![如何绘制 epsilon-net](https://linux22.com/image/409519/%E5%A6%82%E4%BD%95%E7%BB%98%E5%88%B6%20epsilon-net.png)
答案1
可能像这样吗?
\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[font=\sffamily,pics/hexi/.style={code={
\draw[pic actions]
plot[samples at={0,60,...,300},variable=\x]
(\x:1) -- cycle;}},
declare function={rrnd(\x)=2.2+0.2*rnd+0.5*cos(2*\x);}]
\path[scale=0.6,transform shape] foreach \X
[evaluate=\X as \Ymin using {int( (\X<3 || \X>5) ? 2 + (\X==8) :1 + (\X==4))},
evaluate=\X as \Ymax using {int( (\X==1 || \X>6) ? 4 - (\X==1) :5)}] in {1,...,8} {
foreach \Y in {\Ymin,...,\Ymax} {
\ifodd\X
({\X*(1+cos(60))},{\Y*(2*sin(60))})
\else
({\X*(1+cos(60))},{\Y*(2*sin(60))-sin(60)})
\fi pic{hexi}}};
\pgfmathsetseed{137}
\draw[thick,shift={(4,3)}] plot[smooth cycle,samples at={0,30,...,330}]
(\x:{rrnd(\x)});
\path (4,-0.5) node[below]{Totally bounded};
%
\pgfmathsetseed{137}
\draw[thick,shift={(-4,3)}] plot[smooth cycle,samples at={0,30,...,330}]
(\x:{rrnd(\x)});
\path (-4,-0.5) node[below]{Bounded};
\end{tikzpicture}
\end{document}