Spectral interpolation on rhodonea curves
Version: 0.3 (01.10.2019)
Written by Wolfgang Erb
The toolbox RDisk contains a Matlab-implementation for the computation of a spectral interpolation scheme on the unit disk from data samples at the nodes of one or several rhodonea curves .
Rhodonea curves are classical planar curves in the disk that have the characteristic shape of a petalled rose. Sampling along these curves gives node sets that are ideally suited to interpolate functions on the disk. The interpolation spaces are generated by a parity-modified Chebyshev-Fourier basis. One main advantage of this basis is the fact that the interpolant can be calculated efficiently by a fast Fourier transform. This computation of the interpolant is implemented in this toolbox.
To test the package use example_main.m
To see how the interpolation scheme can be applied to the black hole data from the EHT collaboration have a look at example_blackhole.m
To compare interpolation on the rhodonea nodes with a tensor-product interpolation scheme on the disk try example_RDvsTPD.m
To plot the Lagrange functions of the interpolation scheme use example_lagrange.m
To plot the rhodonea varieties and the rhodonea interpolation nodes consisting of intersection and boundary points use plot_rhodonea.m
To plot the Chebyshev-Fourier basis involved in the interpolation try plot_basisfunction.m
Citation and Credits
The analysis of the rhodonea nodes and the construction of the spectral interpolation scheme on the disk is given in
-  Erb, W.
Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk
arXiv:1812.00437 [math.NA] (2018)
Copyright (C) 2018 Wolfgang Erb
This software was written by Wolfgang Erb at the University of Hawaii at Manoa and at the University of Padova
RDisk is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
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