Suggestion for dgrid3d

[Philipp K. J. <ja...@ie...>]

I was just playing with dgrid3d, and had some 
difficulties getting rather "smooth" input data
to come out "just right". So I looked into the
implementation for dgrid3d and wanted to make
a suggestion.

Context:
======
dgrid3d evaluates (possibly ungridded) input data
and calculates a smooth approximation to it on a
regular grid. The values assigned to each grid point
are essentially weighted averages:
	sum_{all points} w_i * data_i
The sum runs over all input data points, and the
weight function w is essentially an inverse power
of the distance between each data point and the
current grid point:
	w = 1/dist**p      for some integer p

Problem:
======
This particular choice of weight function has a few
disadvantages:
1) for dist==0, it is undefined (requiring treatment
	as special case)
2) for dist > 0 but small, the weight can become
	arbitrarily large
3) for large p, each individual data point totally 
	dominates all grid points within dist < 1, but
	is irrelevant once dist > 1, with an abrupt
	change in behaviour at dist=1 if p gets large.
4) no way to control the "radius of influence" or
	catchment area for data points

Suggestion:
========
I think it would be desirable to have a weight function
with the following properties:
1) bounded
2) w( d=0 ) = 1
3) falling smoothly as d -> infty
4) have a parameter which smoothly controls the
	size of the "catchment radius".

A Gaussian is the first thing that comes to mind.

I have tried it and quite like the results. I have 
posted some example images comparing Gaussian
weighting vs the power law weighting at:
	www.philipp-janert.com/gnuplot

Optional:
======
I have hijacked the "norm" parameter to 
control the width of the Gaussian. This is
not ideal - a better solution would be to
extend the dgrid3d option in such a way
that it can take two float values (instead
of an int), which can be used to scale the
x- and y-distances independently.

Attached, you will find a patch file (against 
CVS head) containing the changes to use
a Gaussian instead of a power law. They
do not include the "optional" feature 
mentioned above. 

Please let me know what you think. I have 
not prepared a patch to the documentation
yet - I'd like to hear opinions on this 
suggestion first.

Best,

		Ph.