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Integrating scattered data


From: Jordi Gutiérrez Hermoso
Subject: Integrating scattered data
Date: Mon, 20 Aug 2007 11:27:04 -0500

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?

Thanks,
- Jordi G. H.


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