How to tranch a 3D plot by x or y

Question

When I use a 3D plot in class, I like representing first, 2D plots along each axis (as if I was "tranching" the 3D graph), and then explain the dynamic in 3D. The Final 3D plot is then easier to assimilate for students.

How can I "tranch" properly a 3D plot with a set of 2D plots passing conditional argument in styles ?

So far, I get the result I like by (inefficiently) superposing the plot with 2 different styles.

It works well but I am reinventing the wheel since the 3D plot facets already exist, i'd just need to display them along the x only or along the y only to have what I'd like. I can display, the 2D version in 3D or the 3D only or both which is convenient.

Where am I stuck?

1. I created \newifs to choose whether i wanted a 3D plot or the set of 2D plot. It's too laborious to be correct.
2. As a result, how could I pass the argument equivalent to \newif so that the style takes care of the 2D and/or 3D view (and not plot twice the function with 2 distinct styles). It could also handle the granularity of the samples to see more or less 2D curves.
3. Also, as you can see in the tikzset in comment, 2D/.style 3D/.style generate multiple errors.
4. No problem to "tranch" based on y but \ifTranchX to try along the x is not working

Here is MWE

\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{tikz}
\pgfplotsset{colormap={whitered}{color(0cm)=(white!20!orange); color(2.5cm)=(orange!75!red)}}


\newif\ifTwoD
\newif\ifThreeD
\newif\ifTranchX
\newif\ifTranchY

\TwoDtrue
\ThreeDtrue

%\TranchXtrue
\TranchYtrue


%\tikzset{
%2D/.style  ={samples y=10,mesh,patch type=line,thick},
%3D/.style  ={surf,opacity=0.2},
%}


    \begin{document}

    \begin{tikzpicture}
        \begin{axis}[
    view={-30}{30},
    axis lines=left,
    axis on top,
    axis line style={black!40},
    xlabel style ={sloped},
    ylabel style ={sloped},
    colormap name=whitered,
    ticklabel style={font=\small},
    samples=51]

\ifTwoD     
\ifTranchX
\addplot3[samples=10,mesh,patch type=line,thick]{exp(-x^2-y^2)}; 
\fi    
\ifTranchY
\addplot3[samples y=10,mesh,patch type=line,thick]{exp(-x^2-y^2)}; 
\fi    
\fi    

\ifThreeD   \addplot3 [surf,opacity=0.2]    {exp(-x^2-y^2)};    \fi
    \end{axis}
\end{tikzpicture} 
\end{document}

NB: On a cultural note, i tried to mimic the color of "papier millimétré" I used to work on in the 80's (in France, but maybe elsewhere ?). papier millimétré

Answer 1

This just collects the comments under the post and does not hack any plot handler. I just thought that instead of writing yet another comment I just collect everything in one post which users can just copy. I think that if the we have ifs for the x and y direction, we won't need another if for 2d. These ifs can be turned into pgf keys in the usual way. The \tikzset has to become a \pgfplotsset to be able to "host" genuine pgfplots styles.

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\pgfplotsset{colormap={whitered}{color(0cm)=(white!20!orange); color(2.5cm)=(orange!75!red)}}


\newif\ifThreeD
\newif\ifTranchX
\newif\ifTranchY

\ThreeDfalse
\TranchXfalse
\TranchYfalse


\pgfplotsset{tranch 3d/.is if=ThreeD,
tranch y/.is if=TranchY,tranch x/.is if=TranchX,
2D/.style  ={samples y=10,mesh,patch type=line,thick},
3D/.style  ={surf,opacity=0.2,postaction={draw}},
}


    \begin{document}

    \begin{tikzpicture}
        \begin{axis}[tranch 3d,tranch x,
    view={-30}{30},
    axis lines=left,
    axis on top,
    axis line style={black!40},
    xlabel style ={sloped},
    ylabel style ={sloped},
    colormap name=whitered,
    ticklabel style={font=\small},
    samples=51]

\ifTranchX
\addplot3[2D] (x,y,{exp(-x^2-y^2)}); 
\fi    
\ifTranchY
\addplot3[2D] (y,x,{exp(-x^2-y^2)}); 
\fi    

\ifThreeD   
\addplot3 [3D]    {exp(-x^2-y^2)};    
\fi
    \end{axis}
\end{tikzpicture} 
\end{document}

If you replace tranch x by tranch y you get

and so on and so forth.