Re: Integrating scattered data

[Rupert Swarbrick]

On Tue, 21 Aug 2007 10:46:42 -0500
"Jordi Gutiérrez Hermoso" <address@hidden> wrote:

> On 21/08/07, kensmith <address@hidden> wrote:
> > 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.
> >
> > Do you know anything about how the surface gets from one place to
> > the next?
> 
> What do you mean? No, I don't think I know that. They are scattered
> points without any structure.

I think that kensmith's point was that for a domain (do you mean
domain?) D in R^2, you can define really horrible functions into R
which, although continuous, would defy any attempt to integrate under
them via sampling at points - they could oscillate crazily for example.

I'm afraid I don't know a method for fitting these things, but I
suspect you have to make some mathematical assumptions about smoothness
of the function you're approximating. After which, fitting some sort of
(cubic?) patch or something (or a polygonal surface?) could be assumed
to give you sensible answers.

I realise that I haven't given you anything helpful for actually
computing it though! I suspect your problem will be triangulating
between the points to get a PL approximation to your surface: maybe
there are libraries (matlab needing some conversion?) that do that sort
of thing? I'm sure computer graphics if nothing else would want them!

Rupert

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