Skip to Main content Skip to Navigation
Theses

A Coordinate System associated to a Point Cloud issued from a Manifold: Definition, Properties and Applications

Julia Flötotto 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Surfaces and manifolds represented by a set of discrete points are encountered in various application areas. In this thesis, we define a coordinate system on the manifold associated to such a point set which is a generalization of Sibson's natural neighbor coordinates. We show its fundamental mathematical properties as well as its application to scattered data interpolation on manifolds. Furthermore, we introduce the notion of Voronoi atlas defined as a collection of Voronoi cells that approximate the Voronoi diagram restricted to the manifold. We describe its application in surface reconstruction and re-meshing. In addition, we show the basic properties of natural neighbor coordinates in power diagrams and we survey the interpolation methods based on natural neighbor coordinates. This survey details some proofs that are omitted in the original papers.
Document type :
Theses
Complete list of metadata

Cited literature [94 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00832487
Contributor : Olivier Devillers Connect in order to contact the contributor
Submitted on : Monday, June 10, 2013 - 5:41:55 PM
Last modification on : Saturday, January 27, 2018 - 1:30:48 AM
Long-term archiving on: : Wednesday, September 11, 2013 - 4:15:21 AM

Identifiers

  • HAL Id : tel-00832487, version 1

Collections

Citation

Julia Flötotto. A Coordinate System associated to a Point Cloud issued from a Manifold: Definition, Properties and Applications. Computational Geometry [cs.CG]. Université Nice Sophia Antipolis, 2003. English. ⟨tel-00832487⟩

Share

Metrics

Record views

445

Files downloads

629