pgfplots how to smoothen up a surface plot with coordinates

Question

I have some coordinates not from some particular function...

\begin{document}
    \begin{figure}
        \begin{tikzpicture} 
            \begin{axis} [width=16cm,height=19cm,samples=100]
                \addplot3[surf]  coordinates {  
                (1,1,70)(2,1,48)(3,1,41)(4,1,70)( 5,1,68)(6,1,82)(7,1,38)(8,1,47)(9,1,35)(10,1,66)(11,1,53)(12,1,78)
                (1,2,91)(2,2,43)(3,2,68)(4,2,90)( 5,2,66)(6,2,55)(7,2,66)(8,2,46)(9,2,25)(10,2,38)(11,2,50)(12,2,58)
                (1,3,60)(2,3,68)(3,3,39)(4,3,65)( 5,3,59)(6,3,69)(7,3,72)(8,3,62)(9,3,94)(10,3,36)(11,3,33)(12,3,39)
                (1,4,48)(2,4,80)(3,4,68)(4,4,66)( 5,4,59)(6,4,63)(7,4,93)(8,4,63)(9,4,30)(10,4,52)(11,4,60)(12,4,14)};
            \end{axis}
        \end{tikzpicture}
    \end{figure} 
\end{document}

the result is this...

When I put the option smooth, like that...

\begin{document}
    \begin{figure}
        \begin{tikzpicture} 
            \begin{axis} [width=16cm,height=19cm,samples=100]
                \addplot3[smooth]  coordinates {  
                (1,1,70)(2,1,48)(3,1,41)(4,1,70)( 5,1,68)(6,1,82)(7,1,38)(8,1,47)(9,1,35)(10,1,66)(11,1,53)(12,1,78)
                (1,2,91)(2,2,43)(3,2,68)(4,2,90)( 5,2,66)(6,2,55)(7,2,66)(8,2,46)(9,2,25)(10,2,38)(11,2,50)(12,2,58)
                (1,3,60)(2,3,68)(3,3,39)(4,3,65)( 5,3,59)(6,3,69)(7,3,72)(8,3,62)(9,3,94)(10,3,36)(11,3,33)(12,3,39)
                (1,4,48)(2,4,80)(3,4,68)(4,4,66)( 5,4,59)(6,4,63)(7,4,93)(8,4,63)(9,4,30)(10,4,52)(11,4,60)(12,4,14)};
            \end{axis}
        \end{tikzpicture}
    \end{figure} 
\end{document}

I get the next image...

What I want is to have the continuous surface of the first image but smoothened like the curves in the second, not only along the x axis but also in depth... How can I achieve that???

Answer 1

You can adapt one of the solutions described in How to plot a surface from a set of data? to use the gnuplot backend in PGFPlots to generate a smooth surface:

\documentclass[border= 5mm]{standalone}
\usepackage{pgfplots, filecontents}

\begin{filecontents*}{data.txt}
1   1   70
2   1   48
3   1   41  
4   1   70
 5  1   68
6   1   82
7   1   38
8   1   47
9   1   35
10  1   66
11  1   53
12  1   78
1   2   91
2   2   43
3   2   68
4   2   90
 5  2   66
6   2   55
7   2   66
8   2   46
9   2   25
10  2   38
11  2   50
12  2   58
1   3   60
2   3   68
3   3   39
4   3   65
 5  3   59
6   3   69
7   3   72
8   3   62
9   3   94
10  3   36
11  3   33
12  3   39
1   4   48
2   4   80
3   4   68
4   4   66
 5  4   59
6   4   63
7   4   93
8   4   63
9   4   30
10  4   52
11  4   60
12  4   14
\end{filecontents*}

\begin{document}
    \begin{tikzpicture}
    \begin{axis}
    \addplot3 [surf] gnuplot [raw gnuplot] {
        set dgrid3d 50,50 spline;
        splot 'data.txt';       
    };
    \end{axis}
    \end{tikzpicture}
\end{document}

Answer 2

Automatic smoothening of surfaces is unsupported by pgfplots (i.e. you could file feature requests).

Depending on how you obtain your data files, you may be able to increase the smoothness either by increasing the number of samples or by using higher order patch types which are offered by pgfplots's patchplots library (compare Creating Bezier surfaces using procedural graphics).

If your input is actually a math expression, you may be able to rely on the feature called patch type sampling which is also illustrated in the link mentioned above.

Everything which is beyond these work-arounds would need to be a feature request for pgfplots.