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

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 2

\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}

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}