Plotting with Gnuplot and/or TikZ

Gnuplot, Postscript Terminal

This is very easy to set up; from Python, I am using something like this to produce and plot the data, including labels etc.:

def edgePlotData(edge, title):
    return Gnuplot.Data([(al, gm.siv[p])
                         for al, p in arcLengthIter(edge, wsStats)],
                        title = title, with = "lp ps 0.7")

g = Gnuplot.Gnuplot()
g('set terminal postscript eps color solid')
g('set output "valueplot-flowlines.eps"')
g('set xlabel "arc length distance $t$ from saddle [pixels]"')
g('set ylabel "boundary indicator value $|\vec{b}_g(t)|$"')
g('set arrow from 0,0 to 0,15 nohead lt 0')
g('set label " saddle pos" at 0,14 left')
g.set_range("xrange", (-5, 5))

g('set size 0.8') # larger fonts, please
g.plot(myPlotData(noiseEdge, "undesired, noise-induced edge"),
       myPlotData(goodEdge, "real, high-contrast image edge"),
       myPlotData(weakEdge, "real, low-contrast image edge"),
       myPlotData(streamerEdge, "streamer (converging tangentially to real edges)"))

The result looks like this:

Here are the data files and commands to recreate this "at home":

File: valueplot-flowlines.gnuplot	(627 bytes; Thu, Mar/20/2008)
File: valueplot-flowlines_1.dat	(1533 bytes; Tue, Feb/19/2008)
File: valueplot-flowlines_2.dat	(3876 bytes; Tue, Feb/19/2008)
File: valueplot-flowlines_3.dat	(684 bytes; Tue, Feb/19/2008)
File: valueplot-flowlines_4.dat	(586 bytes; Tue, Feb/19/2008)

AFAIK, this process is standard and has been used like this for years. As Alain Matthes pointed out, you might run into encoding problems nowadays, in the transition phase to UTF-8, which is becoming the new standard for many software packages and platforms.

Another problem arises if one tries to change the font; although Gnuplot allows to change every small detail, I think one usually leaves such things as the font alone, but this results in different fonts in the EPS-embedded plots than in the rest of your LaTeX document.

Also, when using epstopdf to convert the figures for use with pdflatex (and KOMA-Script), their text became garbled, obviously because of a font problem. I had to use epstoeps and epstopdf one after another to fix this.

TODO: Alain mentioned gnuplottex:

This package is very useful; you can, like with tikz, execute some commands with gnuplot and insert the result directly in your document. I use only this method to draw some surfaces z=f(x,y).

Gnuplot, XFig Terminal

The fig-terminal has the advantage of being able to produce "special" text, i.e. text that can be converted into LaTeX commands to get the same font as in the rest of the document and support formulas etc. In the above code, just change the terminal line and output filename (I have also removed the set size, since the LaTeX font size is large enough, and added some formulas to showcase the LaTeX features):

#g('set terminal postscript eps color')
g('set terminal fig metric color textspecial')
g('set output "valueplot-flowlines.fig"')
...
g('set xlabel "arc length distance $t$ from saddle [pixels]"')
g(r'set ylabel "boundary indicator value $|\\vec{b}_g(t)|$"')

Unfortunately, Gnuplot annoyed me here, again (update: this was version 4.0.0 - the current 4.2.2 release does not have this problem): the colors in the resulting document were completely different than in the postscript. (AFAICS, this is not considered as bug, but each terminal may freely choose the plot style appearance.) In particular, the first plot uses black instead of red color, and the "saddle pos" mark in the center is not dotted anymore:

File: valueplot-flowlines_fig.gnuplot	(638 bytes; Thu, Mar/20/2008)
File: valueplot-flowlines.fig	(48.17 kb; Thu, Mar/20/2008)

Thus, I have hacked a small python module gnuplotfig.py, based on my fig.py module, which tries to parse and improve gnuplot's XFig output:

• move separate plots and axis ticks on separate layers (the default puts nearly everything on depth 10)
• heuristically fix colors (in this example you see that the "saddle pos" mark cannot be distinguished from the plot and is also "fixed" to red)
• try to extract value range and store that as XFig comments in the file (gnuplotfig.py offers coordinate conversions based on this)

File: valueplot-flowlines_fixed.fig

(43.74 kb; Thu, Mar/20/2008)

The main benefit from adding the extra indirection via XFig is that XFig supports "special" text, i.e. a flag that marks text as to-be-interpreted by LaTeX. Then, you can use fig2dev with a special target language to produce a PS/PDF with the background and a separate chunk of TeX code that overlays the text using LaTeX. (Details on this process can be found on the "LaTeX and XFig" page available on the XFig homepage.) This is made especially convenient in LyX, which allows you to directly insert the XFig file as "external material" and does all the necessary intermediate steps for you.

The above figure is the result of a LaTeX run using \input{valueplot-flowlines_fixed.pdftex} to include the automatically generated TeX code. The process was facilitated with the following Makefile rules:

%-pdftex.pdf: %.fig
  fig2dev -L pdftex $< $@

%.pdftex: %.fig %-pdftex.pdf
  fig2dev -L pdftex_t -p $*-pdftex.pdf $< $@

%.pdf: %.tex
  pdflatex $<

valueplot-flowlines_fixed_fig_latex.pdf: valueplot-flowlines_fixed.pdftex

Unfortunately, the generated code is cluttered with font-setting commands:

\begin{picture}(4113,2862)(937,-3710)
\put(1363,-3363){\makebox(0,0)[rb]{\smash{{\SetFigFont{10}{12.0}{\familydefault}{\mddefault}{\updefault} 0}}}}
\put(1363,-2887){\makebox(0,0)[rb]{\smash{{\SetFigFont{10}{12.0}{\familydefault}{\mddefault}{\updefault} 5}}}}
\put(1363,-2411){\makebox(0,0)[rb]{\smash{{\SetFigFont{10}{12.0}{\familydefault}{\mddefault}{\updefault} 10}}}}
...
\put(1048,-2114){\rotatebox{90.0}{\makebox(0,0)[b]{\smash{{\SetFigFont{10}{12.0}{\familydefault}{\mddefault}{\updefault}boundary indicator value $|\vec{b}_g(t)|$}}}}}
...
\put(4455,-1465){\makebox(0,0)[rb]{\smash{{\SetFigFont{10}{12.0}{\familydefault}{\mddefault}{\updefault}streamer (converging to real edges)}}}}
\end{picture}%

Even though the font size can be configured within Gnuplot, it would still be better to use LaTeX's default font sizes, or at least commands like small or the like. Also, the line spacing e.g. in the legend is unsatisfactory, and this gets much worse if one uses the above set size ... option of Gnuplot. Resizing using a \resizebox in LaTeX is undesirable since it again affects line widths and font sizes.

On the plus side, we at least have LaTeX fonts and formulas. The effort for creating such plots is larger than with Gnuplot alone, but it can be automated to a fair degree (and is trivial to achieve within LyX).

Gnuplot, XFig Terminal + fig2tikz

The XFig files generated above can be converted to TikZ code using my fig2tikz script:

File: valueplot-flowlines_fixed_fig.tikz

(49.26 kb; Thu, Mar/20/2008)

This already brings many of TikZ's advantages, e.g. you may scale the plot without changing the linewidths etc. Furthermore, the generated code is much cleaner than the above, since fig2tikz has a --nofonts switch that disables the output of font-setting commands:

\path (3.02667,9.33778) node[anchor=base east] { 0};
\path (3.02667,8.28) node[anchor=base east] { 5};
\path (3.02667,7.22222) node[anchor=base east] { 10};
...
\path (2.32667,6.56222) node[anchor=base,rotate=90.0] {boundary indicator value $|\vec{b}_g(t)|$};
...
\path (9.89778,5.12) node[anchor=base east] {streamer (converging to real edges)};

However, the code is far from what I would have written by hand. Especially, all coordinate transformations have been performed by Gnuplot, which is sad since TikZ gives all the necessary features to position the original data points on the plot. (E.g. you could be able to change the plot range etc. in the resulting code, but not using this method.) Also, the interline spacing is still bad.

Gnuplot + TikZ Terminal

Peter Hedwig has written a lua terminal for Gnuplot that comes with a TikZ backend (and only with this) written in lua. See also the example on Kjell's useful site.

Unfortunately, this requires a recompilation of Gnuplot (if you don't download one of the provided binaries, which might on the other hand be missing other features). Even then, the resulting TeX code seems to rely on newer LaTeX packages than I have (still using TeTeX), and did not compile.

Also, this still does not use TikZ's plot command, but simply draws all coordinates using a normal \path with the transformed coordinates (see above), which is unsatisfactory. In the best case, the output is expected to be similar to the above, fig2tikz-generated code.

TikZ 'plot' command

As mentioned above, TikZ itself provides a plot command that can be used within paths to plot data that is provided inline, via external files, or as a mathematical function. (See section 16 in the PGF manual.) One big advantage of this approach is that one can use TikZ's coordinate transformations for mapping the raw data into the figure, which makes it possible to change the plot scale / domain etc. at any time, and allows one to add additional graphical elements (e.g. arrows, text nodes, ...) at the correct positions using the convenient TikZ API. Furthermore, the above-mentioned advantages of using TikZ for the correct line widths and text sizes of course apply to this method, too.

The main disadvantage is the same: you have to use TikZ's coordinate transformations in order to map the data into the desired figure range. Also, there are no axes and ticks drawn automatically, so you have to do everything yourself.

Another major problem is that if your data to be plotted contains too large or too small numbers, you easily exceed the valid range for TeX dimensions (even if only for intermediate states before the transformations are applied). This is stated in the PGF manual and is a known limitation which the user is expected to work around himself, e.g. by scaling the data to be plotted before feeding it to LaTeX.

For example, the data to be plotted can be written to simple ASCII files (suitable for Gnuplot, too) and plotted using the following code:

\begin{tikzpicture}[xscale=0.4,yscale=0.2]

\draw[dotted] (0,0) -- (0,14) node[right] {saddle pos};

\draw[red] plot[mark=+,mark options={scale=0.7}] file{valueplot-flowlines_1.dat};
\draw[green] plot[mark=x,mark options={scale=0.7}] file{valueplot-flowlines_2.dat};
\draw[blue] plot[mark=asterisk,mark options={scale=0.7}] file{valueplot-flowlines_3.dat};
\draw[magenta] plot[mark=square,mark options={scale=0.7}] file{valueplot-flowlines_4.dat};

\end{tikzpicture}

File: valueplot-flowlines_plots.tikz

(467 bytes; Tue, Mar/18/2008)

pgfplots

The pgfplots package by Christian Feuersänger is available via CTAN. It is based on PGF/TikZ and provides some very useful features for plotting:

• The plot area size can be specified and defaults to a sane default; the range of the data to be plotted is auto-detected and the scaling is set up appropriately. It also supports setting the x/yrange to be plotted, and the plot will be scaled and clipped accordingly.
• AFAICS, pgfplots contains special code for handling numbers beyond what TeX/PGF support natively.
• Furthermore, it is possible to have logarithmic scaling along one or both axis.
• Similar to Gnuplot, you can specify multiple data to be plotted, and pgfplots will choose from a set of predefined styles in order to discriminate different plots within the same axis. Even better - it also supports a convenient automatic legend of these styles/plots.

Thus, it fills in many of the gaps left by PGF/TikZ alone, and allows to benefit from all of TikZ's beauty... nearly. I have found many small limitations that stem from the fact that it is not well integrated into TikZ, e.g. I would have expected to be able to easily reference all parts of the plot by using named nodes and anchors, which is not currently possible (the nodes are part of scopes, which prevent access to their content). Christian Feuersänger is working actively on improving this, and he has patiently listened to my requests/comments, but the currently released version is quite limited in this respect.

Similarly, one may specify the TikZ styles for many relevant parts of pgfplots' output, but one has to modify e.g. every axis legend and cannot easily add style options for just a single object.

Another important limitation is that with the release I tested (0.92.3, the current at time of writing), only inline data can be plotted. Christian Feuersänger has since implemented plotting data from files AFAIK, but you cannot simply use all of TikZ's plot sources (e.g. Gnuplot function specifications).

Here is the running example, styled beautifully with pgfplots and TikZ:

\begin{tikzpicture}[mark size=1.5pt,remember picture]

\tikzstyle{plot legend}=[
   rounded corners=2.5pt,inner xsep=3pt,inner ysep=2pt,
   draw=black!50,fill=white,
   font=\footnotesize,cells={anchor=center},
   nodes={inner sep=2pt,text depth=0.15em,rounded corners=0pt,right}]

\tikzstyle{every axis legend}=[plot legend,at={(.85,0.8)},below right]
\tikzstyle{every axis y label}=[at={(0,0.5)},xshift=-25pt,rotate=90]

\begin{axis}[
  xmin=-5,xmax=5,
  ymin=0,ymax=25,
  ytick={0,5,...,25},
  xlabel={arc length distance $t$ from saddle [pixels]},
  ylabel={boundary indicator value $|\vec{b}_g(t)|$}]

\addplot plot coordinates {
  (-6.74792,2.41861) (-6.66786,2.41852) (-6.58805,2.41824) (-6.50996,2.41777) (-6.41075,2.41679) (-6.30551,2.41505) (-6.15340,2.41075) (-5.93965,2.40070) (-5.62466,2.37734) (-5.15092,2.32533) (-4.81777,2.27973) (-4.31289,2.20389) (-3.90792,2.14396) (-3.56562,2.09832) (-3.27459,2.06512) (-3.02640,2.04160) (-2.81205,2.02498) (-2.62515,2.01318) (-2.46036,2.00469) (-2.31403,1.99851) (-2.18241,1.99390) (-2.06229,1.99036) (-1.95106,1.98758) (-1.84645,1.98531) (-1.74609,1.98339) (-1.64791,1.98171) (-1.54947,1.98017) (-1.44841,1.97871) (-1.34122,1.97723) (-1.22126,1.97565) (-1.06446,1.97363) (-0.80552,1.97038) (-0.54659,1.96739) (-0.36271,1.96559) (-0.20000,1.96437) (0.00000,1.96349) (0.10000,1.96337) (0.20000,1.96350) (0.40000,1.96457) (0.66334,1.96786) (0.82469,1.97106) (1.00410,1.97577) (1.20014,1.98238) (1.41256,1.99137) (1.64222,2.00335) (1.88995,2.01902) (2.15698,2.03926) (2.44428,2.06507) (2.75132,2.09742) (3.07466,2.13693) (3.40793,2.18352) (3.74762,2.23692) (4.09685,2.29747) (4.45942,2.36533) (4.83307,2.43910) (5.20177,2.51426) (5.54872,2.58624) (5.87085,2.65390) (6.17726,2.71933) (6.47863,2.78542) (6.78862,2.85637) (7.13375,2.94064) (7.59098,3.06389) (8.13953,3.23189) (8.67260,3.41315) (9.39853,3.66690) (9.83987,3.80614) (10.13601,3.88485) (10.36232,3.93412) (10.54394,3.96577) (10.69550,3.98653) (10.83385,4.00111) (10.95513,4.01094) (11.03401,4.01619) (11.09168,4.01963) (11.14379,4.02251) (11.19194,4.02503) (11.28684,4.02965) (11.33618,4.03190) (11.38800,4.03416) (11.44303,4.03643) (11.50199,4.03872) (11.56561,4.04104) (11.63478,4.04335) (11.70991,4.04562) (11.79157,4.04779) (11.87873,4.04976) (11.96931,4.05140) (12.05829,4.05260) (12.14019,4.05335) (12.20972,4.05369) (12.26727,4.05379)
};
\addlegendentry{undesired, noise-induced edge}

\addplot[mark=|,red] plot coordinates {
  (-3.76974,23.44724) (-3.68200,23.44695) (-3.64029,23.44663) (-3.57390,23.44586) (-3.51311,23.44490) (-3.46300,23.44393) (-3.39804,23.44243) (-3.36070,23.44145) (-3.29129,23.43940) (-3.22822,23.43728) (-3.18614,23.43574) (-3.13754,23.43383) (-3.04637,23.42987) (-2.95967,23.42567) (-2.90068,23.42257) (-2.83380,23.41883) (-2.77416,23.41531) (-2.70061,23.41071) (-2.66154,23.40816) (-2.52857,23.39898) (-2.44938,23.39318) (-2.39931,23.38941) (-2.33883,23.38476) (-2.17413,23.37174) (-2.05644,23.36230) (-1.98196,23.35636) (-1.93330,23.35251) (-1.84825,23.34590) (-1.62954,23.32990) (-1.52996,23.32327) (-1.47585,23.31985) (-1.40329,23.31551) (-1.27105,23.30830) (-1.19944,23.30478) (-1.13051,23.30165) (-1.04894,23.29825) (-0.96702,23.29516) (-0.87382,23.29203) (-0.79070,23.28955) (-0.74927,23.28843) (-0.70129,23.28721) (-0.64637,23.28592) (-0.60115,23.28493) (-0.53219,23.28358) (-0.45855,23.28230) (-0.38244,23.28116) (-0.32153,23.28038) (-0.26284,23.27973) (-0.19690,23.27911) (-0.13978,23.27868) (-0.08064,23.27834) (-0.02275,23.27808) (0.00000,23.27801) (0.10000,23.27787) (0.20000,23.27802) (0.27601,23.27832) (0.36681,23.27891) (0.46110,23.27978) (0.55399,23.28091) (0.64198,23.28223) (0.70081,23.28326) (0.75328,23.28427) (0.81782,23.28563) (0.85871,23.28657) (0.93657,23.28849) (0.98295,23.28974) (1.05394,23.29177) (1.14949,23.29476) (1.16854,23.29539) (1.25761,23.29848) (1.31224,23.30049) (1.37408,23.30286) (1.44949,23.30589) (1.51818,23.30877) (1.57749,23.31135) (1.64391,23.31433) (1.69761,23.31680) (1.77152,23.32030) (1.82174,23.32272) (1.88683,23.32592) (1.95135,23.32914) (2.04539,23.33393) (2.09220,23.33636) (2.15071,23.33942) (2.21378,23.34276) (2.27209,23.34589) (2.32331,23.34867) (2.37362,23.35143) (2.42883,23.35450) (2.48828,23.35785) (2.54699,23.36122) (2.60335,23.36450) (2.65867,23.36780) (2.71561,23.37126) (2.77485,23.37495) (2.83543,23.37882) (2.89585,23.38280) (2.95675,23.38694) (3.01953,23.39134) (3.08437,23.39604) (3.15018,23.40099) (3.21683,23.40618) (3.28460,23.41165) (3.35451,23.41750) (3.42648,23.42374) (3.49957,23.43030) (3.57365,23.43717) (3.64867,23.44436) (3.72416,23.45181) (3.80056,23.45956) (3.87760,23.46758) (3.95468,23.47580) (4.03184,23.48421) (4.10882,23.49279) (4.18576,23.50154) (4.26266,23.51047) (4.33974,23.51959) (4.41715,23.52894) (4.49513,23.53857) (4.57441,23.54856) (4.65443,23.55888) (4.73544,23.56957) (4.81782,23.58073) (4.90189,23.59242) (4.98799,23.60474) (5.07646,23.61781) (5.16730,23.63169) (5.26080,23.64652) (5.35672,23.66236) (5.45528,23.67937) (5.55634,23.69766) (5.65938,23.71731) (5.76425,23.73845) (5.87131,23.76132) (5.98009,23.78602) (6.09098,23.81280) (6.20325,23.84165) (6.31760,23.87290) (6.43432,23.90677) (6.55406,23.94363) (6.67738,23.98385) (6.80482,24.02785) (6.93717,24.07624) (7.07526,24.12974) (7.21979,24.18923) (7.37205,24.25606) (7.53441,24.33248) (7.70924,24.42131) (7.89952,24.52650) (8.10836,24.65314) (8.34148,24.80958) (8.60710,25.00889) (8.91106,25.26703) (9.25007,25.59714) (9.68649,26.09883) (10.13522,26.72731) (10.40807,27.17870) (10.65277,27.63495) (10.90256,28.15483) (11.16477,28.76174) (11.44948,29.49245) (11.77047,30.40424) (12.15016,31.59520) (12.65258,33.31831) (13.42664,36.04860) (13.62630,36.71383) (13.83415,37.37658) (14.01722,37.93327) (14.18297,38.41524) (14.33800,38.84736) (14.48085,39.22980) (14.61486,39.57508) (14.74229,39.89128) (14.86436,40.18308) (14.98202,40.45398) (15.09625,40.70715) (15.20802,40.94540) (15.31824,41.17117) (15.42790,41.38667) (15.53783,41.59355) (15.64893,41.79333) (15.76206,41.98717) (15.87814,42.17606) (15.99810,42.36076) (16.12295,42.54179) (16.25372,42.71942) (16.39138,42.89353) (16.53689,43.06372) (16.69101,43.22914) (16.85414,43.38846) (17.02662,43.54044) (17.20801,43.68337) (17.39742,43.81578) (17.59106,43.93517) (17.78192,44.03878) (17.95844,44.12362) (18.11107,44.18940) (18.24056,44.24023) (18.35635,44.28212) (18.46640,44.31902) (18.57116,44.35166) (18.66833,44.37986) (18.75731,44.40398) (18.84002,44.42498) (18.91841,44.44364) (18.99328,44.46033) (19.06445,44.47519) (19.13176,44.48832) (19.19514,44.49987) (19.25495,44.51004) (19.31152,44.51899) (19.36506,44.52686) (19.46346,44.53976) (19.50769,44.54489) (19.58677,44.55300) (19.65524,44.55890) (19.71276,44.56302) (19.78112,44.56692) (19.84673,44.56961) (19.88347,44.57064) (19.97685,44.57176)
};
\addlegendentry{real, high-contrast image edge}

\addplot plot coordinates {
  (-1.15451,10.36685) (-1.07964,10.36621) (-1.02056,10.36481) (-0.96257,10.36271) (-0.90533,10.35997) (-0.84858,10.35665) (-0.79205,10.35281) (-0.73561,10.34850) (-0.67917,10.34380) (-0.62272,10.33880) (-0.56633,10.33358) (-0.50992,10.32825) (-0.45352,10.32290) (-0.39747,10.31767) (-0.34169,10.31266) (-0.28682,10.30800) (-0.23402,10.30388) (-0.18313,10.30031) (-0.12560,10.29684) (-0.03525,10.29280) (0.00000,10.29174) (0.10000,10.29044) (0.20000,10.29175) (0.28114,10.29471) (0.34449,10.29811) (0.44379,10.30512) (0.53029,10.31253) (0.59874,10.31897) (0.66221,10.32520) (0.72320,10.33125) (0.78138,10.33692) (0.83700,10.34216) (0.89028,10.34690) (0.94149,10.35114) (1.03860,10.35813) (1.12980,10.36322) (1.21498,10.36658) (1.29044,10.36838) (1.37969,10.36912)
};
\addlegendentry{real, low-contrast image edge}

\addplot plot coordinates {
  (-3.14098,15.46859) (-3.05005,15.46793) (-3.03205,15.46764) (-2.93375,15.46514) (-2.84266,15.46145) (-2.76309,15.45344) (-2.68022,15.42299) (-2.61653,15.38079) (-2.43041,15.16335) (-2.21648,14.74227) (-1.83556,13.53895) (-1.54884,12.22611) (-1.26239,10.54200) (-0.83897,7.52613) (-0.20000,3.62234) (-0.00000,3.13037) (0.10000,3.06780) (0.20000,3.12986) (0.40000,3.60861) (0.81954,5.76144) (1.21229,8.25063) (1.49830,9.82046) (1.71955,10.77871) (1.91907,11.45069) (2.13743,12.00227) (2.51547,12.56801) (2.54747,12.59468) (2.67448,12.66844) (2.75913,12.68968) (2.82919,12.69491) (2.90099,12.69776) (2.97321,12.69961) (3.00861,12.70015) (3.07604,12.70055)
};
\addlegendentry{streamer (converging to real edges)}

\draw[dotted] (0,0) -- (0,14) node[right] {saddle pos};

\end{axis}

\end{tikzpicture}

File: valueplot-flowlines_pgfplots.tikz

(8484 bytes; Thu, Mar/20/2008)

Some other small things to be improved were the automatic tick marks, which are not as good as in Gnuplot (heh - that's OK, I find it impressive that it has automatic tick marks at all, but one should be aware of this respect), and if you specify the xrange, the yrange is not computed from just the respective part of the data, but still from the whole set, i.e. you often find yourself having to specify both, when you would just specify one in Gnuplot.

tkz-fct

Alain Matthes' TKZ stuff on AlterMundus contains a tkz-fct package. Again, check the example on Kjell's site. I have not yet checked this out due to time constraints, but I hope I will eventually be able to do so.

pgfgraph

Similar to tkz-fct, I have not yet had a closer look at the pgfgraph package by Pascal Wolkotte, which is another promising extension for plotting with PGF/TikZ.