of IEEE Visualization, pp. 399–405 (2005)
Cheng, S.-W., Dey, T.K.: Quality meshing with weighted delaunay refinement. In: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, pp. 137–146 (2002)
Cheng, S.-W., Dey, T.K., Edelsbrunner, H., Facello, M.A., Teng, S.-H.: Sliver exudation. In: Proceedings of the fifteenth annual symposium on Computational geometry, pp. 1–13. ACM Press, New York (1999)
Cheng, S.-W., Dey, T.K., Ramos, E., Ray, T.: Sampling and meshing a surface with guaranteed topology and geometry. In: Proceedings of ACM Annual Symposium on Computational Geometry (2004)
Cheng, S.-W., Dey, T.K., Ramos, E.A., Ray, T.: Quality meshing for polyhedra with small angles. In: Proceedings of the twentieth annual symposium on Computational geometry, pp. 290–299. ACM Press, New York (2004)
Cheng, S.-W., Dey, T.K., Ray, T.: Weighted delaunay refinement for polyhedra with small angles. In: Proceedings of 14th International Meshing Roundtable, pp. 323–342 (2005)
Dey, T.K., Giesen, J., Ramos, E.A., Sadri, B.: Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction. In: SCG 2005: Proceedings of the twenty-first annual symposium on Computational geometry, pp. 218–227. ACM Press, New York (2005)
Edelsbrunner, H., Guoy, D.: Sink-insertion for mesh improvement. In: SCG 2001: Proceedings of the seventeenth annual symposium on Computational geometry, pp. 115–123 (2001)
Edelsbrunner, H., Guoy, D.: An experimental study of sliver exudation. Eng. Comput. (Lond.) 18(3), 229–240 (2002)
Edelsbrunner, H., Li, X.-Y., Miller, G., Stathopoulos, A., Talmor, D., Teng, S.-H., Ungor, A., Walkington, N.: Smoothing and cleaning up slivers. In: Proceedings of the thirty-second annual ACM symposium on Theory of computing, pp. 273–277. ACM Press, New York (2000)
Rocchia, W., Sridharan, S., Nicholls, A., Alexov, E., Chiabrera, A., Honig, B.: 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. Journal of Computational Chemistry 23(1), 128–137 (2001)
Shewchuk, J.R.: Delaunay refinement mesh generation. PhD thesis (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheng, HL., Shi, X. (2006). Quality Tetrahedral Mesh Generation for Macromolecules. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_22
Download citation
DOI: https://doi.org/10.1007/11940128_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49694-6
Online ISBN: 978-3-540-49696-0
eBook Packages: Computer ScienceComputer Science (R0)