Piecewise polynomial monotonic interpolation of 2D gridded data

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.

Keywords

Visualization Interpolation Monotone Surfaces

Domains

Computer Science [cs] Graphics [cs.GR]

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AllemandGiorgisSpringerBookChapterAuthorPreprint.pdf (11.51 Mo)

TopoPreservImage.png (1.76 Mo)

FunctionReconstruction.png (1.44 Mo)

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https://hal.inria.fr/hal-01059532

Submitted on : Monday, September 1, 2014-11:17:17 AM

Last modification on : Wednesday, May 4, 2022-3:14:20 AM

Long-term archiving on: Thursday, December 4, 2014-2:51:10 PM

Dates and versions

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

Identifiers

HAL Id : hal-01059532 , version 1
DOI : 10.1007/978-3-662-44900-4_5

Cite

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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