如何在任意路径上排列自动机的状态？

Question

我需要在圆形路径上定位自动机的某些状态，使用右、上、左、左上和其他典型的相对替换选项来定位既不容易也不精确。

有没有办法引入一条任意路径来定位状态，而不是典型的网格状结构？...

以下是一个示例：

\documentclass[letter, 11pt]{article}
\usepackage{tikz}
\usetikzlibrary{automata, positioning}

\begin{document}

\begin{center}
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto] 
   \node[state,initial,accepting, initial where=above] (s_00)   {$s_{00}$}; 
   \node[state] (s_23) [above = of s_00]  {$s_{23}$};
   \node[state,accepting] (s_03) [left = of s_23]  {$s_{03}$};
   \node[state,accepting] (s_02) [above = of s_03]  {$s_{02}$};
   \node[state] (s_10) [right = of s_00]  {$s_{10}$}; 
   \node[state] (s_22) [left = of s_00]  {$s_{22}$}; 
   \node[state] (s_13) [left of = s_22]  {$s_{13}$};
   \node[state,accepting] (s_01) [left of = s_13]  {$s_{01}$}; 
   \node[state] (s_14)  [below of = s_01] {$s_{14}$};
   \node[state,accepting] (s_04) [below of = s_14]  {$s_{04}$};
   \node[state,accepting] (s_11)  [below of = s_04] {$s_{11}$}; 
   \node[state] (s_20)  [below = of s_22] {$s_{20}$};
   \node[state,accepting] (s_21) [below of = s_20]  {$s_{21}$}; 
   \node[state] (s_12) [below of = s_21]  {$s_{12}$}; 
   \node[state] (s_24) [below of = s_13]  {$s_{24}$};

   \path[->] 
    (s_00) edge [out=340, in=270] node {$a$} (s_11)
           edge node {$b$} (s_22)
    (s_01) edge node {$a$} (s_14)
           edge node {$b$} (s_24)
    (s_02) edge [in=180, out=180, swap] node {$a$} (s_14)
           edge node {$b$} (s_23)
    (s_03) edge [out=180, in=180, swap] node {$a$} (s_11)
           edge node {$b$} (s_22)
    (s_04) edge node {$a$} (s_14)
           edge node {$b$} (s_24)
    (s_10) edge node {$a$} (s_21)
           edge [bend right, swap] node {$b$} (s_02)
    (s_11) edge node {$a$} (s_24)
           edge node {$b$} (s_04)
    (s_12) edge node {$a$} (s_24)
           edge [out=0, in=90] node {$b$} (s_03)
    (s_13) edge [out=0, in=0] node {$a$} (s_21)
           edge node {$b$} (s_01)
    (s_14) edge node {$a$} (s_24)
           edge node {$b$} (s_04)
    (s_20) edge node {$a$} (s_24)
           edge node {$b$} (s_22)
    (s_21) edge node {$a, b$} (s_24)
    (s_22) edge node {$a$} (s_24)
           edge node {$b$} (s_23)
    (s_23) edge [in=70, out=0] node {$a$} (s_21)
           edge node {$b$} (s_22)
    (s_24) edge [loop above] node {$a, b$} ();
    \end{tikzpicture}
\end{center}
\end{document}

我将把 s_24 放在中间，并在它周围排列一些其他状态（例如 s_11、s_04、s_14、s_01、s_22、s_20、s_21、s_12），形成一个圆形（或通常是任意形状）。

当前阵型如下：

Answer 1

\documentclass[tikz,border=2mm]{standalone}

\usetikzlibrary{automata, positioning, calc}

\begin{document}

\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto] 
   \node[state,initial,accepting, initial where=above] (s_00)   {$s_{00}$}; 
   \foreach \i [count=\ni] in {0,30,60,...,330}
        \node[state] (s_\ni) [above right = {2*sin(\i)} and {2*(cos(\i)} of s_00]  {$s_{\ni}$};
\end{tikzpicture}
\end{document}