间隙平面图中的套管边（交叉点、重绘路径）

Question

为了说明我关于 k 间隙平面图的论文，我想找到一种优雅且可参数化的方法来绘制带有套管边的图形（以清楚地表明交点带电于哪条边）。

具有类似图纸的参考文章

到目前为止，我完成的工作相当混乱，我希望可以简化。我使用 tikzpackage“intersections”在每个交叉点顶部放置一个白色圆盘，并重复应该通过交叉点而不会出现间隙的边缘。“intersections”允许命名所涉及的路径，但我找不到如何命名让命名的路径再次被绘制，而无需重新定义它们（见下面的代码和图像）。

通过“交点”计算交叉点并通过“pgfonlayer”环境将边缘放在不同层上以控制绘制顺序的组合不起作用。也许这个包与不同层上的边缘不兼容。

我很感激任何相关的建议:)

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}

\tikzstyle{vertex}=[circle, draw=black, fill=black, radius = 1mm,
scale = 0.8,anchor=center]

\tikzstyle{crossing}=[circle, radius=0.5pt, fill= white]

\tikzstyle{cased}=[draw=white,line width = 12pt,
double=black,very thick, distance = 2pt]

\begin{tikzpicture}[every node/.style={vertex}]
    \pgfmathtruncatemacro{\n}{4}
    \foreach \pos
    [evaluate=\pos as \angle using (360/\n/2)+\pos*360/\n)]
    in {2,...,\n}
    {%inner  vertices
        \path node (i\pos) at (\angle:2) {};% 
    };
    \foreach \pos
    [evaluate=\pos as \angle using (360/\n/2)+\pos*360/\n)]
    in {1,2,...,\n}
    {%outer vertices
        \node (o\pos) at (\angle:6) {};
    };       

    %bent outer edges
    \pgfmathtruncatemacro{\distA}{10}
    \path[name path=e_o1_o3] (o1.center) .. controls 
    +(30:\distA) and +(60:\distA) .. (o3.center);
    \draw[name path=e_o2_o4] (o2.center) .. controls 
    +(120:\distA) and +(150:\distA) .. (o4.center);

    %straight edges between inner and outer
    %o4.center
    \draw[name path=e_o4_i4]  (o4.center) -- (i4.center);
    %o2.center
    \draw[name path=e_o2_i2]  (o2.center) -- (i2.center);
    %o3.center
    \draw[name path=e_o3_i3]  (o3.center) -- (i3.center);

    %bent edges between inner and outer
    %offset=1
    \pgfmathtruncatemacro{\distI}{2}
    %o1.center
    \draw[name path=e_o1_i4]  (o1.center) .. controls 
    +(-20:\distI) and +(140:\distI) .. (i4.center);
    \path[name path=e_o1_i2]  (o1.center) .. controls 
    +(-70:\distI) and +(130:\distI) .. (i2.center);
    %o4.center
    \draw[name path=e_o4_i3]  (o4.center) .. controls 
    +(-110:\distI) and +(50:\distI) .. (i3.center);
    %o2.center
    \path[name path=e_o2_i3]  (o2.center) .. controls 
    +(20:\distI) and +(-140:\distI) .. (i3.center);
    %o3.center
    \draw[name path=e_o3_i2]  (o3.center) .. controls 
    +(160:\distI) and +(-40:\distI) .. (i2.center);
    \path[name path=e_o3_i4]  (o3.center) .. controls 
    +(110:\distI) and +(-50:\distI) .. (i4.center);

    %bent edges between inner and outer
    %offset=2 (opposite)
    \pgfmathsetmacro{\distG}{5.5}
    %o1.center
    \path[name path=e_o1_i3]  (o1.center) .. controls 
    +(-10:\distG) and +(70:\distG) .. (i3.center);
    %o4.center
    \path[name path=e_o4_i2]  (o4.center) .. controls 
    +(-100:\distG) and +(-20:\distG) .. (i2.center);
    %o2.center
    \draw[name path=e_o2_i4]  (o2.center) .. controls 
    +(80:\distG) and +(160:\distG) .. (i4.center);

    \foreach \pos
    [remember=\pos as \last (initially \n)]
    in {1,2,...,\n}
    {%straight outer edges
        \draw[name path=e_o\pos_o\last] (o\pos.center) -- 
        (o\last.center);
    };
    \foreach \pos
    [remember=\pos as \last (initially \n)]
    in {2,...,\n}
    {%straight inner edges
        \draw (i\pos.center) -- (i\last.center);
    };  

    %crossings
    \begin{scope}[every node/.style={crossing}]
        %crossing e_o1_o3 and e_o2_o4
        \path [draw,name intersections={of={e_o1_o3 and e_o2_o4}}]
        (intersection-1) node (a) {} ;
        %repeat edge drawing
        \draw[name path=e_o1_o3] (o1.center) .. controls 
        +(30:\distA) and +(60:\distA) .. (o3.center);
        %crossing e_o1_i2 and e_o2_i4
        \path [draw,name intersections={of={e_o1_i2 and e_o2_i4}}]
        (intersection-1) node (b) {} ;
        %repeat edge drawing
        \draw[name path=e_o1_i2]  (o1.center) .. controls 
        +(-70:\distI) and +(130:\distI) .. (i2.center);
        %crossing e_o1_i3 and e_o4_i4
        \path [draw,name intersections={of={e_o1_i3 and e_o4_i4}}]
        (intersection-1) node (d) {} ;
        %repeat edge drawing
        \draw[name path=e_o1_i3]  (o1.center) .. controls 
        +(-10:\distG) and +(70:\distG) .. (i3.center);
        %crossing e_o1_i3 and e_o3_i4
        \path [draw,name intersections={of={e_o1_i3 and e_o3_i4}}]
        (intersection-1) node (c) {} ;
        %crossing e_o2_i3 and e_o3_i2
        \path [draw,name intersections={of={e_o2_i3 and e_o3_i2}}]
        (intersection-1) node (e) {};
        %repeat edge drawing
        \draw[name path=e_o2_i3]  (o2.center) .. controls 
        +(20:\distI) and +(-140:\distI) .. (i3.center) ;
        %crossing e_o2_i3 and e_o4_i2
        \path [draw,name intersections={of={e_o2_i3 and e_o4_i2}}]
        (intersection-1) node (f) {} ;
        %crossing e_o3_i4 and e_o4_i3
        \path [draw,name intersections={of={e_o3_i4 and e_o4_i3}}]
        (intersection-1) node (i) {} ;
        %repeat edge drawing
        \draw[name path=e_o3_i4]  (o3.center) .. controls 
        +(110:\distI) and +(-50:\distI) .. (i4.center);
        %crossing e_o3_i4 and e_o4_i2
        \path [draw,name intersections={of={e_o3_i4 and e_o4_i2}}]
        (intersection-1) node (g) {} ;
        %crossing e_o3_i3 and e_o4_i2
        \path [draw,name intersections={of={e_o3_i3 and e_o4_i2}}] 
        (intersection-1) node (h) {} ;
        %repeat edge drawing
        \draw[name path=e_o4_i2]  (o4.center) .. controls 
        +(-100:\distG) and +(-20:\distG) .. (i2.center);
    \end{scope}
\end{tikzpicture}
\end{document}

Answer 1

欢迎！您可以使用这个非常好的knots库。不用自己绘制所有这些路径、查找交叉点、重新绘制它们，让knots我们来帮我们做这些。基本上，只需将所有\draw命令替换为\strand，就可以了。

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{knots,%bbox
}
\begin{document}

\tikzset{vertex/.style={circle, draw=black, fill=black, radius = 1mm,
scale = 0.8,anchor=center}}

\begin{tikzpicture}[every node/.style={vertex},%bezier bounding box
    ]
    \begin{knot}[%draft mode=crossings,
    knot gap=9,%<- controls the gap size
    flip crossing/.list={1,...,9}]
    \pgfmathtruncatemacro{\n}{4}
    \foreach \pos
    [evaluate=\pos as \angle using (360/\n/2)+\pos*360/\n)]
    in {2,...,\n}
    {%inner  vertices
        \path node (i\pos) at (\angle:2) {};% 
    };
    \foreach \pos
    [evaluate=\pos as \angle using (360/\n/2)+\pos*360/\n)]
    in {1,2,...,\n}
    {%outer vertices
        \node (o\pos) at (\angle:6) {};
    };       

    %bent outer edges
    \pgfmathtruncatemacro{\distA}{10}
    \strand (o2.center) .. controls 
        +(120:\distA) and +(150:\distA) .. (o4.center);

    %straight edges between inner and outer
    %o4.center
    \strand  (o4.center) -- (i4.center);
    %o2.center
    \strand  (o2.center) -- (i2.center);
    %o3.center
    \strand  (o3.center) -- (i3.center);

    %bent edges between inner and outer
    %offset=1
    \pgfmathtruncatemacro{\distI}{2}
    %o1.center
    \strand  (o1.center) .. controls +(-20:\distI) and +(140:\distI) .. (i4.center);
    %o4.center
    \strand  (o4.center) .. controls +(-110:\distI) and +(50:\distI) .. (i3.center);
    %o2.center
    %o3.center
    \strand  (o3.center) .. controls +(160:\distI) and +(-40:\distI) .. (i2.center);
    %bent edges between inner and outer
    %offset=2 (opposite)
    \pgfmathsetmacro{\distG}{5.5}
    %o1.center
    %o4.center
    %o2.center
    \strand  (o2.center) .. controls 
    +(80:\distG) and +(160:\distG) .. (i4.center);

    \foreach \pos
    [remember=\pos as \last (initially \n)]
    in {1,2,...,\n}
    {%straight outer edges
        \draw (o\pos.center) --  (o\last.center);
    };
    \foreach \pos
    [remember=\pos as \last (initially \n)]
    in {2,...,\n}
    {%straight inner edges
        \draw (i\pos.center) -- (i\last.center);
    };  
    %crossings
    \strand (o1) .. controls +(30:\distA) and +(60:\distA) .. (o3);
    \strand (o1) .. controls +(-70:\distI) and +(130:\distI) .. (i2);
    \strand (o1) .. controls +(-10:\distG) and +(70:\distG) .. (i3);
    \strand (o2) .. controls +(20:\distI) and +(-140:\distI) .. (i3) ;
    \strand (o3) .. controls +(110:\distI) and +(-50:\distI) .. (i4);
    \strand (o4) .. controls +(-100:\distG) and +(-20:\distG) .. (i2);
    \end{knot}  
\end{tikzpicture}
\end{document}

请注意

1. 你可以翻转路口，如图所示。我希望能够重现你的惯例，但如果没有，你随时可以取消翻转路口；
2. draft mode=crossings,让您找出哪个路口属于哪个数字；
3. \tikzstyle已被弃用；
4. 如果你使用该bbox库，你甚至可以自动修复边界框。截至目前，你需要下载这个文件并将tikzlibrarybbox.code.tex其放在 LaTeX 可以找到的地方，例如与您正在编译的文件相同的目录。如果我理解正确的话，这个库将来可能会成为官方库的一部分。不幸的是，我甚至无法理解最基本的 GitHub 命令和消息，所以我不确定。）