Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2005, Pages 218-227

  Dey, Tamal K ^a   Ramqs, Edgar A ^b   Giesen, Joachim ^c   Sadri, Bardia ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c ETH ZURICH   (Switzerland)

Author keywords

Algorithms; Theory

Indexed keywords

DISTANCE FUNCTION; HAUSDORFF DISTANCE; SAMPLING DENSITY;

APPROXIMATION THEORY; COMPUTATIONAL METHODS; FLOW OF FLUIDS; FUNCTIONS; SAMPLING;

SURFACE STRUCTURE;

EID: 33244478988     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1064092.1064126     Document Type: Conference Paper

References (12)

1. N. Amenta and M. Bern. Surface reconstruction by Voronoi filtering. Discr. Comput. Geom., 22, pp. 481-504, (1999).
2. N. Amenta, M. Bern and D. Eppstein. The crust and the beta-skeleton; combinatorial curve reconstruction. Graphical Models and Image Processing, 60, pp. 125-135 (1998).
3. N. Amenta, S. Choi, T. K. Dey and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Internat. J. Comput. Geom. & Applications, vol. 12, 2002, pages 125-141.
4. N. Amenta, S. Choi and R. Kolluri. The power crust, unions of balls, and the medial axis transform. Computational Geometry: Theory and Applications, 19, pp. 127-153, (2001).
5. J. D. Boissonnat and F. Cazals. Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions. Computational Geometry: Theory and Applications, 22, pp. 185-203, (2002).
6. R. Chaine. A geometric convection approach of 3-D reconstruction. In Proc. Eurographics Sympos. on Geometry Processing, pp. 218 - 229, (2003).
7. T. K. Dey, J. Giesen and S. Goswami. Shape Segmentation and Matching with Flow Discretization. In Proc. 8th Workshop on Algorithms Data Strucutres, pp. 25-36, (2003).
8. T. K. Dey, J. Giesen, S. Goswami and W. Zhao. Shape dimension and approximation from samples. Discr. Comput. Geom., 29, pp. 419-434 (2003).
9. T. K. Dey and W. Zhao. Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee. Algorithmica, 38, pp. 179-200 (2004)
10. H. Edelsbrunner. Surface reconstruction by wrapping finite point sets in space. Discr. Comput. Geom., 32, pp. 231-244, (2004)
11. J. Giesen and M. John. The Flow Complex: A Data Structure for Geometric Modeling. In Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 285-294, (2003)
12. K. Grove. Critical Point Theory for Distance Functions. In Proceedings of Symposia in Pure Mathematics 54(3), pp. 357-385, (1993)