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在 tikz-cd 中绘制到节点本身的圆形路径

tag-icon • tag-icon tikz-arrows tikz-cd
在 tikz-cd 中绘制到节点本身的圆形路径

我想在交换图中绘制一个指向自身节点的圆形箭头。到目前为止，我可以实现的效果如下：

在此处输入图片描述

有没有什么方法可以让环看上去更像真正的圆圈？

下面是 MWE。

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}

\begin{tikzcd}[column sep=large]
    C & D
    \arrow["{F}", bend left = 30, from=1-1, to=1-2]
    \arrow["{G}", bend left = 30, from=1-2, to=1-1]
    \arrow[""{name=0, anchor=center, inner sep=0}, "{G} \,\circ\, {F}", from=1-1, to=1-1, out=-145, in=145, loop, distance=4em]
    \arrow[""{name=1, anchor=center, inner sep=0}, "{F} \,\circ\, {G}", from=1-2, to=1-2, out=35, in=-35, loop, distance=4em]
    \arrow["\theta", shorten <=3pt, shorten >=3pt, Rightarrow, from=0, to=1-1]
    \arrow["\phi"', shorten <=3pt, shorten >=3pt, Rightarrow, from=1, to=1-2]
\end{tikzcd}

\end{document}

答案1

如手册第 3.2 节所述tikz-cd，可以使用to path来调整路径。为了找到弧的适当起始和终止角度，可以使用库测量节点calc。双箭头也是通过 绘制的to path。这些路径在构造上是水平的。为了保留边缘标签，必须将 添加\tikztonodes到 的参数中to path。

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{calc}
\begin{document}
\def\myradius{1.5em}
\begin{tikzcd}[column sep=large]
    C & D
    \arrow["{F}", bend left = 30, from=1-1, to=1-2]
    \arrow["{G}", bend left = 30, from=1-2, to=1-1]
    \arrow["{G} \,\circ\, {F}","\mathstrut"{name=0, anchor=center, inner sep=0}, from=1-1, to=1-1,to path={%
        let \p1=($(\tikztostart.north)-(\tikztostart.south)$),\n1={scalar(asin(0.5*\y1/\myradius))} in 
        (\tikztostart.south)arc[start angle=-\n1,end angle=-360+\n1,radius=\myradius]\tikztonodes (\tikztotarget)}]
    \arrow["{F} \,\circ\, {G}","\mathstrut"{name=1, anchor=center, inner sep=0}, from=1-2, to=1-2,to path={%
    let \p1=($(\tikztostart.north)-(\tikztostart.south)$),\n1={scalar(asin(0.5*\y1/\myradius))} in 
    (\tikztostart.north)arc[start angle=180-\n1,end angle=-180+\n1,radius=\myradius]\tikztonodes (\tikztotarget)}]
    \arrow["\theta", shorten <=3pt, shorten >=3pt, Rightarrow, from=0, to=1-1, to path={(\tikztostart|-\tikztotarget) -- (\tikztotarget)\tikztonodes}]
    \arrow["\phi"', shorten <=3pt, shorten >=3pt, Rightarrow, from=1, to=1-2, to path={(\tikztostart|-\tikztotarget) -- (\tikztotarget)\tikztonodes}]
\end{tikzcd}

\end{document}

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答案2

以下是对已接受答案稍作修改的版本。在水平箭头中，我将箭头的高度与对齐，\tikztostart而不是\tikztotarget对齐，以使其更高。但是，为了正确获取箭头的终点，我手动将 3pt 的水平偏移添加到坐标中，这在代码中看起来相当丑陋。

在此处输入图片描述

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{calc}
\begin{document}

\begin{tikzcd}[column sep=large]
    C & D
    \arrow["{F}", bend left = 30, from=1-1, to=1-2]
    \arrow["{G}", bend left = 30, from=1-2, to=1-1]
    \arrow["{G} \,\circ\, {F}","\mathstrut"{name=0, anchor=center, inner sep=0}, from=1-1, to=1-1,
        to path={let \p1=($(\tikztostart.north)-(\tikztostart.south)$),\n1={scalar(asin(0.5*\y1/1.5em))} in
            (\tikztostart.south) arc[start angle=-\n1,end angle=-360+\n1,radius=1.5em]\tikztonodes (\tikztotarget)}]
    \arrow["{F} \,\circ\, {G}","\mathstrut"{name=1, anchor=center, inner sep=0}, from=1-2, to=1-2,
        to path={let \p1=($(\tikztostart.north)-(\tikztostart.south)$),\n1={scalar(asin(0.5*\y1/1.5em))} in
            (\tikztostart.north) arc[start angle=180-\n1,end angle=-180+\n1,radius=1.5em]\tikztonodes (\tikztotarget)}]
    \arrow["\theta", shorten <=3pt, shorten >=3pt, Rightarrow, from=0, to=1-1, to path={(\tikztostart) -- ($(\tikztotarget|-\tikztostart)+(-3pt,0)$) \tikztonodes }]
    \arrow["\phi"', shorten <=3pt, shorten >=3pt, Rightarrow, from=1, to=1-2, to path={(\tikztostart) -- ($(\tikztotarget|-\tikztostart)+(3pt,0)$) \tikztonodes }]
\end{tikzcd}

\end{document}

答案3

TikZ-CD 使用asymmetrical rectangle的中心锚点不在实际的垂直中心，而是axis_height在基线上方固定距离（），以便同一行节点之间的箭头像数学模式箭头一样绘制。 （这也导致它们始终是水平的。）

在此代码中，绘制圆段以便它穿过起点的中心（并且不接触北锚点或南锚点）。为此，使用了spath3和intersections库。对于水平/垂直以外的任何方向，从数学上讲，执行此操作涉及太多数学运算，我不想弄清楚。从技术上讲，库spath3仅用于移除位于起始节点内的圆段，可以通过了解交点来确定适当的起始和结束角度。

我向 TikZ-CD 添加了两种使用circle around rect node样式的方法：

  1. circle = <padding>（<padding>默认为.5ex，大约为 TikZ-CD 中节点的 inenr sep 的一半）

    如果填充为零，则这将确定半径，使得圆刚好接触目标坐标/节点。

  2. circle to = <angle>围绕起始坐标绘制一个指向 方向<angle>、直径 的圆circle to distance。

代码

\documentclass[tikz]{standalone}
\usepackage{tikz-cd}
\usetikzlibrary{calc, intersections, spath3}
\tikzset{
  circle around rect node/.style n args={3}{insert path={%
    % #1 = node name, #2 = angle, #3 = distance
    (#1.center) edge[
      path only, spath/save global=carn@circle,
      to path={arc[start angle={(180-(#2))}, delta angle=360, radius={(#3)/2}]}](#1)
    (#1.south west) edge[
      path only, spath/save global=carn@rect,
      to path={rectangle(\tikztotarget)}](#1.north east)
    [spath/.cd,
      split at intersections with={carn@circle}{carn@rect},
      remove components={carn@circle}{1,3},
      use=carn@circle]}}}
\tikzcdset{
  circle to distance/.initial=3em,
  circle to/.style={to path={
    [circle around rect node/.expanded={\tikztostart}{#1}
      {\pgfkeysvalueof{/tikz/commutative diagrams/circle to distance}}]
    \tikztonodes}},
  circle/.default=.5ex,
  circle/.style={
    execute at begin to={%
      \path[path only](\tikztostart)
        --coordinate[at end](tikzcd@circleend)(\tikztotarget);},
    to path={
      let \p{tikzcd@diff} = ($(tikzcd@circleend)-(\tikztostart)$) in
      [circle around rect node/.expanded={\tikztostart}
                                         {atan2(\y{tikzcd@diff},\x{tikzcd@diff})}
                                         {veclen(\p{tikzcd@diff})+(#1)}]
      \tikztonodes}}}
\tikzset{
  cd/.code=\tikzcdset{#1},
  cd node/.style={font=,cd=every cell,name={#1}}}
\begin{document}

\begin{tikzcd}[
  column sep=large, bend angle=30,
%  /tikz/column 1/.append style={cd={column sep=normal}},
%  /tikz/column 3/.append style={cd={column sep=normal}},
]
  G \circ F \arrow[r, "\theta", Rightarrow]
& C         \arrow[r, "F", bend left]
            \arrow[l, circle]
& D         \arrow[l, "G", bend left]
            \arrow[r, circle]
& F \circ G \arrow[l, "\phi"', Rightarrow]
\end{tikzcd}

\begin{tikzcd}[column sep=large, bend angle=30]
  C \arrow[r, "F", bend left]
    \arrow[circle to=180, "G \circ F"' cd node=GF]
    \arrow[Rightarrow, shorten <=.8ex, from=GF, "\theta"]
& D \arrow[l, "G", bend left]
    \arrow[circle to=  0, "F \circ G"' cd node=FG]
    \arrow[Rightarrow, shorten <=.8ex, from=FG, "\phi"']
\end{tikzcd}

\begin{tikzpicture}
\node[draw] (A) {A};
\foreach[count=\i] \ang in {0, 45, ..., 359}
  \draw[red!\i0!blue, circle around rect node={A}{\ang}{1cm}];
\end{tikzpicture}
\end{document}

输出

在此处输入图片描述

在此处输入图片描述

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