On the Existence of Solutions to Non-parametric Fairing Problems

Journal of Mathematical Analysis and Applications

Volumn 238, Issue 2, 1999, Pages 540-550

  Kipp, Andreas ^a   Reif, Ulrich ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Existence of solutions; Fairing problem; Fairness functional; Total curvature; Willmore energy

Indexed keywords

EID: 0347594426     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6537     Document Type: Article

References (13)

1. T. DeRose, M. Halstead, and M. Kass, Efficient, fair interpolation using Catmull-Clark surfaces, in "Proceedings of Siggraph '93," pp. 35-44, Apple Computer, Inc., 1993.
2. U. Dierkes, S. Hildebrandt, A. Küster, and O. Wohlrab, "Minimal Surfaces I and II," Springer-Verlag, Berlin/New York, 1991.
3. G. Greiner, Blending techniques based on variational principles, in "Curves and Surfaces in Computer Vision and Graphics III," (J. D. Warren, Ed.), Proc. SPIE 1830 (1992), 174-183.
4. G. Greiner, Curvature continuous blend surfaces, in "Modeling in Computer Graphics," (B. Falcidieno and T. L. Kunii, Eds.), pp. 309-318, Springer-Verlag, Berlin/New York, 1993.
5. G. Greiner and K. Hormann, Interpolating and approximating scattered 3D-data with hierarchical tensor product splines, in "Surface Fitting and Multiresolution Methods," (A. Le Mehaute et al., Eds.), pp. 163-172. Vanderbilt Univ. Press, 1996.
6. R. L. Harder and R. N. Desmarais, Interpolation using surface splines, J. Aircraft 9 (1972), 189-197.
7. K. Höllig, J. Hahn, and U. Reif, Glattes Füllen n-seitiger Lücken, in "Mathematik - Schlüsseltechnologie für die Zukunft," (K. H. Hoffmann et al., Eds.), pp. 347-357. Springer-Verlag, Berlin/New York, 1997.
8. L. Hsu, R. Kusner, and J. Sullivan, Minimizing the squared mean curvature integral for surfaces in space forms. Experiment Math. 1 (1992), 3.
9. R. Leis, "Initial Boundary Value Problems in Mathematical Physics," Teubner, Leipzig, 1986.
10. G. Preissler, "Möbius-Differentialgeometrie von Hyperflächen," Ph.D. thesis, Universität Stuttgart, 1996.
11. A. Röseler, "Nichtlineare Optimierung von Kurven and Flächen mit Hilfe von Splines," Master's thesis, Universität Stuttgart, 1996.
12. L. Simon, Existence of Willmore surfaces, Proc. Centre Math. Anal. Austral. Nat. Univ. 3 (1986), 187-216.
13. T. J. Willmore, Note on embedded surfaces, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 11 (1965), 493-496.