Memoli, FacundoSapiro, Guillermo2007-08-162007-08-162003-05https://hdl.handle.net/11299/3924A new paradigm for computing intrinsic distance functions and geodesics on sub-manifolds of Rd given by point clouds is introduced in this paper. The basic idea is that, as shown here, intrinsic distance functions and geodesics on general co-dimension sub-manifolds of Rd can be accurately approximated by extrinsic Euclidean ones computed inside a thin offset band surrounding the manifold...