Manifoldization of β-shapes in O (n) time

CAD Computer Aided Design

Volumn 42, Issue 4, 2010, Pages 322-339

  Kim, Deok Soo ^a   Lee, Changhee ^a   Cho, Youngsong ^a   Kim, Donguk ^b  

^a Hanyang University   (South Korea)

^b Gangneung Wonju National University   (South Korea)

Author keywords

complex; shape; Mesh; Non manifold; Protein structure; Quasi triangulation; Topology; Voronoi diagram of spheres

Indexed keywords

FLOATING POINT OPERATIONS; GEOMETRIC CHARACTERISTICS; NON-MANIFOLD; PROTEIN DATA BANK; PROTEIN MODELS; PROTEIN STRUCTURES; SPHERICAL ATOMS; SPHERICAL PARTICLE; THREE DIMENSIONAL SPACE; VORONOI DIAGRAMS; WORST CASE;

COMPUTATIONAL GEOMETRY; PROTEINS; SPHERES; STRUCTURAL ANALYSIS; SURFACE STRUCTURE; TOPOLOGY; TRIANGULATION;

THREE DIMENSIONAL;

EID: 77349090881     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2009.12.005     Document Type: Article

References (36)

1. Kim D., Cho C.-H., Cho Y., Ryu J., Bhak J., and Kim D.-S. Pocket extraction on proteins via the Voronoi diagram of spheres. Journal of Molecular Graphics and Modelling 26 7 (2008) 1104-1112
2. Kim D.-S., Cho C.-H., Kim D., and Cho Y. Recognition of docking sites on a protein using β-shape based on Voronoi diagram of atoms. Computer-Aided Design 38 5 (2006) 431-443
3. Kim D.-S., Seo J., Kim D., Ryu J., and Cho C.-H. Three-dimensional beta shapes. Computer-Aided Design 38 11 (2006) 1179-1191
4. Ryu J., Park R., and Kim D.-S. Molecular surfaces on proteins via beta shapes. Computer-Aided Design 39 12 (2007) 1042-1057
5. Edelsbrunner H., Facello M., and Liang J. On the definition and the construction of pockets in macromolecules. Discrete Applied Mathematics 88 (1998) 83-102
6. Heifets A., and Eisenstein M. Effect of local shape modifications of molecular surfaces on rigid-body protein-protein docking. Protein Engineering 16 3 (2003) 179-185
7. Lee B., and Richards F.M. The interpretation of protein structures: Estimation of static accessibility. Journal of Molecular Biology 55 (1971) 379-400
8. Liang J., Edelsbrunner H., Fu P., Sudhakar P.V., and Subramaniam S. Analytical shape computation of macromolecules: I. Molecular area and volume through alpha shape. PROTEINS: Structure, Function, and Genetics 33 (1998) 1-17
9. Peters K.P., Fauck J., and Frömmel C. The automatic search for ligand binding sites in protein of known three dimensional structure using only geometric criteria. Journal of Molecular Biology 256 (1996) 201-213
10. Shoichet B.K., and Kunts I.D. Protein docking and complementarity. Journal of Molecular Biology 221 (1991) 327-346
11. Choi Y. Vertex-based boundary representation of non-manifold geometric models. Ph.D. thesis. USA: Carnegie-Mellon University; 1989.
12. Weiler K. The radial edge structure: A topological representation for non-manifold geometric boundary modeling. In: Wozny M., McLaughlin H., and Encarnacao J. (Eds). Geometric modeling for CAD applications (1988), North Holland, Elsevier Science Publishers B.V. 3-36
13. Yamaguchi Y., and Kimura F. Nonmanifold topology based on coupling entities. IEEE Computer Graphics and Applications 15 1 (1995) 42-50
14. Guéziec A., Taubin G., Lazarus F., and Horn B. Cutting and stitching: Converting sets of polygons to manifold surfaces. IEEE Transactions on Visualization and Computer Graphics 7 2 (2001) 136-151
15. Gursoz E.L., Choi Y., and Prinz F.B. Boolean set operations on non-manifold boundary representation objects. Computer-Aided Design 23 1 (1991) 33-39
16. Lee K. Principles of CAD/CAM/CAE systems (1999), Addison Wesley
17. Rossignac J, Cardoze D. Matchmaker: Manifold BReps for non-manifold r-sets. In: Proceedings of the 5th ACM symposium on solid modeling and applications. 1999 p. 31-41.
18. Sugihara K., and Iri M. A solid modelling system free from topological inconsistency. Journal of Information Processing 12 4 (1989) 380-393
19. Woo T. A combinatorial analysis of boundary data structure schemata. IEEE Computer Graphics and Applications 5 3 (1985) 19-27
20. Ryu J., Cho Y., and Kim D.-S. Triangulation of molecular surfaces. Computer-Aided Design 41 6 (2009) 463-478
21. Kim D., Lee C., Cho Y., and Kim D.-S. Manifoldization of β-shapes by topology operators. Proceedings of the geometric modeling and processing (GMP 2008). Lecture notes in computer science vol. 4975 (2008) 505-511
22. RCSB Protein Data Bank Homepage; 2009. http://www.rcsb.org/pdb/.
23. Kim D.-S., Kim D., Cho Y., and Sugihara K. Quasi-triangulation and interworld data structure in three dimensions. Computer-Aided Design 38 7 (2006) 808-819
24. Boissonnat J.-D., and Delage C. Convex hull and Voronoi diagram of additively weighted points. In: Brodal G., and Leonardi S. (Eds). Proceedings of the 13th annual European symposium on algorithms (ESA 2005). Lecture notes in computer science vol. 3669 (2005), Springer-Verlag 367-378
25. Kim D., and Kim D.-S. Region-expansion for the Voronoi diagram of 3D spheres. Computer-Aided Design 38 5 (2006) 417-430
26. Kim D-S, Cho Y, Kim D. Edge-tracing algorithm for Euclidean Voronoi diagram of 3D spheres. In: Proceedings of the 16th Canadian Conference on Computational Geometry. 2004. p. 176-9.
27. Kim D.-S., Cho Y., and Kim D. Euclidean Voronoi diagram of 3D balls and its computation via tracing edges. Computer-Aided Design 37 13 (2005) 1412-1424
28. Kim D.-S., Cho Y., Kim D., Kim S., Bhak J., and Lee S.-H. Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis. Japan Journal of Industrial and Applied Mathematics 22 2 (2005) 251-265
29. Hilton P.J., and Wylie S. Homology theory: An introduction to algebraic topology (1967), Cambridge University Press
30. Munkres J.R. Elements of algebraic topology (1984), Perseus Press
31. Kim D.-S., Seo J., Kim D., Cho Y., and Ryu J. The β-shape and β-complex for analysis of molecular structures. In: Gavrilova M. (Ed). Generalized voronoi diagrams: A geometry-based approach to computational intelligence. The book series on computational intelligence (2008)
32. Seo J, Cho Y, Kim D, Kim D-S. An efficient algorithm for three-dimensional β-complex and β-shape via a quasi-triangulation. In: Proceedings of the ACM symposium on solid and physical modeling. 2007. p. 323-8.
33. Edelsbrunner H., and Mücke E.P. Three-dimensional alpha shapes. ACM Transactions on Graphics 13 1 (1994) 43-72
34. Bondi A. van der Waals volumes and radii. Journal of Physical Chemistry 68 (1964) 441-451
35. Mäntylä M. An introduction to solid modeling (1988), Computer Science Press
36. Koltun W.L. Precision space-filling atomic models. Biopolymers 3 6 (1965) 665-679