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| Variable order two-dimensional surface splines http://forum.alglib.net/viewtopic.php?f=2&t=4640 |
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| Author: | Juan Conejero [ Mon Sep 09, 2024 9:07 am ] |
| Post subject: | Variable order two-dimensional surface splines |
Hi all, I have a request. Would it be possible to implement an RBF interpolation with the following basis function: f(r) = (r^2)^(m-1) * ln( r^2 ) for r > 0 f(0) = 0, where m >= 2 is a function order parameter? We develop a software platform specialized in astronomy and astrophotography. We use this variable order function in our traditional RBF interpolation implementation (based on dense systems, hence requiring O(n^3) time). It is very useful with m <= 6 to model complex local distortions accurately in our astrometric solutions (where we must find a correspondence between a set of detected star positions on an image and the corresponding celestial coordinates in a star catalog). Having this variable order RBF in ALGLIB with its fantastic O(n^2) DDM implementation would be highly nice since it would allow us to include many more stars in our astrometric solutions. The change with respect to the thin plate spline RBF should be trivial. Thank you in advance for your attention. |
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