# Plotting an implicit function using pgfplots

What is the correct way to plot an implicit function using pgfplots? Consider the following example:

\documentclass{standalone}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}
set contour base;
set cntrparam levels discrete 0.0;
unset surface;
set view map;
set isosamples 500;
splot exp(x)*cos(y)-1-x;
};
\end{axis}
\end{tikzpicture}

\end{document}


This is what the function looks like in gnuplot:

pgfplots, however, connects function's segments, which is unexpected:

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The development version of PGFPlots includes an empty line option that can be set to jump to get the desired behaviour. If you're using TeXLive, you can update PGFPlots through tlmgr by temporarily using the repository http://tlcontrib.metatex.org/2010. – Jake May 16 '11 at 16:41
@Jake: Consider posting this as an answer. Using the empty line option to allow interrupted plots works very well except gaps between segments become visible: i.imgur.com/8k3pp.png. Is there a way to fix this? – caustic May 16 '11 at 20:28
I'm afraid not, because that's just the data gnuplot generates (the gaps are also visible in the gnuplot screenshot in your question). If you increase the line width to thick and plot the contour for 0.003 instead of 0.0, it looks okay. – Jake May 16 '11 at 20:59

The development version of PGFPlots includes an empty line option that can be used to influence the behaviour. It is set to jump by default, which breaks the plot when an empty line is encountered. If you're using TeXLive, you can update PGFPlots through tlmgr by temporarily using the repository http://tlcontrib.metatex.org/2010.

The gap at the intersections is a numerical artefact introduced by gnuplot. It can't be fixed completely, but by plotting with a thicker line, and choosing a slightly different contour line to be plotted, it can be glossed over:

\documentclass{article}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}
raw gnuplot,
thick,
empty line = jump % not strictly necessary, as this is the default behaviour in the development version of PGFPlots
] gnuplot {
set contour base;
set cntrparam levels discrete 0.003;
unset surface;
set view map;
set isosamples 500;
splot exp(x)*cos(y)-1-x;
};
\end{axis}
\end{tikzpicture}

\end{document}


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