The curvature of characteristic curves on surfaces

Analyzing and interrogating designed surfaces remains an important and widely researched issue in computer-aided geometric design (CAGD). Treating families of characteristic curves on the surface proves a popular method of doing this. We show 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.