Sure, we could have a plot near the top of sample1d. There are similar types of plots in the test/sample1d dir. Note, however, that -Fs is the only directive that takes the fit argument, so -Fa0.001 is meaningless and perhaps should result in an error.
Also, since you are not using nex.txt for anything other than plotting you should just pipe it through plot to shorten the script.
Maybe only use half the data to make it easier to see the differences between the splines?

I found the example. I remove the slope and curvature graphs. I think it is a better graph.

cat << EOF > t.txt
0	0
1	1
2	1.5
3	1.25
4	1.5
4.5	3
5	2
6	2.5
EOF
# Splines
gmt begin doc_splines png
gmt sample1d t.txt -T0.01 -Fc | gmt plot -R-0.1/6.1/-0.1/3.1 -JX6i/3i -Bafg -By+l"u(x)" -BWSne -W1p
gmt sample1d t.txt -T0.01 -Fl | gmt plot -W1p,blue
gmt sample1d t.txt -T0.01 -Fa | gmt plot -W1p,red 
gmt sample1d t.txt -T0.01 -Fn | gmt plot -W1p,darkgreen
gmt plot t.txt -Sc0.1i -Gred -Wthin
gmt legend -DjTL+w1.9i+o0.1i -F+p1p+gwhite+s << EOF
S 0.2i - 0.3i - 1p 	0.5i Cubic spline
S 0.2i - 0.3i - 1p,red	0.5i Akima spline
S 0.2i - 0.3i - 1p,blue	0.5i Linear spline
S 0.2i - 0.3i - 1p,darkgreen 0.5i Nearest neighbor
EOF
gmt end 

Yes, very nice. But a few questions:

1. We should also show the smoothing spline -Fs too, no?
2. Seems like this is a great example to use -l for auto legend since you are just doing lines and labels?

I’ve never seen a figure in a program’s docs (I think?). Love the idea.

Check out grdseamount or movie or events.

The new version of the figure.

cat << EOF > t.txt
0	0
1	1
2	1.5
3	1.25
4	1.5
4.5	3
5	2
6	2.5
EOF
# Splines
gmt begin doc_splines png
gmt sample1d t.txt -T0.01 -Fc  | gmt plot -R-0.1/6.1/-0.1/3.1 -JX6i/3i -Baf -By+l"u(x)" -BWSne -W1p -l"Cubic spline (-Fc)"
gmt sample1d t.txt -T0.01 -Fs1 | gmt plot -W1p,orange -l"Smooth cubic spline (-Fs1)"
gmt sample1d t.txt -T0.01 -Fl  | gmt plot -W1p,blue -l"Linear spline (-Fl)"
gmt sample1d t.txt -T0.01 -Fa  | gmt plot -W1p,red -l"Akima spline (-Fa)"
gmt sample1d t.txt -T0.01 -Fn  | gmt plot -W1p,darkgreen -l"Nearest neighbor (-Fn)"
gmt plot t.txt -Sc0.1i -Gred -Wthin -l"Data"
gmt legend -DjTL+w1.9i+o0.1i -F+p1p+gwhite+s 
gmt end 

Nice! Would you like to try to make this into doc/scripts/GMT_splines.sh and follow the Contributing Guide on documentation on how to add a new test or script? I've followed @meghanrjones's write-up myself and it should be OK. You can see in the doc/rst/source/movie.rst or others for what to do to add a figure to the documentation. If you start such a pull request then I can help if you get stuck. Look at the other scripts in doc/script for how to set up names etc.

Oh, maybe add "x" as label to go with the u(x) for the y-axis?

Nice example! I would suggest using SI units rather than US units in the script.

Awesome example @Esteban82! I can answer questions about the process for adding it to the docs if you decide to do that. In order to push the example image to the dvc repo, you would need to let me or @seisman know after you've created a DAGsHub account so that we can give you write permissions.

Yes, I will try to add the figure.

I only have one doubts. What is the optimal height and length (-JX) of the graph for the docs? I think it should be shorter.

Most of the time I prefer figs with aspect ratios as you have it. Wider than the hight. I think it is OK.

OK. This is -JX15c/6c.

Awesome example @Esteban82! I can answer questions about the process for adding it to the docs if you decide to do that. In order to push the example image to the dvc repo, you would need to let me or @seisman know after you've created a DAGsHub account so that we can give you write permissions.

Thanks Max. This is my account: https://dagshub.com/Esteban82

Great, you've been added to the team on DAGsHub and should be good to go. Let me know if you run into any problems.

@PaulWessel : on the same track #6611 ... @Esteban82's work could be extended?