A β-Shape from the Voronoi Diagram of Atoms for Protein Structure Analysis
In this paper, we present a β-shape and a β-complex for a set of atoms with arbitrary sizes for a faster response to the topological queries among atoms. These concepts are the generalizations of the well-known α-shape and α-complex (and their weighted counterparts as well). To compute a β-shape, we first compute the Voronoi diagram of atoms and then transform the Voronoi diagram to a quasi-triangulation which is the topological dual of the Voronoi diagram. Then, we compute a β-complex from the quasi-triangulation by analyzing the valid intervals for each simplex in the quasi-triangulation. It is shown that a β-complex can be computed in O(m) time in the worst case from the Voronoi diagram of atoms, where m is the number of simplices in the quasi-triangulation. Then, a β-shape for a particular β consisting of k simplices can be located in O(log m + k) time in the worst case from the simplicies in the β-complex sorted according to the interval values.
KeywordsVoronoi diagram of spheres α-shape α-complex β-shape β-complex
Unable to display preview. Download preview PDF.
- 8.Edelsbrunner, H.: Weighted alpha shapes. Technical Report UIUCDCS-R-92-1760, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL (1992)Google Scholar
- 13.(RCSB Protein Data Bank Homepage), http://www.rcsb.org/pdb/
- 15.Kim, D.S., Cho, Y., Kim, D., Cho, C.H.: Protein sructure analysis using Euclidean Voronoi diagram of atoms. In: Proceedings of the International Workshop on Biometric Technologies (BT 2004), pp. 125–129 (2004)Google Scholar
- 16.Kim, D.S., Cho, Y., Kim, D., Kim, S., Bhak, J., Lee, S.H.: Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis. In: Proceedings of the 1st International Symposium on Voronoi Diagrams in Science and Engineering (VD 2004), pp. 137–144 (2004)Google Scholar
- 17.Cho, Y., Kim, D., Kim, D.S.: Topology representation for the Voronoi diagram of 3D spheres. International Journal of CAD/CAM 5(3) (2005) (in press)Google Scholar
- 18.Kim, D.-S., Kim, D., Cho, Y., Sugihara, K.: Quasi-triangulation and interworld data struction in three dimensions. Computer-Aided Design (2005) (submitted)Google Scholar