How to use the results of `raw output` to create a smooth plot

Question

As by my previous question on plotting an implicit curve I've got some output. But as you can see it is not quite what it should be (apart from your browser's downscaling by a factor 2 of course.

The code used to reproduce this is (run with --shell-escape, of course)

\begin{tikzpicture}[xscale=1,yscale=.25]
  \draw plot[id=curve, raw gnuplot] function{
    f(x,y) = y**2 + (x**2 - 5)*(4*x**4 - 20*x**2 + 25);
    set xrange [-4:4];
    set yrange [-15:15];
    set view 0,0;
    set isosample 1000,1000;
    set size square;
    set cont base;
    set cntrparam levels incre 0,0.1,0;
    unset surface;
    splot f(x,y)
  };
\end{tikzpicture}

I presume gnuplot returns the coordinates of end points of line segments and it's up to TikZ to connect them. But the results are not quite satisfactory because gnuplot returns the segments in a strange order. At least, that's what I assume given the graph. Now, as the documentation on raw gnuplot is rather sparse and there are not much examples of this to be found on the Internet, certainly not with surface plots or implicit functions, I hope someone could give some pointers (or a full-fledged answer, you won't see me complaining).

EDIT: As @Yossi pointed out, the .table file gnuplot creates contains several parts of the curve separated by 2 new lines each. Now TikZ connects these parts but it shouldn't. We're getting there :).

Answer 1

Based on @Jan's answer, I modified pgfmoduleplot.code.tex such that it now produces a new plot for each segment in the file.

The complete definition of \pgf@readxyfile now reads

\def\pgf@readxyfile{%
  \read1 to \pgf@temp%
  \let\par=\pgf@savedpar%
  \edef\pgf@temp{\pgf@temp}%
  \ifx\pgf@temp\pgfutil@empty%
  \else\ifx\pgf@temp\pgf@partext%
    \pgfplotstreamstart%
    \pgfplotstreamend%
  \else%
    \expandafter\pgf@parsexyline\pgf@temp\pgf@stop%
  \fi\fi%
  \ifeof1\else\expandafter\pgf@readxyfile\fi%
}

The result of this is the removal of the connecting line segments. The only downside is that the resulting curve is not connected, at 1000 samples in each direction there is one small gap, as can be seen in the screenshot:

I don't know whether this code breaks anything else, but it (almost) solved my problem. Thank you Jan for the tips!

Answer 2

I don't think it is possible without modifying pgf. The problem is that pgf reads the .table file generated by gnuplot using the \pgfplotxyfile command, which ignores everything except the first two numbers on each line, and ignores empty lines. You would have to change that so that each empty line in the .table file would end current plotstream and start a new plotstream.

I wonder if simply changing the definition of \pgfplotxyfile would be enough, or if that would break anything else. It would be probably safer to define new command, \pgfplotxyfilewithbreaks, and write a new plot handler, based on the gnuplot one but replacing calls to \pgfplotxyfile by \pgfplotxyfilewithbreaks.