Re: Integrating scattered data

[kensmith]

On Monday 20 August 2007 09:27, Jordi Gutiérrez Hermoso wrote:
> I have a surface in some irregular domain of R^2 that I'm sampling at
> scattered, unstructured points. I'd like to find the volume under
> this surface.
>
> Ideally, I'd like to not interpolate to points not in my data set,
> since my surface is rather wiggly and I don't think interpolation
> could be very accurate. A Delaunay triangulation is an obvious first
> step, and then I could compose my surface of triangles to get some
> sort of O(h) integration.
>
> Can I do better? Are there routines already in Octave to help me do
> this? Is it possible to do some analogue of Simpson's rule to get
> O(h^2) precision?

I think you left out an important bit of information.

Do you know anything about how the surface gets from one place to the 
next?

Also, do you know what happens off the edges?

Things like Simpsons rule assume straight lines in how the curve goes 
from point to point.  In effect, they are interpolating the points 
between using that rule.

>
> Thanks,
> - Jordi G. H.
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