[Tex/LaTex] Make plot smoother in pgfplots

Question

I'm trying to plot a function using pgfplots:

\documentclass{scrartcl}

\usepackage{pgfplots}
\pgfplotsset{compat = 1.12}

\newcommand{\param}{2.0}

\begin{document}
        \begin{tikzpicture}
          \begin{axis}[view={40}{50}]
            \addplot3[surf, domain = 0:1, y domain = 0:1, unbounded coords=jump,
            samples = 50]
            {x^(-\param-1)*y^(-\param-1)*(x^(-\param)+y^(-\param)-1)^(-1/\param-2)+\param*x^(-\param-1)*y^(-\param-1)*(x^(-\param)+y^(-\param)-1)^(-1/\param-2)};
        \end{axis}
      \end{tikzpicture}
\end{document}

This results in:

Compared with (plotted in the OS X Grapher application)

the plot generated by pgfplots is a lot "rougher" near x=y=0. I have tried increasing the number of samples from the default to 50 but that hasn't really improved the plot much.

Answer 1

The default surface plot of pgfplots uses two triangles for each rectangular patch segment. Usually, the diagonal does not matter much -- but in this case, it really matters and the result is unsuitable.

Note that shader=interp appears to select the other diagonal (unintentionally, but it does). A simple solution would be to add shader=interp, unless you really need the grid lines.

\documentclass{standalone}

\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{compat = 1.12}

\newcommand{\param}{2.0}

\begin{document}
        \begin{tikzpicture}
          \begin{axis}[view={40}{50}]
            \addplot3[surf, domain = 0:1, y domain = 0:1, unbounded coords=jump,
                shader=interp,
                samples = 25]
            {x^(-\param-1)*y^(-\param-1)*(x^(-\param)+y^(-\param)-1)^(-1/\param-2)+\param*x^(-\param-1)*y^(-\param-1)*(x^(-\param)+y^(-\param)-1)^(-1/\param-2)};
        \end{axis}
      \end{tikzpicture}
\end{document}