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复杂图表中的箭头交叉

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复杂图表中的箭头交叉

在此处输入图片描述我使用 tikzpicture 绘制了一个图表，但其中的箭头相互交叉。如何保持每个级别的水平箭头完整并在交叉点处断开其他箭头？

这是我的代码：

%\documentclass[reqno]{amsart}
\documentclass[border=5mm]{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm,amsxtra}
\usepackage{cite}
\usepackage{enumerate}
\usepackage[mathscr]{eucal}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{tikz-cd}
\usepackage{tkz-graph}
\usepackage{tkz-berge}
\usetikzlibrary{positioning,arrows,shapes.geometric,trees,matrix}
\usepackage{graphicx}
\usepackage{mathtools}
\usetikzlibrary{positioning}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{caption}



\begin{document}






\begin{tikzpicture}
  \matrix (m) [matrix of math nodes, row sep=1.6cm,
    column sep=0.4cm]{
    &&Level(1,3)&&&&\\
     &Level(2,2)&Level(2,3)&& Level(2,5)&&Level(2,7)\\
     &&Level(3,3)&& Level(3,5)&&Level(3,7)\\
      Level(4,1)&Level(4,2)&& Level(4,4)&&Level(4,6)&  \\
      &Level(5,2)&& Level(5,4)&&Level(5,6)& \\
       Level(6,1)&& Level(6,3)&& Level(6,5)&&\\
        Level(7,1) && Level(7,3)&& Level(7,5)&&\\};
  \path[-stealth]
(m-7-1) edge (m-7-3) edge (m-6-1)

(m-7-3) edge (m-7-5) 
        edge (m-6-3)

(m-7-5) edge (m-6-5) 
        edge (m-5-6)

(m-6-1) edge (m-6-3) 
        edge (m-4-1)

(m-6-3) edge (m-6-5) 
        edge (m-4-4)

(m-6-5) edge (m-4-6)
(m-5-2) edge (m-5-4) 
        edge (m-4-2)
        edge (m-3-3)

(m-5-4) edge (m-4-4) 
        edge (m-5-6)
        edge (m-3-5)
(m-5-6) edge (m-3-7)
(m-4-2) edge (m-4-4) 
        edge (m-2-2) 
        edge (m-2-3)

(m-4-4) edge (m-4-6) 
        edge (m-2-5)

(m-3-3) edge (m-2-3) 
        edge (m-3-5)

 (m-3-5) edge (m-3-7)
 (m-2-2) edge (m-1-3)
 (m-2-3) edge (m-1-3)
 (m-2-5) edge (m-2-7)
 ;

\path[>=stealth,-,thick]
(m-7-1) edge [double, minimum width=3cm] (m-5-2)
(m-6-1) edge [double, minimum width=3cm] (m-4-2)
(m-5-6) edge [double, minimum width=3cm] (m-4-6)
(m-4-1) edge [double, minimum width=3cm] (m-2-2)
(m-4-6) edge [double, minimum width=3cm] (m-2-7)
(m-3-5) edge [double, minimum width=3cm] (m-2-5)
(m-3-7) edge [double, minimum width=3cm] (m-2-7)
(m-2-3) edge [double, minimum width=3cm] (m-2-5)
;
\end{tikzpicture}


\end{document}

答案1

标准技巧是在下面画一条粗白线，可以使用 来实现preaction。此答案带有样式on top，可以像 一样使用(m-6-5) edge[on top] (m-4-6)。您需要最后绘制最顶部的连接。目前，白线的默认线宽为，4pt但您可以根据需要进行调整。

\documentclass[border=5mm]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}[on top/.style={preaction={draw=white,-,line width=#1}},
on top/.default=4pt]
  \matrix (m) [matrix of math nodes, row sep=1.6cm,
    column sep=0.4cm]{
    &&Level(1,3)&&&&\\
     &Level(2,2)&Level(2,3)&& Level(2,5)&&Level(2,7)\\
     &&Level(3,3)&& Level(3,5)&&Level(3,7)\\
      Level(4,1)&Level(4,2)&& Level(4,4)&&Level(4,6)&  \\
      &Level(5,2)&& Level(5,4)&&Level(5,6)& \\
       Level(6,1)&& Level(6,3)&& Level(6,5)&&\\
        Level(7,1) && Level(7,3)&& Level(7,5)&&\\};
  \path[-stealth]
(m-7-1) edge (m-7-3) edge (m-6-1)

(m-7-3) edge (m-7-5) 
        edge (m-6-3)

(m-7-5) edge (m-6-5) 
        edge (m-5-6)

(m-6-1) edge (m-4-1)

(m-6-3) edge (m-6-5) 

(m-5-4) edge (m-4-4) 

(m-5-2) edge (m-5-4) 
        edge (m-4-2)
        edge (m-3-3)

(m-5-4)   edge (m-5-6)
        edge (m-3-5)
(m-5-6) edge (m-3-7)
(m-4-2)  edge (m-2-2) 
        edge (m-2-3)



(m-3-3) edge (m-2-3) 
        edge (m-3-5)

 (m-3-5) edge (m-3-7)
 (m-2-2) edge (m-1-3)
 (m-2-3) edge (m-1-3)
 (m-2-5) edge (m-2-7)
(m-4-2) edge[on top] (m-4-4) 
(m-4-4) edge[on top] (m-4-6) 
(m-6-5) edge[on top] (m-4-6)
(m-4-4) edge[on top] (m-2-5)
(m-6-3) edge[on top] (m-4-4)
 ;

\path[>=stealth,-,thick]
(m-7-1) edge [double] (m-5-2)
(m-6-1) edge [double] (m-4-2)
(m-5-6) edge [double] (m-4-6)
(m-4-1) edge [double] (m-2-2)
(m-3-5) edge [double] (m-2-5)
(m-3-7) edge [double] (m-2-7)
(m-2-3) edge [double] (m-2-5)
(m-4-6) edge [double,on top=5pt] (m-2-7)
;
\path[-stealth] (m-6-1) edge[on top] (m-6-3) ;
\end{tikzpicture}
\end{document}

在此处输入图片描述

@egreg 称此代码“尴尬”。然而，在我看来，最多余的事情是必须手动添加条目的位置（但我不喜欢使用“尴尬”这样的词）。无论如何，这可以像定义样式一样容易地实现

level/.style={
execute at begin node={\text{Level}(\the\pgfmatrixcurrentrow,\the\pgfmatrixcurrentcolumn)}
}

它会用到以下代码中，其中还包含一些绘制箭头的循环。

\documentclass[border=5mm]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}[on top/.style={preaction={draw=white,-,line width=#1}},
on top/.default=4pt,level/.style={
execute at begin node={\text{Level}(\the\pgfmatrixcurrentrow,\the\pgfmatrixcurrentcolumn)}
}]
  \matrix (m) [matrix of math nodes,nodes=level,row sep=1.6cm,
    column sep=0.4cm]{
    &&{}&&&&\\
     &{}&{}&& {}&&{}\\
     &&{}&& {}&&{}\\
      {}&{}&& {}&&{}&  \\
      &{}&& {}&&{}& \\
       {}&& {}&& {}&&\\
        {} && {}&& {}&&\\};
\path[-stealth] 
 (m-6-1) edge (m-4-1) (m-4-2) edge (m-2-2) (m-2-3) edge (m-1-3)
 (m-4-2) edge (m-2-3) (m-5-2) edge (m-3-3) 
 (m-5-4) edge (m-3-5) (m-7-5) edge (m-5-6) (m-5-6) edge (m-3-7)
 (m-2-2) edge (m-1-3);
\path[-stealth,every edge/.append style={on top}]  
foreach \Y [count=\Z] in {3,5,7}{ 
  foreach \X in {1,3,5}
 {(m-\Y-\the\numexpr\X+3-\Z\relax) edge (m-\the\numexpr\Y-1\relax-\the\numexpr\X+3-\Z\relax)
 \ifnum\X<5
 (m-\Y-\the\numexpr\X+3-\Z\relax) edge (m-\Y-\the\numexpr\X+5-\Z\relax)
 \ifnum\the\numexpr\Y*10+\X=31
 \else
 (m-\the\numexpr\Y-1\relax-\the\numexpr\X+3-\Z\relax) edge (m-\the\numexpr\Y-1\relax-\the\numexpr\X+5-\Z\relax)
 \fi
 \fi
 }} (m-4-4) edge (m-2-5) (m-6-3) edge (m-4-4);
 \path[thick,every edge/.append style={double,on top=5pt}] 
  (m-4-1) edge (m-2-2) (m-6-1) edge (m-4-2) (m-7-1) edge (m-5-2)
  (m-2-3) edge (m-2-5) (m-2-7) edge (m-3-7)
  (m-2-7) edge (m-4-6) (m-4-6) edge (m-6-5);
\path[-stealth,every edge/.append style={on top}]  (m-6-1) edge (m-6-3); 
\end{tikzpicture}
\end{document}

这些信息，连同这个答案，可以简化 egreg 的答案并纠正那里的箭头（以便有一个 3D 印象）。

\documentclass{article}
\usepackage{geometry}
\usepackage{amsmath}
\usepackage{tikz-cd}
\usetikzlibrary{backgrounds}

\newcommand{\level}{\text{level}(\the\pgfmatrixcurrentrow,\the\pgfmatrixcurrentcolumn)}

\begin{document}

\begin{tikzcd}[column sep=1.5em,row sep=large,arrows={crossing over},
execute at end picture={
\begin{scope}[on background layer]
 \path[->] (\tikzcdmatrixname-6-2) edge (\tikzcdmatrixname-6-4)
 (\tikzcdmatrixname-6-4) edge (\tikzcdmatrixname-6-6)
 (\tikzcdmatrixname-4-5) edge (\tikzcdmatrixname-4-7);
\end{scope}}]
&&
\level
\\ \\
&
\level \arrow[uur] &
\level \arrow[uu] \arrow[rr,thick,equals] &&
\level \arrow[rr] \arrow[ddl,leftarrow] &&
\level \arrow[ddl,thick,equals]
\\
&&
\level \arrow[u] \arrow[ddl,leftarrow] &&
\level \arrow[u,thick,equals]  \arrow[ddl,leftarrow] &&
\level \arrow[u,thick,equals]
\\
\level \arrow[uur,thick,equals] &
\level \arrow[uu] \arrow[rr] \arrow[uur] &&
\level \arrow[rr] \arrow[ddl,leftarrow] &&
\level \arrow[ddl,leftarrow]
\\
&
\level \arrow[u] \arrow[ddl,leftarrow] &&
\level \arrow[u]  &&
\level \arrow[u,thick,equals] \arrow[uur]
\\
\level \arrow[uu] \arrow[uur,thick,equals] \arrow[rr] &&
\level \arrow[rr] &&
\level
\\
\level \arrow[u] \arrow[rr] &&
\level \arrow[u] \arrow[rr] &&
\level \arrow[u] \arrow[uur]
\end{tikzcd}
\end{document}

在此处输入图片描述

答案2

对于crossing over稍后绘制的箭头，擦除与其相交的部分箭头。

\documentclass{article}
\usepackage{geometry}
\usepackage{amsmath}

\usepackage{tikz-cd}

\newcommand{\level}{\mathrm{Level}}

\begin{document}

\begin{tikzcd}[column sep=1.5em,row sep=large,arrows={crossing over}]
&&
\level(1,3)
\\ \\
&
\level(2,2) \arrow[uur] &
\level(2,3) \arrow[uu] \arrow[rr,thick,equals] &&
\level(2,5) \arrow[rr] \arrow[ddl,leftarrow] &&
\level(2,7) \arrow[ddl,thick,equals]
\\
&&
\level(3,3) \arrow[u] \arrow[rr] \arrow[ddl,leftarrow] &&
\level(3,5) \arrow[u,thick,equals] \arrow[rr] \arrow[ddl,leftarrow] &&
\level(3,7) \arrow[u,thick,equals]
\\
\level(4,1) \arrow[uur,thick,equals] &
\level(4,2) \arrow[uu] \arrow[rr] \arrow[uur] &&
\level(4,4) \arrow[rr] \arrow[ddl,leftarrow] &&
\level(4,6) \arrow[ddl,leftarrow]
\\
&
\level(5,2) \arrow[u] \arrow[rr] \arrow[ddl,leftarrow] &&
\level(5,4) \arrow[u] \arrow[rr] &&
\level(5,6) \arrow[u,thick,equals] \arrow[uur]
\\
\level(6,1) \arrow[uu] \arrow[uur,thick,equals] \arrow[rr] &&
\level(6,3) \arrow[rr] &&
\level(6,5)
\\
\level(7,1) \arrow[u] \arrow[rr] &&
\level(7,3) \arrow[u] \arrow[rr] &&
\level(7,5) \arrow[u] \arrow[uur]
\end{tikzcd}

\end{document}

在此处输入图片描述

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