Reversing a path in TikZ

Question

When I use \path plot function {x^2}; in tikz, it plots it left-to-right (the default domain is -5:5). This is annoying, because, for example, one cannot pile on -- plot function {x^2 + 1} -- cycle; and then fill the whole thing; it doesn't fill the obvious cycle, but rather the self-intersecting one going between opposite corners as it "returns carriage", so to speak.

Is there some way to get plot function to generate points in the reverse order? Alternatively, is there some way of getting tikz to draw a path in the reverse order the points were specified? (This last one is of more general utility, since the orientation of a path is used a lot.)

Answer 1

If you use PGFplots for plotting your functions, the paths will be reversed and connected appropriately by using stack plots=y in the axis options and issuing \closedcycle after the second plot:

\documentclass{article}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
    stack plots=y,
    hide axis
]
\addplot [draw=orange,thick]{x^2};
\addplot [draw=orange, thick, fill=yellow] {1} \closedcycle;
\end{axis}
\end{tikzpicture}

\end{document}

If all you want is the filled path, you can disable the axes by using hide axis.

Answer 2

With the current implementation of plot function, I don't think it is possible since pgf reads sequencially the file output by gnuplot. Since gnuplot computes values of the function from the lowest value of x to the highest value, the reverse order is not possible (see file pgfmoduleplot.code.tex) (I may have missed a gnuplot option to do so).

However, you can achieve what you want with the pgf math engine like in the following, reversing the bounds of the domain.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=.25]
  \fill plot (\x,\x^2) -- plot[domain=5:-5] (\x,\x^2 + 1) -- cycle;
\end{tikzpicture}
\end{document}

Note: this is my first contrib to tex.se. Hope it is formatted ok.

Answer 3

Actually you can force Gnuplot compute the path in the order you want. The idea is to use Gnuplot's parametric curve representation.

In the following example (in the %% Good section, the %% Bad section is just here to show what happens if the trick is not used), I draw the first curve normally, and the second one using the trick. Each value of the parameter t which lives between 0 and 1 is sent to the desired interval (here [2,-1] in that order) using the barycentric formula : x = (1-t) *2 + t *(-1)

More generally, if you want to send [0,1] on to [a,b] starting with b you just use (1-t)*b + t*a.

\documentclass{article}
\usepackage{tikz}
\begin{document}

%% Requires Gnuplot !

%% Functions definition
\newcommand{\funcf}[1]{(#1)**2)}   % it is wise to always put the #1 argument between ()
\newcommand{\funcg}[1]{1+(#1)**2)}

%% Bad 
\begin{tikzpicture}
    \fill
        plot[domain=-1:2, id=funcf] function {\funcf{x}}
        --  
        plot[domain=2:-1, id=funcgbad] function {\funcg{x}} % inverting boundaries does *NOT* work with Gnuplot
        -- cycle;
\end{tikzpicture}


%% Good 
\begin{tikzpicture}
    \fill
        plot[domain=-1:2, id=funcf] function {\funcf{x}}
        --  
        plot[domain=0:1, parametric, id=funcggood] function {(1-t)*2+t*(-1),\funcg{(1-t)*2+t*(-1)}} 
        -- cycle;
\end{tikzpicture}

\end{document}