[Gnuplot-bugs] improved interpolation (smoothing)

[<pl...@pi...>]

Hi,

I'll just throw this idea as a new topic since Daniel and Ethan are  
touching on this in the "Small technicality on dynarray" discussion but  
that thread is getting a bit long for me to add an /off.

I think it would be very useful to add lanczos filter as an interpolation  
method. The existing splines are fine but have a strong tendancy to extend  
well outside the path of the existing data when the data has a lot of  
fluctuations, a common situation. Although the implementation is correct  
this can be very misleading when viewing data presented with this sort of  
"smoothing". Far from averaging out variations it often exagerates  
excursions and can give a visual impression of oscillations that are not  
truely in the data.

Current devel version of Gimp contains such interpolation which is applied  
separatly in x and y and could probably be easily integrated into gnuplot.  
Each data point is derived from a weighted mean of 7 surrounding points in  
the source data using a precalculated look-up of the Lanczos function.

It effectively applies a windowed sinc function which provides a good  
quality lowpass filter, the technique is convolution with an approximation  
to the Fourrier transform of a step function in the frequency domain.

For example, the results on image processing make a better job of removing  
staircasing and pixelisation than the bicubic interpolation based on  
Catmull-Rom splines.

I can give more detail and precise reference to the source if you want to  
follow up the idea.

regards, Peter.