pgfplots: How to smoothen a 3D surface plot?

Question

Long time has passed - based on this and this question I would like to know if pgfplots does already support surface smoothening of coordinate based 3D plots in 2019?

Minimum Working Example (MWE):

\documentclass{standalone}
\usepackage{pgfplots,pgfplotstable}
\usepackage{filecontents}

\begin{filecontents}{testdata.csv}
    x;y;z
    0;0;4
    0;1;4
    0;2;4
    1;0;2
    1;1;2
    1;2;2
    2;0;3
    2;1;3
    2;2;3
    3;0;0
    3;1;0
    3;2;0
\end{filecontents}

\begin{document}
    \begin{tikzpicture}
        \begin{axis}[table/col sep = semicolon]
            \addplot3[mesh, mesh/cols=3,surf, shader=interp] table[x=x, y=y, z=z] {testdata.csv};
        \end{axis}
    \end{tikzpicture}
\end{document}

Screenshot of the result:

Screenshot of the desired state:

As you can see, the desired state represents some beautiful grid lines as well as smoothened curves instead of rough peaks. Is this purely possible with pgfplots nowadays?

Unfortunately combining [surf] and [smooth] of a plot does not work.

score 3 · Accepted Answer · answered May 20 '19 at 17:24

I do not think that, as of now, there is a smooth option for surface plots. However, you can smoothen out the table data yourself. As any smoothening, this comes with a prescription and with parameters. If you draw a 1D curve you can specify the tension, so you may want to think of the \mysigmax and \mysigmay parameters in the following code as serving a similar purpose.

\documentclass{standalone}
\usepackage{pgfplots,pgfplotstable}
\pgfplotsset{compat=1.16}
\usepackage{filecontents}

\begin{filecontents*}{testdata.csv}
    x;y;z
    0;0;4
    0;1;4
    0;2;4
    1;0;2
    1;1;2
    1;2;2
    2;0;3
    2;1;3
    2;2;3
    3;0;0
    3;1;0
    3;2;0
\end{filecontents*}

\begin{document}
\begin{tikzpicture}
  \pgfplotstableread[col sep=semicolon]{testdata.csv}\datatable
  \pgfplotstablegetrowsof{\datatable}
  \pgfmathtruncatemacro{\Xmax}{\pgfplotsretval-1}
  \pgfmathsetmacro\mysum{0}
  \pgfmathsetmacro\mysigmax{0.5}
  \pgfmathsetmacro\mysigmay{0.3}
  \pgfplotsforeachungrouped \X in {0,...,\Xmax}{
     \pgfplotstablegetelem{\X}{x}\of{\datatable}
     \edef\myx{\pgfplotsretval}
     \pgfplotstablegetelem{\X}{y}\of{\datatable}
     \edef\myy{\pgfplotsretval}
     \pgfplotstablegetelem{\X}{z}\of{\datatable}
     \edef\myz{\pgfplotsretval}
     \edef\mysum{\mysum+\myz*exp(-((x-\myx)^2/\mysigmax+(y-\myy)^2/\mysigmay))}
  }
  %\typeout{\mysum}
        \begin{axis}[table/col sep = semicolon]
            %\addplot3[mesh, mesh/cols=3,surf, shader=interp] table[x=x, y=y, z=z] {testdata.csv};
            \addplot3[surf,domain=0:3,domain y=0:2] {\mysum};
        \end{axis}
\end{tikzpicture}
\end{document}

If you set \mysigmay to 3 instead you get

pgfplots: How to smoothen a 3D surface plot?

1 Answers1