[SciPy-user] [Fwd: 3D interpolation over irregular data]

mark starnes m.starnes05@imperial.ac...
Thu Jul 31 06:12:10 CDT 2008


Hi José,

Thanks for your comments.  Knowing that other people split the
interpolation into regions is useful.  I'll be attempting an approach
similar to that you suggested; splitting the domain, not around each
desired point but into regions containing sets of points.

I didn't expect the effect you mention about accuracy being related to
the number of points.  Looks like I need to read up on the theory....

Thanks again,

Mark.


José María García Pérez wrote:
> Mark,
> From my experience working with RBF, they work pretty well even when you
> use few points for the interpolation. They track non linear behavior
> very well.
> I have worked with RBF with very big FEM models (200000-500000 grid
> points) and with more than 3D (in other disciplines), but I don't take
> all the points at the same. What I would do is to use for example the
> 100 nearest points to the geometric point where you want to interpolate
> (probably with 10 would be enough). That's something you can try: test
> using 10, 20, 50, 100 points, and you will see that the difference is
> small pretty soon, and for sure smaller that the error you may expect
> from a CFD simulation.
> Hope this tip helps!
> José M.
> 
> 
> 2008/7/31 mark starnes <m.starnes05@imperial.ac.uk
> <mailto:m.starnes05@imperial.ac.uk>>
> 
>     Hi again, Stéfan.
> 
>     Is Robert Kern's package limited to two-dimensional data?  I've had a
>     look and can't see any three-dimensional options.
> 
>     Best regards,
> 
>     Mark.
> 
>     Stéfan van der Walt wrote:
>     > Hi Mark
>     >
>     > 2008/7/30 mark starnes <m.starnes05@imperial.ac.uk
>     <mailto:m.starnes05@imperial.ac.uk>>:
>     >> Hi everyone,
>     >>
>     >> I've looked through the list here and in Numpy-users, and checked the
>     >> 'net but can't find an answer to this problem (with luck, I've missed
>     >> something obvious!).
>     >>
>     >> I've an array of velocities at 80,000 points, irregularly spaced
>     (from a
>     >> CFD analysis).  I'd like to generate the interpolated velocity at any
>     >> position in the domain, to map the data to an acoustics analysis on a
>     >> different mesh.
>     >>
>     >> I tried a least squares approach but the errors are too large using
>     >> polynomials and trigonometric functions.  My conclusion is that I
>     need a
>     >> nearest-neighbour type interpolation routine.
>     >
>     > Also take a look at
>     >
>     >
>     http://www.scipy.org/Cookbook/Matplotlib/Gridding_irregularly_spaced_data
>     >
>     > Robert Kern's delaunay package does natural neighbour
>     interpolation, IIRC.
>     >
>     > Regards
>     > Stéfan
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