Stability of curvature measures

Eurographics Symposium on Geometry Processing

Volumn 28, Issue 5, 2009, Pages 1485-1496

  Chazal, F ^a   Cohen Steiner, D ^b   Lieutier, A ^c   Thibert, B ^c  

^a INRIA SACLAY   (France)

^b INRIA   (France)

^c UNIV GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78651364042     PISSN: 17278384     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (35)

1. M. BERGER: Geometry II, Translated from French, Springer Verlag, 1987.
2. F. CAZALS AND M. POUGET: Estimating differential quantities using polynomial fitting of osculating jets, Symposium on Geometry Processing 2003, 177-187, Aachen, Germany.
3. CGAL, Computational Geometry Algorithms Library, http://www.cgal.org/.
4. F. CHAZAL, D. COHEN-STEINER, A. LIEUTIER: Normal cone Approximation and Offset Shape Isotopy. INRIA Technical report Number 6100. January 2007. To appear in Computational Geometry: Theory and Applications.
5. F. CHAZAL AND D. COHEN-STEINER AND A. LIEUTIER: A Sampling Theory for Compacts in Euclidean Space, SoCG, 2006. To appear in Discrete & Computational Geometry.
6. F. CHAZAL, D. COHEN-STEINER, A. LIEUTIER, B. THIBERT: Shape Smoothing Using Double Offset. Symposium on Solid and Physical Modeling 2007: 183-192.
7. F. CHAZAL, D. COHEN-STEINER, A. LIEUTIER, B. THIBERT: Stability of Curvature Measures, INRIA Technical Report n 6756, december 2008, 37 pages. http://hal.inria.fr/inria-00344903/fr/
8. F. CHAZAL, D. COHEN-STEINER, Q. MÉRIGOT: Stability of Boundary Measures, INRIA's Technical report N 6219, June 2007.
9. J. CHEEGER: Critical Points of Distance Functions and Applications to Geometry, Geometric Topology: recent developments, Montecatini Terme, 1990, Springer Lecture Notes, 1504, 1-38, 1991.
10. J. CHEEGER, W. MULLER AND R. SCHRADER: On the curvature of piecewise flat spaces, Comm. Math. Phys. 92, 1984, 405-454.
11. F.H. CLARKE: Optimization and NonSmooth Analysis, 1983, Wiley-Interscience, Kluwer Academic.
12. D. COHEN STEINER: Quelques problèmes liés à la discrétisation de surfaces, thèse de l'école polytechnique, 2004.
13. D. COHEN STEINER, J.M. MORVAN: Restricted Delaunay Triangulations and Normal Cycle, SoCG 2003.
14. D. COHEN-STEINER AND J.-M. MORVAN: Second Fundamental Measure of Geometric Sets and Local Approximation of Curvatures, Journal of Differential Geometry, Vol 74, n3, p 363-394, 2007.
15. G. DZIUK: Finite elements for the Beltrami operator on arbitrary surfaces. In Partial Differential equations and calculus of variations, 1357 of LNM, 142-155. Springer, 1988.
16. H. EDELSBRUNNER AND ERNST P. MÜCKE: Three-Dimensional Alpha Shapes, ACM TRansactions on Graphics, Vol 13, n1, pp 43-72, 1994.
17. H. EDELSBRUNNER: The Union of Balls and its Dual Shape, Symp on Comp. Geom, 1993. pp 218-231.
18. L. FANGHUA, Y. XIAOPING: Geometric Measure Theory: an introduction, Science Press, third edition, 2002.
19. H. FEDERER: Curvature measures, Trans. Amer. Math. Soc 93 (1959) 418-491.
20. J. FU: Monge-Ampère functions, 1, Indiana Univ Math. J. 38 (1989), 745-771.
21. J. GIESEN AND M. JOHN: The Flow Complex: A Data Structure for Geometric Modeling, Symposium on Discrete Algorithms, 285-294, 2003.
22. K. GROVE: Critical Point Theory for Distance Functions, Proc. of Symposia in Pure Mathematics, Vol 54, Part 3, 1993.
23. K. HILDEBRANDT, K. POLTHIER, M. WARDETZKY, On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces. in Geometriae Dedicata 123, 2006, pp. 89-112.
24. Q.-X. HUANG, S. FLORY, N. GELFAND, M. HOFER, H. POTTMANN: Reassembling Fractured Objects by Geometric Matching, ACM Trans. Graphics 25 (2006), 569-578 (Proc. SIGGRAPH).
25. E. KALOGERAKIS, P.D. SIMARI, D. NOWROUZEZAHRAI, K. SINGH: Robust statistical estimation of curvature on discretized surfaces. SGP 2007: 13-22
26. C. LANGE, K. POLTHIER: Anisotropic smoothing of point sets,. Computer Aided Geometric Design 22(7): 680-692 (2005)
27. n has the same homotopy type as its medial axis, Computer-Aided Design, 36, 1029-1046, 2004, Elsevier
28. F. MORGAN: Geometric Measure Theory, Acad. Press, INC, 1987.
29. J.-M. MORVAN: Generalized Curvatures. Geometry and Computing, Vol 2. Springer Verlag, 2008.
30. H. POTTMANN, J. WALLNER, Y. YANG, Y LAI, S. HU: Principal curvatures from the integral invariant viewpoint, Computer Aided Geom. Design 24 (2007), 428-442.
31. H. POTTMANN, J. WALLNER, Q. HUANG, Y. YANG: Integral Invariants for Robust Geometry Processing, Computer Aided Geometric Design 26 (2009), 37-60.
32. S. PETITJEAN: A survey of methods for recovering quadrics in triangle meshes, ACM Comput. Surv., Vol 34, 2, 2002, pages 211-262
33. S. RUSINKIEWICZ: Estimating Curvatures and Their Derivatives on Triangle Meshes. Symposium on 3D Data Processing, Visualization, and Transmission. 2004.
34. J. RATAJ, M. ZÄHLE: Curvatures and Currents for Unions of Sets with positive reach II, Ann. Global Anal. Geom. 20 (2001) 1-21.
35. J. RATAJ, M. ZÄHLE: Normal Cycles of Lipschitz Manifolds by approximation with parallel sets, Diff. Geom. Appl. 19 (2003) 113-126.