Invariant smoothness measures for surfaces

Advances in Computational Mathematics

Volumn 8, Issue 1-2, 1998, Pages 49-63

  Mehlum, Even ^a   Tarrou, Christian ^b  

^a SINTEF   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Curvature; Curvature variation; Fairness functionals; Surface analysis; Surface smoothness; Variational surface design

Indexed keywords

EID: 0032326864     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018931910836     Document Type: Article

References (11)

1. L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces (Dover, New York, 1960).
2. O. Giering, Über das lokale Verhalten von Flächenkurven, Archiv d. Math. 17 (1966) 172-182.
3. G. Greiner, Surface construction based on variational principles, in: Wavelets, Images and Surface Fitting, eds. P.J. Laurent, A. Le Méhauté and L. Schumaker (A.K. Peters, Wellesley, 1994) pp. 277-286.
4. G. Greiner, Variational design and fairing of spline surfaces, in: Proc. EUROGRAPHICS '94 (Blackwell, 1994) pp. 143-154.
5. Ø. Hammer, Extensions of the minimum curvature method for geological horizon modelling, Master's Thesis, University of Oslo, Norway (1996).
6. A. Kolb, H. Pottmann and H.-P. Seidel, Fair surface reconstruction using quadratic functionals, in: Proc. EUROGRAPHICS '95 (Blackwell, 1995) pp. 469-479.
7. G.A. Korn and T.M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968).
8. J. Kåsa and G. Westgaard, Analysis of curvature related surface properties, report STF42 A96001, SINTEF, Oslo, Norway (1996).
9. T. Maekawa, F.-E. Wolter and N.M. Patrikalakis, Umbilics and lines of curvature for shape interrogation, Computer Aided Geometric Design 13 (1996) 133-161.
10. E. Mehlum, Curve and surface fitting based on variational criteriae for smoothness, Ph.D. Thesis, University of Oslo, Norway (1969). (Also available as Research Report at SINTEF.)
11. H. Moreton and C. Séquin, Functional optimization for fair surface design, ACM Computer Graphics 26 (1992) 167-176.