# Piecewise polynomial monotonic interpolation of 2D gridded data

* Corresponding author
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.
keyword :
Document type :
Book sections
Domain :

Cited literature [19 references]

https://hal.inria.fr/hal-01059532
Contributor : Georges-Pierre Bonneau <>
Submitted on : Monday, September 1, 2014 - 11:17:17 AM
Last modification on : Friday, October 11, 2019 - 2:48:02 PM
Long-term archiving on: Thursday, December 4, 2014 - 2:51:10 PM

### Files

AllemandGiorgisSpringerBookCha...
Files produced by the author(s)

### 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⟩

Record views