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Book Sections Year : 2014

Piecewise polynomial monotonic interpolation of 2D gridded data

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.
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Dates and versions

hal-01059532 , version 1 (01-09-2014)

Identifiers

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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, pp.73-91, 2014, Mathematics and Visualization, 978-3-662-44899-1. ⟨10.1007/978-3-662-44900-4_5⟩. ⟨hal-01059532⟩
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