Identifying flat and tubular regions of a shape by unstable manifolds

Proceedings SPM 2006 - ACM Symposium on Solid and Physical Modeling

Volumn 2006, Issue , 2006, Pages 27-38

  Goswami, Samrat ^a   Dey, Tamal K ^b   Bajaj, Chandrajit L ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Delaunay triangulation; Point cloud; Unstable Manifold; Voronoi diagram

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; ELECTRONIC DOCUMENT IDENTIFICATION SYSTEMS;

DELAUNAY TRIANGULATION; POINT CLOUD; UNSTABLE MANIFOLD; VORONOI DIAGRAM;

SURFACE STRUCTURE;

EID: 33745956038     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1128888.1128892     Document Type: Conference Paper

References (23)

1. BAJAJ, C., BERNARDINI, F., AND XU, G. 1995. Automatic reconstruction of surfaces and scalar fields from 3D scans. In ACM SIGGRAPH, 109-118.
2. BERMAN, H. M., WESTBROOK, J., FENG, Z., GILLILAND, G., BHAT, T., WEISSIG, H., SHINDYALOV, I., AND BOURNE, P., 2000. The protein data bank. Nucleic Acids Research, 235-242.
3. BERNARDINI, F., BAJAJ, C., CHEN, J., AND SCHIKORE, D. 1999. Automatic reconstruction of 3d cad models from digital scans. Int. J. on Comp. Geom. and Appl. 9, 4-5, 327-369.
4. CGAL CONSORTIUM. CGAL: Computational Geometry Algorithms Library, http://www.cgal.org.
5. CHAINE, R. 2003, A geometric convection approach of 3-d reconstruction, In Proc, Eurographics Sympos. on Geometry Processing, 218-229.
6. CHAZAL, F., AND LIEUTIER, A. 2004, Stability and homotopy of a subset of the medial axis. In Proc. 9th ACM Sympos. Solid Modeling and Applications, 243-248.
7. COCONE, Tight Cocone Software for surface reconstruction and medial axis approximation, http://www.cse.ohio-state.edu/~tamaldey/cocone.html
8. DEY, T. K., AND GOSWAMI, S. 2003. Tight cocone: A water-tight surface reconstructor. In Proc. 8th ACM Sympos. Solid Modeling and Applications, 127-134.
9. DEY, T. K., AND GOSWAMI, S. 2004, Provable surface reconstruction from noisy samples. In Proc. 20th ACM-SIAM Sympos. Comput. Geom., 330-339.
10. DEY, T. K., AND ZHAO, W. 2004. Approximating the Medial axis from the Voronoi diagram with convergence guarantee. Algorithmica 38, 179-200.
11. DEY, T. K., GIESEN, J., AND GOSWAMI, S. 2003. Shape segmentation and matching with flow discretization, In Proc. Workshop Algorithms Data Strucutres (WADS 03), F. Dehne, J.-R. Sack, and M. Smid, Eds., LNCS 2748, 25-36.
12. DEY, T. K., GIESEN, J., RAMOS, E., AND SADRI, B. 2005. Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction, In Proc. 21st ACM-SIAMSympos. Comput. Geom., 218-227.
13. EDELSBRUNNER, H. 2002. Surface reconstruction by wrapping finite point sets in space. In Ricky Pollack and Eli Goodman Festschrift, B. Aronov, S. Basu, J. Pach, and M. Sharir, Eds. Springer-Verlag, 379-404.
14. GIESEN, J., AND JOHN, M. 2003. The flow complex: a data structure for geometric modeling, In Proc. 14th ACM-SIAM Sympos. Discrete Algorithms, 285-294.
15. KATZ, S., AND TAL, A. 2003. Hierarchical mesh decomposition using fuzzy clustering and cuts. In Trans. on Graphics, vol. 3, 954-961.
16. MORTARA, M., PATANÈ, G., SPAGNUOLO, M., FALCIDIENO, B., AND ROSSIGNAC, J. 2004. Blowing bubbles for the multi-scale analysis and decomposition of triangle meshes. Algorithmica 38, 227-248.
17. MORTARA, M., PATANÈ, G., SPAGNUOLO, M., FALCIDIENO, B., AND ROSSIGNAC, J. 2004. Plumber: a multi-scale decomposition of 3d shapes into tubular primitives and bodies. In Proc. 9th ACM Sympos. Solid Modeling and Applications, 139-158.
18. POTTMANN, H., HOFER, M., ODEHNAL, B., AND WALLNER, J. 2004. Line geometry for 3d shape understanding and reconstruction. Computer Vision - ECCV 3021, 1, 297-309.
19. SHINAGAWA, Y., KUNNI, T., BELAYEV, A., AND TSUKIOKA, T. 1996. Shape modeling and shape analysis based on singularities. Internat. J. Shape Modeling 2, 85-102.
20. SIDDIQI, K., SHOKOUFANDEH, A., DICKINSON, J., AND ZUCKER, S. 1998. Shock graphs and shape matching, Computer Vision, 222-229.
21. VÁRADY, T., MARTIN, R., AND COX, J. 1997, Reverse engineering of geometric models - an introduction. Computer Aided Design 29, 255-268.
22. VERROUST, A., AND LAZARUS, F. 2000, Extracting skeletal curves from 3d scattered data. The Visual Computer 16, 15-25.
23. WU, J., AND KOBBELT, L. 2005. Structure recovery via hybrid variational surface approximation. Computer Graphics Forum 24, 3, 277-284.