Plotting simple implicit equations

Question

I would like to plot the graph of a simple equation like x^2+xy+2y^2=1 using TikZ. There are some posts on implicit plots here, but nothing worked in my case.

I am using TeXShop Version 3.92 and \documentclass{book}.

Answer 1

Question 18359

The answer of question 18359 works for me. Changed line:

splot x^2 + x*y + 2*y^2 - 1;

And I added the line

set samples 500;

for a smoother curve.

Full example:

\documentclass{article}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}
  \begin{axis}
    \addplot +[no markers,
      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;
      set samples 500;
      splot x^2 + x*y + 2*y^2 - 1;
    };
  \end{axis}
\end{tikzpicture}

\end{document}

This solution requires that gnuplot is installed and available on the command line. Depending on the TeX configuration (texmf.cnf in TeX Live), usually option -shell-escape (TeX Live)/-enable-write18 (MiKTeX) for the TeX compiler is needed to run the example, see the comment of Sari.

Question 285246

The example of question 285246 also works with the following function:

f(x,y) = x**2 + x*y + 2*y**2 - 1;

(x² is expressed as x**2.)

Full example:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \draw plot[id=question1, raw gnuplot] function{
    f(x,y) = x**2 + x*y + 2*y**2 - 1;
    set xrange [-4:4];
    set yrange [-4:4];
    set view 0,0;
    set isosample 1000, 1000;
    set size square;
    set contour base;
    set cntrparam levels incre 0,0.1,0;
    unset surface;
    splot f(x,y);
  };
\end{tikzpicture}
\end{document}

Answer 2

What about this?

\documentclass{article}
\usepackage{pgfplots} % It is based on tikz!
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot3[
surf,
samples=20,
domain=-100:100,
y domain=-100:100
] 
{x^2+x*y+2*y^2-1};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 3

\begin{tikzpicture}
    \begin{axis}[hide axis,xmin=-2,xmax=2,ymin=-2,ymax=2,]
    \addplot [blue,thick,domain=0:360,samples=200]({(cos(x)+sin(x)},{sin(x)});
    \end{axis}
\end{tikzpicture}

Answer 4

If you don't mind a not-tikz solution, the mfpic package, interface to the MetaPost language, seems to work quite well in this kind of problem with its \levelcurve command.

\documentclass[border=3bp]{standalone}
\usepackage[metapost, mplabels, truebbox]{mfpic}
  \setlength{\mfpicunit}{1cm}
  \opengraphsfile{\jobname}
\begin{document}
\begin{mfpic}[2]{-1.5}{1.5}{-1.5}{1.5}
  \drawcolor[gray]{0.7}
  \gridlines{.5,.5}
  \drawcolor{black}
  \levelcurve{origin, .01}{x**2 + x*y + 2(y**2) < 1}
  \doaxes{xy}
  \tlpointsep{3bp}
  \tlabels{[tc]{(-1, 0)}{$-1$} [tc]{(1, 0)}{$1$} [tc]{(\xmax, 0)}{$x$}}
  \tlabels{[cr]{(0, -1)}{$-1$} [cr]{(0, 1)}{$1$} [cr]{(0, \ymax)}{$y$}}
\end{mfpic}
\closegraphsfile
\end{document}

With TeXShop, process this TeX file with (PDF)LaTeX, then with MetaPost, and finally with LaTeX again.

See the mfpic documentation p.44-45 for more information on this most useful command.