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解释

@Gonzalo Medina 提供了一个解决方案均等划分多边形线段

用正方形尝试了同样的原理。没有用。参见下面的代码。tikzMiddleLeft BottomSide中有关键字吗？


\begin{tikzpicture}
[scale=1.5]

\draw   (0,0) coordinate (a)  --  
        (6,0) coordinate (b)  --  
        (6,6.0) coordinate (c)  --  
        (0,6) coordinate (d)  -- cycle;

\draw   (1.0,1.0) coordinate (a')  --  
    (5,1.0) coordinate (b')  --  
    (5,5) coordinate (c')  -- 
    (1.0,5) coordinate (d')  -- cycle;

\draw (a) -- (a')   (b) -- (b') (c) -- (c') (d) -- (d');

(a) -- coordinate (MiddleLeft) (a')
(b) -- coordinate (MiddleRight) (b')
\DivideSide{5}{right}{left}{BottomSide}
% Labels for the bottom side
\node at
  ( $ (MiddleRight)!0.5!(BottomSide1) $ )
  {h};  
\node at
  ( $ (BottomSide1)!0.5!(BottomSide2) $ )
  {i};  
\node at
  ( $ (BottomSide2)!0.5!(BottomSide3) $ )
  {j};  
\node at
  ( $ (BottomSide3)!0.5!(BottomSide4) $ )
  {k};  
\node at
  ( $ (BottomSide4)!0.5!(MiddleLeft) $ )
  {l};  
\end{tikzpicture}

答案1

在此处输入图片描述

代码：

\documentclass[varwidth=100cm,border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,shapes.geometric}

\tikzset{
  myshape/.style 2 args={
    inner sep=0pt,
    regular polygon,
    regular polygon sides=#1,
    minimum size=#2
  }
}

\newcommand\DrawShape[3]{
  \node[draw,myshape={#1}{#2}] (inner) {};
  \node[draw,myshape={#1}{#3}] (outer) {};
  \node[myshape={#1}{0.5*#3+0.5*#2}] (in) {};
  \node[myshape={#1}{#3+40pt}] (outside) {};
  \node[myshape={#1}{#2-40pt}] (inside) {};
  \foreach \Value in {1,...,#1}
  {
    \draw  (inner.corner \Value) -- (outer.corner \Value);
  }  
}

\newcommand\LabelsIn[3]{
  \foreach \Text [count=\Total] in {#1} {}
  \foreach \Value [count=\Num,evaluate=\Value as \Parts using \Value/\Total] in {1,...,\numexpr\Total-1\relax}
  {
    \draw 
      ( $ (inner.corner #2)!\Parts!(inner.corner #3) $ ) -- 
      ( $ (outer.corner #2)!($(inner.corner #2)!\Parts!(inner.corner #3)$)!(outer.corner #3) $ );
  }
  \foreach \Text [count=\Num,evaluate=\Text as \Parts using (\Num/\Total)-1/(2*\Total)] in {#1} 
  {
    \path[]
      ( $ (inner.corner #2)!\Parts!(inner.corner #3) $ ) -- node {\Text}
      ( $ (outer.corner #2)!($(inner.corner #2)!\Parts!(inner.corner #3)$)!(outer.corner #3) $ );
  }
}

\newcommand\LabelsInside[3]{
  \foreach \Text [count=\Total] in {#1} {}
  \foreach \Text [count=\Num,evaluate=\Text as \Parts using (\Num/\Total)-1/(2*\Total)] in {#1} 
  {
    \path[]
      ( $ (inner.corner #2)!\Parts!(inner.corner #3) $ ) -- node[pos=-0.4] {\Text}
      ( $ (outer.corner #2)!($(inner.corner #2)!\Parts!(inner.corner #3)$)!(outer.corner #3) $ );
  }
}

\newcommand\LabelsOutside[3]{
  \foreach \Text [count=\Total] in {#1} {}
  \foreach \Text [count=\Num,evaluate=\Text as \Parts using (\Num/\Total)-1/(2*\Total)] in {#1} 
  {
    \path[]
      ( $ (inner.corner #2)!\Parts!(inner.corner #3) $ ) -- node[pos=1.4] {\Text}
      ( $ (outer.corner #2)!($(inner.corner #2)!\Parts!(inner.corner #3)$)!(outer.corner #3) $ );
  }
}


\begin{document}

\begin{tikzpicture}
\DrawShape{3}{7cm}{10cm}
\LabelsIn{1,2,3,4}{1}{2}
\LabelsInside{A,B,C,D}{1}{2}
\LabelsOutside{a,b,c,d}{1}{2}
\LabelsIn{5,6}{2}{3}
\LabelsInside{E,F}{2}{3}
\LabelsOutside{e,f}{2}{3}
\LabelsIn{7,8,9}{3}{1}
\LabelsInside{G,H,I}{3}{1}
\LabelsOutside{g,h,i}{3}{1}
\end{tikzpicture}\qquad
\begin{tikzpicture}
\DrawShape{4}{8cm}{12cm}
\LabelsIn{A,B,C}{1}{2}
\LabelsInside{1,2,3}{1}{2}
\LabelsOutside{a,b,c}{1}{2}
\LabelsIn{D,E}{2}{3}
\LabelsInside{4,5}{2}{3}
\LabelsOutside{d,e}{2}{3}
\LabelsIn{F,G}{3}{4}
\LabelsInside{6,7}{3}{4}
\LabelsOutside{f,g}{3}{4}
\LabelsIn{H,I,J,K,L}{4}{1}
\LabelsInside{8,9,10,11,\raisebox{-30pt}{12}}{4}{1}
\LabelsOutside{h,i,j,k,l}{4}{1}
\end{tikzpicture}\par\bigskip
\begin{tikzpicture}
\DrawShape{5}{8cm}{12cm}
\LabelsIn{7,8,9}{1}{2}
\LabelsIn{e,f,g,h,i}{2}{3}
\LabelsIn{p,q,r}{3}{4}
\LabelsIn{1,2,3}{4}{5}
\LabelsIn{$\alpha$,$\beta$}{5}{1}
\LabelsOutside{A,B}{5}{1}
\LabelsOutside{M,N,O,P,Q}{2}{3}
\LabelsInside{x,y,z}{1}{2}
\LabelsInside{G,H,I}{3}{4}
\end{tikzpicture}

\end{document}

解释

  • 基本命令是

    \DrawShape{<number of sides>}{<inner length>}{<outer length>}

    例如，

    \begin{tikzpicture}
\DrawShape{3}{7cm}{10cm}
\end{tikzpicture}

    生产

    在此处输入图片描述

    该图形的各个角都会被自动编号1,...,<number of sides>。

  • 要将标签放在您使用的一侧

    \LabelsIn{<list of labels>}{<start corner>}{<end corner>}

    例如，

    \begin{tikzpicture}
\DrawShape{3}{7cm}{10cm}
\LabelsIn{1,2,3,4}{1}{2}
\end{tikzpicture}

    生产

    在此处输入图片描述

  • 命令\LabelsInside和\LabelsOutside具有类似的语法，用于将标签放置在侧面的外部或内部。例如：

    \begin{tikzpicture}
\DrawShape{3}{7cm}{10cm}
\LabelsIn{1,2,3,4}{1}{2}
\LabelsIn{$\alpha$,$\beta$}{2}{3}
\LabelsIn{A,B,C,D}{3}{1}
\LabelsInside{p,q,r,s}{3}{1}
\end{tikzpicture}

    结果是

    在此处输入图片描述

答案2

需要进行一些调整（例如定位），但大部分工作已经完成：

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{calc}
\def\empty{}
\tikzset{pics/divided polygon/.style args={#1#2#3#4}{code={%
\def\N{#1}\def\R{#2}\def\r{#3}\def\Labels{#4}
\begin{scope}[rotate=270-180/\N-360/\N]
\path \foreach \i in {1,...,\N} { (360/\N*\i:\R) coordinate (n-\i-1) };
\path \foreach \i in {1,...,\N} { (360/\N*\i:{\R+\r/cos(180/\N)}) 
  coordinate (n-\i-2) };
\foreach \i in {1,2}
  \draw (n-1-\i) \foreach \j in {2,...,\N}{ -- (n-\j-\i) } -- cycle;
\foreach \l in {1,...,\N} \draw (n-\l-1) -- (n-\l-2);
\end{scope}
\foreach \labels [count=\i, evaluate={\j=int(mod(\i,\N)+1);}] in \Labels{
\foreach \a [count=\nlabels, remember=\nlabels] in \labels{}
\ifnum\nlabels>1
\foreach \k  in {2,...,\nlabels}
  \draw ($(n-\i-1)!{(\k-1)/\nlabels}!(n-\j-1)$) 
    coordinate (@) -- ($(n-\i-2)!(@)!(n-\j-2)$);
\fi
\foreach \l [count=\k] in \labels
\path 
  ($(n-\i-1)!{(\k-.5)/\nlabels}!(n-\j-1)$) 
    coordinate (side-\i-inner label-\k)
  ($(n-\i-2)!(side-\i-inner label-\k)!(n-\j-2)$) 
    coordinate (side-\i-outer label-\k)
  ($(side-\i-inner label-\k)!0.5!(side-\i-outer label-\k)$)
    coordinate (side-\i-label-\k);
\pgfpointadd{\pgfpointanchor{n-\i-1}{center}}%
  {\pgfpointanchor{n-\j-1}{center}}%
\pgfgetlastxy\px\py%
\pgfmathparse{Mod(atan2(\py/2,\px/2),360)}%
\let\sideangle=\pgfmathresult
\pgfmathparse{Mod(\pgfmathresult,180)-90}%
\let\textangle=\pgfmathresult%
\foreach \l [count=\k]  in \labels{
  \tikzset{get labels/.expand once=\l}
  \node [rotate=\textangle, text height=1em, text depth=.5em, 
    anchor=center, every main label/.try] 
    at (side-\i-label-\k) {\mainlabel};
  \node  [rotate=\textangle, text height=1em, text depth=.5em, 
    anchor={(\sideangle < 180) ? 270 : 90}, every outer label/.try] 
      at (side-\i-outer label-\k) {\outerlabel};
  \node  [rotate=\textangle, text height=1em, text depth=.5em, 
    anchor={(\sideangle >= 180) ? 270 : 90}, every inner label/.try]  
      at (side-\i-inner label-\k)  {\innerlabel};
}}}},
get labels/.style={.. get labels=#1///@},
.. get labels/.code args={#1/#2/#3/#4@}{%
  \def\mainlabel{#1}\def\outerlabel{#3}\def\innerlabel{#2}%
},
every outer label/.style={inner sep=0 },
every inner label/.style={inner sep=0 }}
\begin{document}
\begin{tikzpicture}
\pic at (0,0) {divided polygon={3}{2}{0.5}%
  {{a/A/$\alpha$,b//$\beta$,c/C},{d//$\delta$,e//$\epsilon$},{f/F}}};
\pic at (8,0) {divided polygon={4}{2}{0.5}%
    {{a/A, b/B/$\beta$, c},{d,e},{f},{g,h,i,j}}};
\pic at (0,8) {divided polygon={5}{2}{1}%
  {{a/A,b/B,c},{d//$\delta$,e},{f/F},{g//$\gamma$,h,i,j/J},{k}}};
\pic at (8,8) {divided polygon={6}{3}{1}%
  {{a/A/$\alpha$,b,c},{d,e},{f},{g,h,i//$\iota$},{j/J,k/K/$\kappa$},{l}}};  
\end{tikzpicture}
\end{document}

在此处输入图片描述

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