我想要绘制一个非凸集，如下图所示，并且我喜欢从我的 MWE 开始：
\documentclass[12pt,a4paper]{book}
\usepackage{tikz}
\usetikzlibrary{calc, shadings}
\usetikzlibrary{positioning,arrows.meta}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
extended line/.style={shorten >=-#1,shorten <=-#1},
extended line/.default=1cm]
\coordinate (A) at (0,2);
\coordinate (B) at (4.5,0);
\draw (A)--(B) node[anchor=north west] {\small $p'x=\alpha$} coordinate[midway] (M) coordinate[pos=0.85](k);
\draw[-latex] (M) node[dot=above left:$x_{0}$] at (M) {} --($(M)!2cm!90:(B)$) node[anchor=north west]{$p$};
\end{tikzpicture}
\end{document}
也许类似的东西可能会有用，但我不知道这种语法是如何工作的（这是来自>子图中 TikZ 图片的对齐）
\draw[fill=gray!30] (0,0) to [out=140,in=90] (-1,-1) node[anchor=south west]{$A$}
to [out=-90,in=240] (0.8,-0.6)
to [out=60,in=-60] (1.2,1.2)
to [out=120,in=90] (0.3,0.7)
to [out=-90,in=20] (0.3,0)
to [out=200,in=-40] (0,0);
\draw (-0.5,-0.5) -- (0.7,0.7);
\fill (-0.5,-0.5) circle[radius=1.5pt];
\fill (0.7,0.7) circle[radius=1.5pt];
答案1
\documentclass[12pt,a4paper]{book}
\usepackage{tikz}
\usetikzlibrary{calc, shadings}
\usetikzlibrary{positioning,arrows.meta}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
extended line/.style={shorten >=-#1,shorten <=-#1},
extended line/.default=1cm]
\coordinate (A) at (0,2);
\coordinate (B) at (4.5,0);
\draw (A)--(B) node[anchor=north west] {\small $p'x=\alpha$} coordinate[midway] (M) coordinate[pos=0.85](k);
\draw[-latex] (M) node[dot=above left:$x_{0}$] at (M) {} --($(M)!2cm!90:(B)$) node[anchor=north west]{$p$};
\pgfmathsetmacro{\myslope}{atan2(2,-4.5)}
\draw[fill=gray!30] (M) to[out=\myslope,in=0] ++ (-2,0.5) to[out=180,in=90] ++ (-1,-0.5)
to[out=-90,in=90] ++ (2,-2) to[out=-90,in=90] ++ (-3,-1)
to[out=-90,in=180] ++(4,-1) to[out=0,in=\myslope+180] cycle;
\end{tikzpicture}
\end{document}
