Construct colormap for iso / level surface in PGFplots

Question

I am trying to construct a plot of a surface in 3d of which the color of the surface is dependent on the z coordinate. The difficult part is that I need the color to vary 'discretely', not continuously. I believe they call these plots something like iso or level surfaces, if I'm not mistaken.

Examples:

For a color varying continuously with the z coordinate, the construction in PGFplots is easy. The \addplot3[surf,shader=faceted interp] ... works just fine for this.

A minimum working example is

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}
            \addplot3
            [
                surf,
                domain=-1:1,
                y domain=-1:1,
                samples=50, % DECREASE FOR SHORTER COMPILATION.
                shader=faceted interp,
                colormap name={hot}
            ] {exp(-10*(x^2+y^2))};
        \end{axis}
    \end{tikzpicture}
\end{document}

which results in . How should I modify this LaTeX code to get discrete color variation like in the first two pictures?

Answer 1

Conform the suggestion of Jake, defining a 'discrete' colormap, one can construct the desired iso / level surface.

The code in question,

\documentclass{standalone}
\usepackage{pgfplots}

\pgfplotsset
{
    colormap={redgreenblue}%
    {
        [2pt] % colormap steps: 2pt
        % blue: from 0000 to 1000
        rgb(0000pt)=(0,0,1);
        rgb(1000pt)=(0,0,1);
        % green:  from 1000 to 2000
        rgb(1000pt)=(0,1,0);
        rgb(2000pt)=(0,1,0);
        % red: from 2000 to 3000
        rgb(2000pt)=(1,0,0);
        rgb(3000pt)=(1,0,0);
    }
}

\begin{document}
    \begin{tikzpicture}
        \begin{axis}
            \addplot3
            [
                surf,
                domain=-1:1,
                y domain=-1:1,
                samples=50, % DECREASE FOR SHORTER COMPILATION.
                shader=faceted interp,
                %colormap name={hot}
            ] {exp(-10*(x^2+y^2))};
        \end{axis}
    \end{tikzpicture}
\end{document}

results in