Medial axis approximation and unstable flow complex

Proceedings of the Annual Symposium on Computational Geometry

Volumn 2006, Issue , 2006, Pages 327-336

  Giesen, Joachim ^a   Ramos, Edgar A ^b   Sadri, Bardia ^b  

^a ETH ZURICH   (Switzerland)

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

Author keywords

Flow Complex; Gradient Flow; Medial Axis Approximation; Stable and Unstable Manifolds

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL GEOMETRY; INFORMATION ANALYSIS; TOPOLOGY;

FLOW COMPLEX; GRADIENT FLOW; MEDIAL AXIS APPROXIMATION; STABLE AND UNSTABLE MANIFOLDS;

APPROXIMATION THEORY;

EID: 33748030765     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1137856.1137905     Document Type: Conference Paper

References (13)

1. N. Amenta and M. W. Bern. Surface reconstruction by voronoi filtering. Discrete & Computational Geometry, 22:481-504, 1999.
2. N. Amenta, M. W. Bern, and D. Eppstein. The crust and the β-skeleton: Combinatorial curve reconstruction. Graphical Models and Image Processing, 60(2):125-135, 1998.
3. N. Amenta, S. Choi, and R. K. Kolluri. The power crust, unions of balls, and the medial axis transform. Computational Geometry, 19(2-3):127-153, 2001.
4. D. Attali, J.-D. Boissonnat, and H. Edelsbrunner. Stability and computation of the medial axis - a state-of-the-art report. Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, 2004.
5. J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Computational Geometry, 22(1-3):185-203, 2002.
6. F. Chazal and A. Lieutier. The λ-medial axis. Graphical Models and Image Processing, 67(4):304-331, 2005.
7. T. Culver, J. Keyser, and D. Manocha. Exact computation of the medial axis of a polyhedron. Computer Aided Geometric Design, 21(1):65-98, 2004.
8. T. K. Dey, J. Giesen, E. A. Ramos, and B. Sadri. Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction. In Symposium on Computational Geometry (SCG), pages 218-227, 2005.
9. T. K. Dey and W. Zhao. Approximating the medial axis from the voronoi diagram with a convergence guarantee. Algorithmica, 38:179-200, 2003.
10. J. Giesen and M. John. The flow complex: A data structure for geometric modeling. In Symposium on Discrete Algorithms (SODA), pages 285-294, 2003.
11. K. Grove. Critical point theory for distance functions. Symposia in Pure Mathematics, 54(3):357-385, 1993.
12. A. Hatcher. Algebraic Topology. Cambridge University Press, 2001.
13. A. Lieutier. Any bounded open subset of ℝ has the same homotopy type as its medial axis. Computer-Aided Design, 36(11):1029-1046, 2004.