Piecewise polynomial monotonic interpolation of 2D gridded data
| Autor: | Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann, Fabien Vivodtzev |
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| Přispěvatelé: | Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio, Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Mathematical analysis
Monotone cubic interpolation Monotonic function 010103 numerical & computational mathematics 01 natural sciences [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR] Interpolation 010101 applied mathematics Maxima and minima Monotone Surfaces Monotone polygon Saddle point Piecewise Partial derivative 0101 mathematics Mathematics Visualization |
| Zdroj: | Topological and Statistical Methods for Complex 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⟩ Mathematics and Visualization ISBN: 9783662448991 Topological and Statistical Methods for Complex Data, Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces |
| DOI: | 10.1007/978-3-662-44900-4_5⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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