On the geodesic torsion of a tangential intersection curve of two surfaces in \(\mathbb R^3\) (Q2850101)

A non-transversal intersection of two surfaces is considered. If the intersection is a curve locally, its tangent vector is computed using Darboux frames of the curve on each of the surfaces. A normal plane of the curve is computed using the geodesic torsion of the intersection curve.NEWLINENEWLINEThere are several cases which can occur depending on the geodesic curvature of specially chosen curves on both intersecting surfaces.NEWLINENEWLINEThree types of intersecting surfaces are considered: both surfaces given parametrically, one of the surfaces given parametrically and the other given implicitly and, finally, both surfaces given implicitly.NEWLINENEWLINEExamples for all these cases are given for certain technical surfaces.