[vtkusers] Plotting ungridded data

[Jordi Gutiérrez Hermoso]

On 18/07/07, Kenneth Sloan <kennethrsloan at gmail.com> wrote:
>
> On Jul 18, 2007, at 5:40 PM, Jordi Gutiérrez Hermoso wrote:
>
> > I have a set of triplets (x,y,z) where each triplet is a sampling from
> > a smooth function z = f(x,y). How can I most easily interpolate the
> > surface these points define? Do I need to a Delaunay triangulation, or
> > is there a different method?
>
> Are there many cases where <x1,y1,z1> and <x2,y2,z2> are in the set
> of samples and <x1,y1> is very close to <x2,y2> but z1 and z2 are
> very different?

Hopefully not. This is supposed to be the solution of a wave equation
without shocks.

> That is - how RELIABLE are your samples?

Good, I hope. I won't know with much certainty until I manage to
visualise them. :-)

> If you have multiple z values at (nearly) the same <x,y> locations,
> then you might want to consider what (and when) you are going to do
> about it.

The points are more or less regularly spaced, just in a slightly
irregular manner. I'm hoping that the function values at each point
are smoothly varying, but this is just hope.

> But...that said...a standard thing to do is to compute the Delaunay
> triangulation of the <x,y> points in the z=0 plane and then lift each
> point to the <x,y,z> point on the surface (pulling the triangles up
> by the vertices).  This should give reasonable results.

Ok, that's what I thought.

> There are also about 100 other methods of "interpolating a surface
> through data points".

Really? I didn't know of any until today when someone suggested a
Delaunay triangulation. :-)

I usually work with PDEs where the gridding is part of the PDE solver
data, but now that I'm working with meshless methods, I'm not sure how
to visualise this data.

> Given the triangulation, there are a number of methods to produce
> smoother surfaces

This may not be necessary. But in case it is, can you just name what
such methods are called, where can I look them up?

Thank you very much for your response.

- Jordi G. H.