Piecewise polynomial monotonic interpolation of 2D gridded data

Léo Allemand-Giorgis 1, * Georges-Pierre Bonneau 1, * Stefanie Hahmann 2, * Fabien Vivodtzev 3
* Auteur correspondant
1 MAVERICK - Models and Algorithms for Visualization and Rendering
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 IMAGINE - Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
3 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
Abstract : A method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C$^1$-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C$^1$ surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm.
keyword : Monotone Surfaces Interpolation Visualization
Type de document :
Chapitre d'ouvrage
Bennett, Janine; Vivodtzev, Fabien; Pascucci, Valerio. Topological and Statistical Methods for Complex Data, Springer, pp.73-91, 2014, Mathematics and Visualization, 978-3-662-44899-1. 〈10.1007/978-3-662-44900-4_5〉
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger

TopoPreservImage.png
TopoPreservImage.png
FunctionReconstruction.png
FunctionReconstruction.png
https://hal.inria.fr/hal-01059532
Contributeur : Georges-Pierre Bonneau <>
Soumis le : lundi 1 septembre 2014 - 11:17:17
Dernière modification le : lundi 15 octobre 2018 - 16:02:02
Document(s) archivé(s) le : jeudi 4 décembre 2014 - 14:51:10

Fichiers

AllemandGiorgisSpringerBookCha...
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

CEA | INRIA | UGA | LJK | LJK_GI | LJK_GI_IMAGINE | LJK_GI_MAVERICK | DAM

Citation

Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann, Fabien Vivodtzev. Piecewise polynomial monotonic interpolation of 2D gridded data. Bennett, Janine; Vivodtzev, Fabien; Pascucci, Valerio. Topological and Statistical Methods for Complex Data, Springer, pp.73-91, 2014, Mathematics and Visualization, 978-3-662-44899-1. 〈10.1007/978-3-662-44900-4_5〉. 〈hal-01059532〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

926

Téléchargements de fichiers

1750

Contact


archive-ouverte@inria.fr