[Tex/LaTex] How to fill an area with fading color

Question

I want to fill an area on a x–y plane with fading color, but have no idea how to do it. I know how to fill shapes with color, but not how to do it when the area is not a well defined shape.

Let me be more specific:
I drew a rough sketch of the implicit function y^2-x^2=a^2:

\documentclass{article}

\usepackage{tikz}

\begin{document}

        \begin{center}
        \begin{tikzpicture}
          \draw[->] (-3,0) -- (3,0) node[right] {$x$};
          \draw[->] (0,-3) -- (0,3) node[above] {$y$};

          \draw (-3,3) parabola bend (0,1.25) (3,3);
          \draw (-3,-3) parabola bend (0,-1.25) (3,-3);
        \end{tikzpicture}
        \end{center}

\end{document}

This produces the following:

Now I want to fill the area that enclosed between these two parabolas with a color that fades away at the right and left edges (to emphasize the fact that the area goes further away to infinity).

Can it be done?

Thanks in advanced!

Answer 1

May be you should use pgfplots which offers fill between facility. But here is a tikz version:

\documentclass{article}

\usepackage{tikz}

\begin{document}

        \begin{center}
        \begin{tikzpicture}
          \draw[thick] (-3,3) parabola bend (0,1.25) (3,3);
          \draw[thick] (-3,-3) parabola bend (0,-1.25) (3,-3);
          \fill[left color = olive!10,right color = olive!10, middle color=olive]
                (-3,3) parabola bend (0,1.25) (3,3) -- (3,-3) parabola bend (0,-1.25) (-3,-3)
                -- (-3,3) -- cycle;
          \draw[->] (-4,0) -- (4,0) node[right] {$x$};
          \draw[->] (0,-3) -- (0,3) node[above] {$y$};
        \end{tikzpicture}
        \end{center}

\end{document}

Using pgfplotsand its fillbetween library, your code would look something like:

\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.11}

\begin{document}

\begin{center}
\begin{tikzpicture}
\begin{axis}[
  axis lines=middle,
  xtick=\empty,
  ytick=\empty,
  ]
  \addplot[blue,name path=U] {sqrt(3^2+x^2)};
  \addplot[blue,name path=L] {-sqrt(3^2+x^2)};
  \addplot[left color=cyan!05,right color=cyan!05,middle color=cyan!80!black] 
  fill between[of=U and L,soft clip={domain=-5:5},];
\end{axis}
\end{tikzpicture}
\end{center}

\end{document}

And the result: