# Natural Neighbour Coordinates of Points on a Surface

1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Natural neighbour coordinates and natural neighbour interpolation have been introduced by Sibson for interpolating multivariate scattered data. In this paper, we consider the case where the data points belong to a smooth surface $ßs$, i.e. a $(d-1)$-manifold of $\R ^d$. We show that the natural neighbour coordinates of a point $X$ belonging to $ßs$ tends to behave as a local system of coordinates on the surface when the density of points increases. Our result does not assume any knowledge about the ordering, connectivity or topology of the data points or of the surface. An important ingredient in our proof is the fact that a subset of the vertices of the Voronoi diagram of the data points converges towards the medial axis of $ßs$ when the sampling density increases.
Keywords :
Type de document :
Rapport
[Research Report] RR-4015, INRIA. 2000, pp.26
Domaine :

https://hal.inria.fr/inria-00072626
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 10:26:28
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:16:06

### Identifiants

• HAL Id : inria-00072626, version 1

### Citation

Jean-Daniel Boissonnat, Frédéric Cazals. Natural Neighbour Coordinates of Points on a Surface. [Research Report] RR-4015, INRIA. 2000, pp.26. 〈inria-00072626〉

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