Stability and homotopy of a subset of the medial axis

ACM Symposium on Solid Modeling and Applications, SM

Volumn , Issue , 2004, Pages 243-248

  Chazal, F ^a   Lieutier, A ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b DASSAULT SYSTÈMES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER AIDED DESIGN; FUNCTIONS; GEOMETRY; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

3D VORONOI DIAGRAMS; HAUSDROFF DISTANCE PERTURBATIONS; MEDIAL AXIS; SURFACE RECONSTRUCTION ALGORITHMS;

SET THEORY;

EID: 21644474392     PISSN: 18117783     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. N. Amenta, S. Choi, T. Dey, N. Leekha A simple algorithm for homeomorphic Surface Reconstruction. International Journal of Computational Geometry and Applications Vol.12, No. 1,2(2002) pp.125-141
2. N. Amenta, S. Choi, R. Kolluri The Power Crust, unions of balls, the Medial Axis Transform Computational:Theory and Applications, 2001 Vol.19:(2-3), pp.127-153
3. N. Amenta, M. Bern Surface Reconstruction by Voronoi Filtering Discrete and Computational Geometry, no 22 pp.481-504(1999)
4. R.Blanding, C.Brooking, M.Ganter, D.Storti A skeletal-based solid editor proceedings of the Fifth ACM Symposium on Solid Modeling and Applications (1999), pp.141-150
5. J.D. Boissonnat, F. Cazals Smooth surface reconstruction via natural neighbour interpolation of distance functions. 16th ACM Symp. Computational Geometry (2000) pp.223-232
6. F. Chazal, A. Lieutier, Stability and homotopy of a subset of the medial axis. Preprint Inst. Math. Bourgogne, CNRS UMR 5584, available at http://math.u-bourgogne.fr/topo/chazal/publications.htm 2,3,4,5
7. F. Chazal, R. Soufflet, Stability and finiteness properties of medial axis and skeleton, Journal of Dynamical and Control Systems, Vol. 10, No. 2, 149-170, 2004.
8. T.Culver, J.Keyser, D.Manocha Accurate Computation of the Medial Axis of a Polyhedron proceedings of the Fifth ACM Symposium on Solid Modeling and Applications (1999), pp.179-190
9. T. K. Dey, W. Zhao. Approximate medial axis as a Voronoi subcomplex. In 7th ACM Symposium on Solid Modeling and Applications, (2002) pages 356-366.
10. T. K. Dey, W. Zhao Approximating the medial axis from the Voronoi diagram with a convergence guarantee Algorithmica, Vol. 38 (2004), 179-200.
11. T. K. Dey, J. Giesen, M. John Alpha-Shapes and Flow Shapes are Homotopy Equivalent. Proc. 35rd Annual ACM Symposium on the Theory of Computing (STOC), (2003).
12. H. Edelsbrunner Surface reconstruction by wrapping finite point sets in space, in Ricky Pollack and Eli Goodman Festschrift ed. B. Aronov, S. Basu, J. Pach and M. Sharir.
13. M.Etzion, A.Rappoport Computing the Voronoi Diagram of a 3-D Polyhedron by Separate Computation of its Symbolic and Geometric Parts proceedings of the Fifth ACM Symposium on Solid Modeling and Applications (1999), pp.167-178 1, 2 1
14. M.Foskey,M.C.Lin,D.Manocha Efficient Computation of a Simplified Medial Axis, proc. of the Eighth ACM Symposium on Solid Modeling and Applications (2003), pp.96-107 3
15. W. Fulton. Algebraic Topology, A First Course. Graduate Texts in Mathematics. Springer-Verlag. 3
16. J. Giesen, M. John, The Flow Complex: A Data Structure for Geometric Modeling. Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), (2003) 285-294. 2
17. A. Lieutier, Medial Axis Homotopy, Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications 2003. 2, 3, 4, 6
18. G. Matheron. Examples of Topological Properties of Skeletons (Chapter 11), On the Negligibility of the Skeleton and the Absolute Continuity of Erosions (Chap 12), In Image Analysis and Math. Morphology, Volume 2: Theoretical Advances, Ed. by Jean Serra, pages 216-256. Academic Press, 1988.
19. J. R.Munkres. Elements of Algebraic Topology. Addison-Wesley Publishing Company, 1984. 1 3
20. A.Sheffer,M.Etzion,A.Rappoport, M. Bercovier Hexahedral Mesh Generation using the Embedded Voronoi Graph Proc, 7th International meshing Roundtable, Sandia National Lab, pp.347-364, Oct 1998 1
21. K.Suresh Automating the CAD/CAE Dimensional Reduction Process proceedings of the Eighth ACM Symposium on Solid Modeling and Applications (2003), pp.76-85 1