Euclidean Voronoi diagram of 3D balls and its computation via tracing edges

CAD Computer Aided Design

Volumn 37, Issue 13, 2005, Pages 1412-1424

  Kim, Deok Soo ^a   Cho, Youngsong ^a   Kim, Donguk ^a  

^a Hanyang University   (South Korea)

Author keywords

Apollonius problem; Edge tracing; Euclidean Voronoi diagrams; Rational quadratic B zier

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; GRAPH THEORY; PROBLEM SOLVING; THREE DIMENSIONAL;

APOLLONIUS PROBLEM; EDGE-TRACING; EUCLIDEAN VORONOI DIAGRAMS; RATIONAL QUADRATIC BÉZIER;

COMPUTER AIDED DESIGN;

EID: 22944434527     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2005.02.013     Document Type: Article

References (36)

1. B. Angelov, J.-F. Sadoc, R. Jullien, A. Soyer, J.-P. Mornon, and J. Chomilier Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds Proteins: Struct Funct Genet 49 4 2002 446 456
2. F. Aurenhammer Power diagrams: properties, algorithms and applications SIAM J Comput 16 1987 78 96
3. F. Aurenhammer Voronoi diagrams - a survey of a fundamental geometric data structure ACM Comput Surv 23 3 1991 345 405
4. H. Blum A transformation for extracting new descriptors of shape Proceedings of symposium models for perception of speech & visual form 1967 p. 362-80
5. H. Blum, and R.N. Nagel Shape description using weighted symmetric axis features Pattern Recogn 10 1978 167 180
6. G. Farin Curves and surfaces for computer-aided geometric design: a practical guide 4th ed 1996 Academic Press San Diego
7. Gavrilova M. Proximity and Applications in General Metrics. Ph.D. Thesis: The University of Calgary, Dept. of Computer Science, Calgary, AB, Canada; 1998.
8. M. Gavrilova, and J. Rokne Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space Comput Aided Geometric Des 20 4 2003 231 242
9. A. Goede, R. Preissner, and C. Frömmel Voronoi cell: new method for allocation of space among atoms: elimination of avoidable errors in calculation of atomic volume and density J Comput Chem 18 9 1997 1113 1123
10. M. Held On the computational geometry of pocket machining 1991 Springer Berlin
11. D.-S. Kim, D. Kim, and K. Sugihara Voronoi diagram of a circle set from Voronoi diagram of a point set: I. Topology Comput Aided Geometric Des 18 6 2001 541 562
12. D.-S. Kim, D. Kim, and K. Sugihara Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry Comput Aided Geometric Des 18 6 2001 563 585
13. D.-S. Kim, Y.-C. Chung, J.J. Kim, D. Kim, and K. Yu Voronoi diagram as an analysis tool for spatial properties for ceramics J Ceram Process Res 3 3 2002 150 152
14. D.-S. Kim, Y. Cho, D. Kim, and C.-H. Cho Protein structure analysis using Euclidean Voronoi diagram of atoms Proceedings of international workshop on biometric technologies (BT 2004). Special forum on modeling and simulation in biometric technology 2004 p. 125-9
15. D.-S. Kim, Y. Cho, and D. Kim Edge-tracing algorithm for Euclidean Voronoi diagram of 3D spheres Proceedings of 16th canadian conference on computational geometry 2004 p. 176-9
16. D.G. Kirkpatrick Efficient computation of continuous skeletons Proceedings of 14th IEEE symposium foundations of computer science 1979 p. 18-27
17. D.T. Lee Medial axis transformation of a planar shape IEEE Trans Pattern Anal Machine Intell 4 1982 363 369
18. V.A. Luchnikov, N.N. Medvedev, L. Oger, and J.-P. Troadec Voronoi-Delaunay analyzis of voids in systems of nonspherical particles Phys Rev E 59 6 1999 7205 7212
19. J.C.G. Montoro, and J.L.F. Abascal The Voronoi polyhedra as tools for structure determination in simple disordered systems J Phys Chem 97 16 1993 4211 4215
20. K. Ohno, K. Esfarjani, and Y. Kawazoe Computational materials science from ab initio to Monte Carlo methods 1999 Springer Berlin
21. A. Okabe, B. Boots, K. Sugihara, and S.N. Chiu Spatial tessellations: concepts and applications of Voronoi diagrams 2nd ed 1999 Wiley Chichester
22. M. Paluszny, and W. Boehm General cyclides Comput Aided Geometric Des 15 7 1998 699 710
23. Pottman H. personal communication. 2004.
24. F.M. Richards The interpretation of protein structures: total volume, group volume distributions and packing density J Mol Biol 82 1974 1 14
25. J. Rokne Appolonius's 10th problem J. Arvo Graphics Gems II 1991 Academic Press New York 19 24
26. M.I. Shamos, and D. Hoey Closest-point problems Proceedings of the 16th annual IEEE symposium on foundations of computer science 1975 p. 151-62
27. K. Sugihara A simple method for avoiding numerical errors and degeneracy in Voronoi diagram construction. IEICE Transactions Fundamentals E75-A 1992 468 477
28. K. Sugihara, and M. Iri Construction of the Voronoi diagram for 'one million' generators in single precision arithmetic Proc IEEE 80 1992 1471 1484
29. K. Sugihara, M. Sawai, H. Sano, D.-S. Kim, and D. Kim Disk packing for the estimation of the size of a wire bundle Jpn J Ind Appl Math 21 3 2004 259 278
30. A.H. Thiessen Precipitation averages for large areas Monthly Weather Rev 39 1911 1082 1084
31. V.P. Voloshin, S. Beaufils, and N.N. Medvedev Void space analysis of the structure of liquids J Mol Liq 96-97 2002 101 112
32. Will H.-M. Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology. Ph.D. Thesis, ETH, Zurich; 1999.
33. C. Yap Robust geometric computation J.E. Goodman J. O'Rourke Handbook of discrete and computational geometry 1997 CRC Press LLC New York
34. Computational Geometry Algorithms Library (CGAL) Homepage. http://www.cgal.org/.
35. The CORE Homepage. http://www.cs.nyu.edu/exact/core/.
36. RCSB Protein Data Bank (PDB) Homepage. http://www.rcsb.org/pdb/.