s.surf.tps-dmin

[Helena Mitasova]

>is the dmin parameter in s.surf.tps there for computational efficiency
>(to thin out points), or is there some void in my understanding of the
>algorithm?

The main purpose is to remove identical points in case they were
not removed before but 
it is there also for the computational efficiency and numerical stability.
If there are two points too close to each other, after noramlization
the distance can get very close to zero,
and if the distance between two points converges to zero also the 
determinant of the system of linear equations converges to zero
and the solution gets unstable.

>I have run a series of experiments wherein I delineated a path through
>an analytical surface. The path reflects traverses made by some sort
>of vehicle (I included "turnarounds" at the end of each traverse). I
>looked at several different sampling frequencies (density of points)
>along this path and minimized the MSE for each sample set to determine
>optimum tension/smoothing parameters. I have found that at the two
>highest frequencies, the MSE increases substantially.  This seems
>counter-intuitive. Any guesses here?

this sounds like the case when your points are so close to each
other that the distance is very close to 0. 
How do you control the distance when you generate the path? 
Did you look at the resulting surfaces and displayed the deviations
in sites to see where the error increases? This can help you to
find  out which points cause the increase in MSE. If you
won't be able to explain the increase in MSE, you can send us the data,
we will be glad to look at it.
The work that you are doing sounds really interesting 
we will  be grateful for a preprint of the paper (or your disertation)
including the results of this work, when it is done.

thanks,

Lubos and Helena