Recovering structure from r-sampled objects

Computer Graphics Forum

Volumn 28, Issue 5, 2009, Pages 1349-1360

  Aichholzer, O ^a   Aurenhammer, F ^b   Kornberger, B ^a   Plantinga, S ^c   Rote, G ^d   Sturm, A ^d   Vegter, G ^c  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^c UNIVERSITY OF GRONINGEN   (Netherlands)

^d FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

TOPOLOGY;

INTERPOLATING SUBDIVISION; LEVEL OF DETAIL; MEDIAL AXIS; POINT CLOUD; POLYTOPES; SAMPLE POINT; SURFACE COVERING; WEIGHTED ALPHA SHAPES;

APPROXIMATION ALGORITHMS;

EID: 70049093869     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2009.01512.x     Document Type: Article

References (26)

1. Aichholzer O., Aurenhammer F., Hackl T., Kornberger B., Peternell M., Pottmann H. : Approximating boundary-triangulated objects with balls. In Proc. 23rd European Workshop on Computational Geometry (Graz, 2007 pp. 130 133.
2. Aichholzer O., Aurenhammer F., Hackl T., Kornberger B. : Scalable piecewise linear approximations of 3d medial axes. Manuscript, 2009.
3. Amenta N., Bern M. : Surface reconstruction by voronoi filtering. Discrete & Computational Geometry 22 (1999 481 504.
4. Attali D., Boissonnat J.-D. : Complexity of the Delaunay triangulation of points on polyhedral surfaces. Discrete & Computational Geometry 30 (2003 437 452.
5. Attali D., Boissonnat J.-D., Edelsbrunner H. : Stability and computation of medial axes - a state-of-the-art report. In Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration (2007 Müller T., Hamann B., Russell B. Eds.), Springer Series on Mathematics and Visualization.
6. Amenta N., Choi S., Kolluri R. K. : The power crust, unions of balls, and the medial axis transform. Computational Geometry: Theory and Applications 19 (2001 127 153.
7. Aim@shape shape repository. http://shapes.aim-at-shape.net/.
8. Amenta N., Kolluri R. : Accurate and efficient unions of balls. In Proc. 16th Ann. Symp. Computational Geometry (Hong Kong, 2000 ACM, pp. 119 128.
9. Amenta N., Kolluri R. : The medial axis of a union. of balls. Computational Geometry: Theory and Applications 20 (2001 25 37.
10. Boissonnat J.-D., Cazals F. : Natural neighbor oordinates for points on a surface. Computational Geometry: Theory and Applications 19 (2001 155 173.
11. Bradshaw G., O'Sullivan C. : Adaptive medial-axis approximation for sphere-tree construction. ACM Transactions on Graphics 23 (2004 1 26.
12. Buchin K., Plantinga S., Rote G., Sturm A., Vegter G. Convex approximation by spherical patches. In Proc. 23rd European Workshop on Computational Geometry (Graz, 2007 pp. 26 29.
13. Chazals F., Cohen-Steiner D., Lieutier A. : A sampling theory for compact sets in Euclidean spaces. Discrete & Computational Geometry 41 (2009 461 479.
14. CGAL, Computational Geometry Algorithms Library. http://www.cgal.org/.
15. Chazal F., Lieutier A. : Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees. Computational Geometry: Theory and Applications 40 (2008 156 170.
16. Dey T. K., Giesen J., Hudson J. : Delaunay based shape reconstruction from large data. In Proc. IEEE Symp. Parallel and Large-Data Visualization and Graphics (San Diego, 2001 pp. 19 27.
17. Edelsbrunner H. : The union of balls and its dual shape. Discrete & Computational Geometry 13 (1995 415 440.
18. Giesen J., Miklos B., Pauly M. : Medial approximation of planar shapes from union of balls: A simpler and more robust algorithm. In Prof. 19th Canad. Conf. Comput. Geom. (CCCG) (2007 pp. 105 108.
19. Guibas L. J., Oudot S. Y. : Reconstruction using witness complexes. Discrete & Computational Geometry 40, 3 (2008 325 356.
20. Hubbard P. : Approximating polyhedra with spheres for time-critical collision detection. ACM Transactions on Graphics 15 (1996 179 210.
21. Kazhdan M., Bolitho M., Hoppe H. : Poisson surface reconstruction. In Eurographis Symposium on Geometry Processing (2006 pp. 61 70.
22. Niyogi P., Smale S., Weinberger S. : Finding the homology of submanifolds with high confidence from random samples. Discrete & Computational Geometry 39 (2008 419 441.
23. Ranjan V., Fournier A. : Matching and interpolation of shapes using unions of circles. Computer Graphics Forum 15 (1996 129 142.
24. Sud A., Foskey M., Manocha D. : Homotopy-preserving medial axis simplification. Int. J. Computational Geometry & Applications 17 (2007 423 451.
25. Scharf A., Shamir A. : Feature-sensitive 3d shape matching. In Proc. Computer Graphics International (CGI'04) (2004 pp. 1530 1552.
26. Yang Y., Brock O., Moll R. : Efficient and robust computation of an approximated medial axis. In Proc. 9th ACM Symp. Solid Modeling and Applications (2004 pp. 15 24.