Piecewise polynomial monotonic interpolation of 2D gridded data

Léo Allemand-Giorgis; Georges-Pierre Bonneau; Stefanie Hahmann; Fabien Vivodtzev

Piecewise polynomial monotonic interpolation of 2D gridded data

Léo Allemand-Giorgis ^{1, *} Georges-Pierre Bonneau ^{1, *} Stefanie Hahmann ^{2, *} Fabien Vivodtzev ³

* 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

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

Document type :

Book sections

Domain :

Computer Science [cs] / Graphics [cs.GR]

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https://hal.inria.fr/hal-01059532
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Submitted on : Monday, September 1, 2014 - 11:17:17 AM
Last modification on : Friday, October 11, 2019 - 2:48:02 PM
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