如何绘制在线和重力作用下的带有球的实体树？

Question

我想画一个图的物理模型，每个顶点都有一个球，每条边都有一根绳子。在这个模型中，如果你把一个球举得足够高，其他球也会随之被拉起，受到弦的压力和重力。如下图所示。

然而，使用tikz-qtree，我只能画出一棵普通的树，无法将绳子或重力形象化（而且有点丑）。

因此，我想知道

如何绘制在线和重力作用下的带有球的实体树？

---

我使用的代码tikz-qtree如下。

\documentclass{standalone}
\usepackage{tikz}
\usepackage{tikz-qtree}

\begin{document}

\begin{tikzpicture}
  \node [draw, circle] (r) at (0,0) {$r$};
  \node [draw, circle, blue, very thick] (s) at (2,0) {$s$};
  \node [draw, circle] (t) at (4,0) {$t$};
  \node [draw, circle] (u) at (6,0) {$u$};

  \node [draw, circle] (v) at (0,-2) {$v$};
  \node [draw, circle] (w) at (2,-2) {$w$};
  \node [draw, circle] (x) at (4,-2) {$x$};
  \node [draw, circle] (y) at (6,-2) {$y$};

  \draw (r) to (v);
  \draw (r) to (s);
  \draw (s) to (w);
  \draw (t) to (u);
  \draw (t) to (w);
  \draw (t) to (x);
  \draw (u) to (x);
  \draw (u) to (y);
  \draw (x) to (y);
  \draw (y) to (u);
\end{tikzpicture}

\begin{tikzpicture}[]
  \tikzset{level distance = 36pt, sibling distance = 25pt}
  \tikzset{every node/.style = {draw, circle}}

  \Tree [.\node[blue, very thick](s){$s$}; 
            [.$r$ $v$ ]
            [.\node(w){$w$}; 
                [.\node(t){$t$}; \node(u){$u$}; ] 
                [.\node(x){$x$}; \node(y){$y$}; ]
            ] 
        ]

  % cross edges
  \draw [dashed, thick, red] (t) to [out = -45, in = 225] (x);
  \draw [dashed, thick, red] (u) to [out = -45, in = 225] (y);
  \draw [dotted, thick, purple] (x.-110) to (u);
\end{tikzpicture}

\end{document}

Answer 1

以下是最新 PGF 版本中图形绘制的一些示例。我不太确定定义新边的最佳方法，但至少我使用的方法似乎有效。它需要lualatex：

\documentclass[border=5]{standalone}
\usepackage{tikz}
\usetikzlibrary{topaths,graphs,graphdrawing,decorations}
\usegdlibrary{layered,trees}
\pgfdeclaredecoration{squiggle}{draw}{
\state{draw}[width=\pgfdecoratedpathlength]{
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathcurveto{\pgfpoint{0.25*\pgfdecoratedpathlength}{0.25*\pgfdecoratedpathlength}}%
    {\pgfpoint{0.75*\pgfdecoratedpathlength}{-0.25*\pgfdecoratedpathlength}}%
    {\pgfpoint{\pgfdecoratedpathlength}{0pt}}
}}

\tikzgraphsset{
 edge squiggle/.style={
   new --/.code n args={4}{
    \path [-, every new --/.try]
      (##1\tikzgraphleftanchor)
      edge[##3, decoration=squiggle, decorate] ##4
      (##2\tikzgraphrightanchor);}
  },
  edge loop/.style={
   new --/.code n args={4}{
    \draw [-, every new --/.try]
     (##1)
      edge [out=260, in=280, looseness=3] ##4
       (##2);}
  }
}

\begin{document}
\tikz\graph [nodes={shape=circle, fill=gray!50}, edge squiggle, 
  chain shift=(0:2cm), group shift=(270:2cm)]{
  E -- S -- A;
  D -!- C -- B;
  D -- E; D -- S;
  C -- S; B -- A; 
};

\hskip1cm

\tikz\graph [layered layout, nodes={shape=circle, fill=gray!50},
  level distance=1.5cm] {
  S -- {A -- B, C -- B, E, D};
  {[edge loop] E -- D};
  {[same layer] A, C, D, E};
};
\end{document}