Given a single path initially defined by edges on a FDynamicMesh (the SurfaceMesh), this class uses an intrinsic mesh with the same vertex set to minimize the length of the path on the surface mesh. This is done iteratively by a succession of local path deformations comprised of (local) intrisic edge flips and path re-routing, each deformation locally reduces the path length. The resulting path is comprised of intrinsic mesh edges.