The Community for Technology Leaders
RSS Icon
Issue No.06 - November-December (1997 vol.17)
pp: 88-96
This article shows how to compute the curvature and geodesic curvature of characteristic curves on surfaces, such as contour lines, lines of curvature, asymptotic lines, isophotes, and reflection lines. For particular surface curves the authors introduce their "thickness" as another characteristic property. Although it is not possible to describe these curves in an explicit parametric form, the authors find closed formulas for their curvatures and "thickness." They also discuss how to use curvature and "thickness" of the characteristic surface curves as surface interrogation tools.
Holger Theisel, Gerald Farin, "The Curvature of Characteristic Curves on Surfaces", IEEE Computer Graphics and Applications, vol.17, no. 6, pp. 88-96, November-December 1997, doi:10.1109/38.626974
1. H. Davis, Introduction to Vector Analysis, Allyn and Bacon, Boston, 1967.
2. H. Theisel, Vector Field Curvature and Applications, PhD thesis, Dept. of Computer Science, Univ. of Rostock, Germany, 1996.
3. G.E. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, fourth ed. Academic Press, 1996.
4. W. Boehm, "Smooth Curves and Surfaces," Geometric Modeling: Algorithms and New Trends, G. Farin, ed., SIAM, Philadelphia, 1987, pp. 175-184.
5. T. Poeschl, "Detecting Surface Irregularities Using Isophotes," Computer Aided Geometric Design, Vol. 1, No. 2, 1984, pp. 163-168.
6. H. Hagen et al., "Surface Interrogation Algorithms," IEEE Computer Graphics and Applications, Vol. 12, No. 5, Sept. 1992, pp. 53-60.
7. R. Klass, "Correction of Local Surface Irregularities Using Reflection Lines," Computer Aided Design, Vol. 12, No. 2, March 1980, pp. 73-77.
8. E. Kaufmann and R. Klass, "Smoothing Surfaces Using Reflection Lines for Families of Splines," Computer Aided Design, Vol. 10, No. 6, 1988, pp. 312-316.
9. S. Hahmann, Stabilitäts-und Qualitätsanalyse von Freiformflächen (Stability Analysis and Interrogation of Surfaces), PhD thesis, University of Kaiserslautern, Germany, 1994 (in German).
10. J. Beck, R. Farouki, and J. Hinds, "Surface Analysis Methods," IEEE Computer Graphics and Applications, Vol. 6, No. 12, Sept. 1986, pp. 18-36.
11. J. Dill, "An Application of Color Graphics to the Display of Surface Curvature," Computer Graphics, Vol. 15, No. 3, Aug. 1981, pp. 153-161.
17 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool