How does TikZ/pgf resp. pgfplots do data smoothing?

Question

I am plotting smoothed data curves by applying the smooth option to the according diagram curve like this:

\addplot[color=black, mark=none, smooth] table[x=time, y=measured, col sep=semicolon] {./data.csv};

I was using those plots internally only. However, since those should be used for a scientific publication in the future I need some information about the smoothing polynomial in order to back the plotting up a bit.

I had a look into both the pgfplots manual and the pgf/TikZ manual which do not seem to provide any further information about the used smoothing polynomial or algorithm.

So does anyone know which approach/algorithm is used to smooth the data before plotting?

See What “smooth” plot interpolation algorithm does pgfplots use?. I would not recommend using this for a scientific publication. In that case, you should fit an explicit function, like shown in pgfplots/gnuplot: How to find the curve-fitting function passing through certain points and plot it? or Smooth curve through points with pgfplots — Jake, Feb 20 '17 at 14:39

score 4 · Accepted Answer · answered Feb 20 '17 at 14:39

4

Smoothing is not done globally hence there is no actual smoothing polynomial is used. Instead of connecting the consecutive points with line segments, a bezier curve is used to connect consecutive points in the parsed input stream with approx equal in out angles defined by the control points of the Bezier curves. Hence if there is a steep change between points you should expect overshoots/undershoots. This is also mentioned in the manual under smooth key.

You can see the actual code in pgflibraryplothandlers.code.tex file line 24. The \pgfplothandlercurveto macro definition is the actual algortihm.

In scientific publications, you should not alter the data with smooth keys for aesthetic reasons, or smoothen for a purpose with the provided actual code how it is done.

answered Feb 20 '17 at 14:39

percusse

157,807

Thanks for the information, that explains a lot of anomalous behavior. There are better ways of smoothing than bezier curves. Hmmm. – JPi Feb 20 '17 at 16:27
2

@JPi: It's worth keeping in mind that the smooth key is a TikZ key, not a PGFPlots key: this function was originally intended for drawing, not for smoothing data plots. – Jake Feb 20 '17 at 17:24
@Jake It was intended for plots though hence the plot handler. Only in the regular paths there are very few points. – percusse Feb 20 '17 at 18:05
How hard would it be to add one's own smoothing algorithm? – JPi Feb 20 '17 at 18:07
@JPi Current one is also a smoothing algorithm. Depends on the complexity. – percusse Feb 20 '17 at 18:09
@percusse: Yes, it is, but not a good one. I can compute the numbers easily in Lua...... – JPi Feb 21 '17 at 00:36

How does TikZ/pgf resp. pgfplots do data smoothing?

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