融合不同的路径

Question

假设我们有四个节点 a、b、c 和 d。例如：

\coordinate [label=left:a]  (a) at (0,4);
\coordinate [label=right:b] (b) at (4,4);
\coordinate [label=left:c]  (c) at (0,0);
\coordinate [label=right:d] (d) at (4,0);

让我们在 {(a,b), (a,c), (c,d), (d,b), (b,a)} 中的每对之间绘制一些任意路径。例如：

\draw [red]    (a) to [bend left=30]                   (c);
\draw [blue]   (b) to [out=45, in= -50]                (a);
\draw [orange] (c) to [controls=+(45:6) and +(170:6)]  (d);
\draw [green!60!black,decorate,decoration={snake,pre length=1pt}] (d) -- (b);

据我所知

\path (a) -- (c) -- (d) -- (b) -- cycle;

被视为一条路径，因此我们可以填充此路径内的区域；但是在上面的例子中，我们有四条路径，因此填充区域对于 tikZ 来说是没有意义的。

我的问题：是否可以融合所有路径（例如）以创建一条可填充路径，例如\fill [blue!10] (a) -- (c) -- (d) -- (b) -- cycle;或其他路径？换句话说，我想孵化表面 S。

全部代码：

\documentclass[tikz, border=1cm]{standalone}

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\mathversion{bold}

\begin{document}

\begin{tikzpicture}
\coordinate [label=left:a]  (a) at (0,4);
\coordinate [label=right:b] (b) at (4,4);
\coordinate [label=left:c]  (c) at (0,0);
\coordinate [label=right:d] (d) at (4,0);

\foreach \p in {a,b,c,d}{
\fill[red] (\p) circle (2pt);}

\draw [red]    (a) to [bend left=30]                   (c);
\draw [blue]   (b) to [out=45, in= -50]                (a);
\draw [orange] (c) to [controls=+(45:6) and +(170:6)]  (d);
\draw [green!60!black,decorate,decoration={snake,pre length=1pt}] (d) -- (b);
\node at (2,2.5) {$S$};

\end{tikzpicture}

\end{document}

更清楚的是，我在创建（易碎的）tcolorbox时遇到了这个问题

我想填充空白表面 S，但是有四条路径我无法做到这一点。

Answer 1

当然可以。您不能用不同的颜色绘制路径，但您当然可以组合要填充的路径，然后明确地单独绘制彩色路径，或者通过edges 绘制彩色路径。

\documentclass[tikz, border=1cm]{standalone}

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\mathversion{bold}

\begin{document}

\begin{tikzpicture}
\coordinate [label=left:a]  (a) at (0,4);
\coordinate [label=right:b] (b) at (4,4);
\coordinate [label=left:c]  (c) at (0,0);
\coordinate [label=right:d] (d) at (4,0);

\foreach \p in {a,b,c,d}{
\fill[red] (\p) circle (2pt);}
\path[decoration={snake,pre length=1pt},fill=blue!20]
 (a) to [bend left=30]                   (c)
 to [controls=+(45:6) and +(170:6)](d)
 decorate {  -- (b)}  
 to [out=45, in= -50]   cycle;
\draw [red]    (a) to [bend left=30]                   (c);
\draw [blue]   (b) to [out=45, in= -50]                (a);
\draw [orange] (c) to [controls=+(45:6) and +(170:6)]  (d);
\draw [green!60!black,decorate,decoration={snake,pre length=1pt}] (d) -- (b);
\node at (2,2.5) {$S$};
\end{tikzpicture}

\end{document}

并添加even odd rule，即

\path[decoration={snake,pre length=1pt},fill=blue!20,even odd rule]
 (a) to [bend left=30]                   (c)
 to [controls=+(45:6) and +(170:6)](d)
 decorate {  -- (b)}  
 to [out=45, in= -50]   cycle;

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