表面上的一个点

Question

我怎样才能在 tikz 中做出以下动作？

Answer 1

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16,width=14cm}
\begin{document}
\begin{tikzpicture}[declare function={f(\x,\y,\z)=30+20*exp(-(\x*\x+\y*\y)/\z);}]
\begin{axis}[axis lines=middle,
    xmin=0,xmax=12.5,ymin=0,ymax=12.5,zmin=0,zmax=50,smooth,
    view={115}{20},
    xtick=\empty,ytick=\empty,ztick=\empty,
    xlabel=$x$,ylabel=$y$,zlabel=$z$]
   \draw[dashed] (4.5,0,0)node[above left]{$x_0$} -- (4.5,4.5,0)
     -- (0,4.5,0) node[above right]{$y_0$}
     (4.5,4.5,0) -- (4.5,4.5,{f(4.5-4,4.5-4,8)});
   \addplot3[surf,fill=cyan,fill opacity=0.4,domain=0:8,domain
   y=0:8,samples=11,samples y=11,point meta=1] 
   {f(x-4,y-4,8)};
   \node[circle,inner sep=2pt,fill,
    label=above right:{$(x_0,y_0,z_0)$}] at (4.5,4.5,{f(4.5-4,4.5-4,8)}){};
\end{axis}
\end{tikzpicture}
\end{document}