Abstract
Voronoi diagram for 3D balls can be applicable to various fields in science and engineering. The edge-tracing algorithm constructs the Voronoi diagram in O(mn) time in the worst-case where m and n are the numbers of edges and balls, respectively. The computation time of the algorithm is dominated by finding the end vertex of a given edge since all edges in the Voronoi diagram should be traced essentially. In this paper, we define the feasible region which a ball to define the end vertex of a given edge should intersect. Then, balls which do not intersect the feasible region are filtered out before finding an end vertex since they cannot define an end vertex. Therefore, we improve the runtime-performance of the edge-tracing algorithm via the feasible region.
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Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley & Sons, Chichester (1999)
Goede, A., Preissner, R., Frömmel, C.: Voronoi cell: New method for allocation of space among atoms: Elimination of avoidable errors in calculation of atomic volume and density. Journal of Computational Chemistry 18(9), 1113–1123 (1997)
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)
Kim, D.S., Cho, C.H., Kim, D., Cho, Y.: Recognition of docking sites on a protein using β-shape based on voronoi diagram of atoms. Computer-Aided Design (2005) (in printing)
Richards, F.M.: The interpretation of protein structures: Total volume, group volume distributions and packing density. Journal of Molecular Biology 82, 1–14 (1974)
Aurenhammer, F.: Power diagrams: Properties, algorithms and applications. SIAM Journal on Computing 16, 78–96 (1987)
Boissonnat, J.D., Karavelas, M.I.: On the combinatorial complexity of Euclidean Voronoi cells and convex hulls of d-dimensional spheres. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 305–312 (2003)
Gavrilova, M.: Proximity and Applications in General Metrics. PhD thesis, Department of Computer Science, The University of Calgary, Calgary, Canada (1998)
Gavrilova, M., Rokne, J.: Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space. Computer Aided Geometric Design 20(4), 231–242 (2003)
Kim, D.S., Cho, Y., Kim, D.: Euclidean Voronoi diagram of 3D balls and its computation via tracing edges. Computer-Aided Design 37(13), 1412–1424 (2005)
Luchnikov, V.A., Medvedev, N.N., Oger, L., Troadec, J.P.: Voronoi-Delaunay analysis of voids in systems of nonpherical particles. Physical Review E 59(6), 7205–7212 (1999)
Will, H.M.: Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology. PhD thesis, Swiss Federal Institute of Technology, Zurich (1999)
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 printing)
RCSB Protein Data Bank Homepage (2005), http://www.rcsb.org/pdb/
Halperin, D., Overmars, M.H.: Spheres, molecules, and hidden surface removal. In: Proceedings of the 10th ACM Symposium on Computational Geometry, pp. 113–122 (1994)
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© 2006 Springer-Verlag Berlin Heidelberg
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Cho, Y., Kim, D., Lee, H.C., Park, J.Y., Kim, DS. (2006). Reduction of the Search Space in the Edge-Tracing Algorithm for the Voronoi Diagram of 3D Balls. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_13
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DOI: https://doi.org/10.1007/11751540_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34070-6
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