Fill the area between two curves calculated by pgfplots

Question

This is essentially the same question as fill the area between two curves when their coordinates are known.

In that question, the curves were defined by known coordinates. I want to fill the area between two curves but I want the curves to be calculated from pgfplots (or gnuplot).

Let's say that the curves are defined by these functions:

f(x) = sqrt(x)

g(x) = sqrt(x/2)

Answer 1

Version 1.10 of pgfplots has been released just recently, and it comes with a new solution for the problem to fill the area between plots.

Note that the old solution is still possible and still valid; this here is merely an update which might simplify the task. In order to keep the knowledge base of this site up-to-date, I present a solution based on the new fillbetween library here:

\documentclass{standalone}
\usepackage{tikz,pgfplots}

\pgfplotsset{compat=1.10}
\usepgfplotslibrary{fillbetween}

\begin{document} 
\begin{tikzpicture}
    \begin{axis}[thick,smooth,no markers]
        \addplot+[name path=A,black] {sqrt(x)};
        \addplot+[name path=B,black] {sqrt(x/2)};

        \addplot[blue!50] fill between[of=A and B];
    \end{axis}
\end{tikzpicture}
\end{document}

The solution relies on \usepgfplotslibrary{fillbetween} which activates the syntax \addplot fill between[of=<first> and <second>]. The style for the filled region is given in the option list as usual, it is blue!50. Note that the fill between segment will automatically be drawn on a separate layer, i.e. it is behind the main paths.

Answer 2

You can (ab)use stack plots. Simply subtract the first function from the second to undo the stacking.

\documentclass{article}
\usepackage{tikz,pgfplots}

\begin{document} 
\begin{tikzpicture}
    \begin{axis}[stack plots=y,thick,smooth,no markers]
        \addplot+[black]              gnuplot{sin(x)};
        \addplot+[black,fill=blue!50] gnuplot{cos(x)-sin(x)} 
          \closedcycle;
    \end{axis}
\end{tikzpicture}
\end{document}

To get a better looking result, you should probably draw the filling and the curves separately:

\begin{axis}[stack plots=y,thick,smooth,no markers]
    \addplot+[black]                  gnuplot{sin(x)};         % sin
    \addplot+[black]                  gnuplot{cos(x)-sin(x)};  % cos
    \addplot[fill=blue!50,draw=none]  gnuplot{sin(x)-cos(x)}   % fill to sin
       \closedcycle;
\end{axis}

Answer 3

Result:

Code below. I'm assuming you're ok with defining the horizontal axis as an evenly-spaced set of points across an interval. I'm using pgfplotstable to define table elements in terms of mathematical expressions, and then using those tables to define paths like you saw in the linked question.

\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\begin{document}

% Make two tables for the data -- use the same column names for each
\pgfplotstablenew[
  create on use/x/.style={create col/expr={.5+\pgfplotstablerow*0.05}},
  create on use/y/.style={create col/expr={sqrt(\thisrow{x}}},
  columns={x,y}]
  {21}
  \ftable
%\pgfplotstabletypeset\ftable
\pgfplotstablenew[
  create on use/x/.style={create col/expr={.5+\pgfplotstablerow*0.05}},
  create on use/y/.style={create col/expr={sqrt(\thisrow{x}/2)}},
  columns={x,y}]
  {21}
  \gtable
%\pgfplotstabletypeset\gtable
% Sort the second table by the x value, from largest to smallest
\pgfplotstablesort[sort cmp={float >}]\gsorted{\gtable}
%\pgfplotstabletypeset\gsorted
% Concatenate the tables -- now filledcurve contains the edge of
% a polygon bounded by curves f and g
\pgfplotstablevertcat{\filledcurve}{\ftable}
\pgfplotstablevertcat{\filledcurve}{\gsorted}
% Draw the curves and the polygon
\begin{tikzpicture}
\begin{axis}
\addplot[fill=gray!40,draw=none] table {\filledcurve};
\addplot[red] table {\ftable};
\addplot[blue] table {\gtable};
\end{axis}
\end{tikzpicture}

\end{document}

Answer 4

\documentclass[11pt]{article}
\usepackage{pst-plot}

\begin{document}

\begin{psgraph}{->}(0,0)(5,2.5){6cm}{5cm}
\pscustom[fillstyle=solid,fillcolor=black!20,
          linestyle=none]{
  \psplot[algebraic]{1}{4}{sqrt(x)}
  \psplot[algebraic]{4}{1}{sqrt(x/2)} }
\psplot[algebraic,linecolor=red,linewidth=1pt]{1}{4}{sqrt(x)}
\psplot[algebraic,linecolor=blue,linewidth=1pt]{4}{1}{sqrt(x/2)}
\end{psgraph}

\end{document}