Marching along surface/surface intersection curves with an adaptive step length (Q1195757)

Given two \(C^ 2\) parametric surfaces and a point on their intersection, the direction of the intersection curve at that point is given by the two normals at that point. The data also allow one to calculate a Taylor polynomial approximation to the intersection curve. Taking the second order approximation, i.e., a parabolic arc, lets one determine a stepsize by the requirement that the arc should not deviate from the chord joining its endpoints by more than a given tolerance. This condition can be evaluated using only derivatives up to order 2. An iterative procedure can then be used to determine a point on the intersection curve close to the endpoint of the arc.