Distance functions and geodesics on point clouds

Abstract

A 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...