OrthoMap: Homeomorphism-guaranteeing normal-projection map between surfaces

Abstract

Consider two (n—1)-dimensional manifolds, S and Sʹ in Rn. We say that they are projection-homeomorphic when the closest projection of each one onto the other is a homeomorphism. We give tight conditions under which S and Sʹ are projection-homeomorphic. These conditions involve the local feature size for S and for Sʹ and the Hausdorff distance between them. Our results hold for arbitrary n.