A coordinate system associated to a point cloud issued from a manifold : definition, properties and applications

摘要: Surfaces and manifolds represented by a set of discrete points are encountered in various application areas. In this thesis, we define coordinate system on the manifold associated to such point which is generalization Sibson's natural neighbor coordinates. We show its fundamental mathematical properties as well scattered data interpolation manifolds. Furthermore, introduce notion Voronoi atlas defined collection cells that approximate diagram restricted manifold. describe surface reconstruction re-meshing. addition, basic coordinates power diagrams survey methods based This details some proofs omitted original papers.