Shortening three-dimensional curves via two-dimensional flows (Q1346844)

In order to find a geodesic connecting two given points on a surface, one may start with an arbitrary smooth curve connecting the two points and then modify the curve by a surface normal flow proportional to the geodesic curvature. The fixed points of this flow are the geodesics. The authors note that it is easier computationally to project the problem into a plane. They derive the new flow equation and indicate how to discretize the problem for a stable, adaptive algorithm (with special attention to the endpoints.).