Issue No.06 - November-December (1997 vol.17)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/38.626974
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