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 Post subject: General question - 2D & 3D interpolation
PostPosted: Tue Sep 19, 2017 8:13 am 
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Joined: Tue Sep 19, 2017 7:40 am
Posts: 1
Hi Alglib

A general question. We are looking for a library to interpolate point values in 3D space to a 2D surfaces (X,Y,Z) . Like a digital elevation model, generated from a series of point measurements.

Are there functionalities for this in ALGLIB?

Which types of interpolation rutines would you suggest?

We are currently using IDW and Kriging to generate 2D surfaces, but are looking for a set of more flexible, robust and fast interpolators to offer to our customers.

Please advice

Thank you for providing a fantastic library - and thank you for the release of the new Delphi versio - we wil llook into this :-)

Best
Torben


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 Post subject: Re: General question - 2D & 3D interpolation
PostPosted: Tue Sep 19, 2017 1:06 pm 
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Joined: Fri May 07, 2010 7:06 am
Posts: 798
Hi!

Yes, ALGLIB has such functionality - hierarchical RBFs. It supports both modelling Z(x,y) and F(x,y,z). You should use rbf subpackage - http://www.alglib.net/translator/man/manual.delphi.html#unit_rbf - and activate/tweak HRBF algorithm with rbfsetalgohierarchical() function.

NOTE: from your words I assume that you want to use Delphi version :) if you want to use C++ or C#, replace "delphi" in URL with "cpp" or "csharp" for appropriate manual file.

NOTE 2: if you want, you can write to me - sergey.bochkanov at alglib.net - and I can help you to tune HRBFs to your specific task. The most important points are: typical number of points, spatial extent (in meters) and typical search radius (in meters).


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 Post subject: Re: General question - 2D & 3D interpolation
PostPosted: Wed Dec 06, 2017 12:37 am 
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Joined: Mon Nov 20, 2017 11:14 pm
Posts: 6
Sergey,

Have you considered possibilities for generalizing the Spline2D and Spline3D routines, themselves, to irregular grids; possibly with the help of Delaunay Triangulation (as well as adding routines for triangulation, itself)?

A suitably-defined generalization may be sufficiently power to enable one to combine RBF, IDW and Spline{2,3}D into a single form.

I use the following modification for IDW, by the way: f(r) = (R - r)/(R + kr), for |r| < R; f(r) = 0, for |r| >= R, where k is an adjustable parameter in the range 0 to 1. This regularizes IDW by removing the singularity from 1/r (since it is equivalent to f(r) = 1/(r + e) - 1/(R + e) up to scale) and it removes the long-distance tail with the upper bound R.

It might be worth keeping IDW around and adding this modification in the routines.


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 Post subject: Re: General question - 2D & 3D interpolation
PostPosted: Wed Dec 06, 2017 9:56 am 
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Joined: Fri May 07, 2010 7:06 am
Posts: 798
Hi!

Do you have telepathic abilities? :))))) For the last month I am thinking on implementation of 2D and 3D penalized regression splines similar to spline1dfitpenalized(), but generalized to 2D/3D (and on speeding up single dimensional penalized regression splines). It is possible to implement them quite efficiently (avoiding need to solve large NxN or NxNxN dense linear systems) by splitting problem to smaller ~20x20 or ~20x20x20 chunks.

However, I did not thought on merging them with RBFs.... in my opinion, both options are quite powerful alone.


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