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
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.
Type de document :
Chapitre d'ouvrage
Bennett, Janine; Vivodtzev, Fabien; Pascucci, Valerio. Topological and Statistical Methods for Complex Data, Springer, 2014, Mathematics and Visualization, 978-3-662-44899-1
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Dernière modification le : jeudi 17 mars 2016 - 01:05:39
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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, 2014, Mathematics and Visualization, 978-3-662-44899-1. 〈hal-01059532〉

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