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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.
Cited literature [19 references]
https://hal.inria.fr/hal-01059532
Contributor : Georges-Pierre Bonneau Connect in order to contact the contributor
Submitted on : Monday, September 1, 2014 - 11:17:17 AM
Last modification on : Friday, November 5, 2021 - 2:58:02 PM
Long-term archiving on: : Thursday, December 4, 2014 - 2:51:10 PM
Contributor : Georges-Pierre Bonneau Connect in order to contact the contributor
Submitted on : Monday, September 1, 2014 - 11:17:17 AM
Last modification on : Friday, November 5, 2021 - 2:58:02 PM
Long-term archiving on: : Thursday, December 4, 2014 - 2:51:10 PM
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