TikZ – Inline icons for rotations

Question

Is there a way to create icons such as the one below using \tikz? I know there probably is a way, but I have been having trouble with getting the right positioning of the arrows and I really do not have a clue how to do this properly. I would also like to do other rotations and other polygons.

The image comes from a video by 3Blue1Brown.

I have tried the following:

\newcommand{\polyrot}[3][1ex]{\ \tikz[baseline=-3pt, inner sep=0pt] {%
    \node[draw,
          regular polygon,
          regular polygon sides=#2,
          minimum size={2 * #1},
          line width=1pt] (p)
        (0,0) {};
    \draw [->] (0, 0) arc ({360/#2}:{360/#2 + #3}:{3 * #1});
    }}

However, that just gets the positioning of the arrow completely wrong.

Answer 1

Here is an automated solution. Define a macro \polyrot that takes 3 arguments, one optional:

\polyrot[<tikz options>]{<num sides>}{<rotation angle>}

tikz options can include color, scale, etc.

\documentclass{article}

\usepackage{gensymb}
\usepackage{tikz}
\usetikzlibrary {shapes.geometric, arrows.meta}

\newcommand{\circrad}{.6}
\newcommand{\polyrot}[3][]{\tikz[baseline, thick, #1]{
    \node[regular polygon, regular polygon sides=#2, draw, minimum size=1cm] {}; 
    \draw[-{Triangle[angle=60:3pt]}] (5:\circrad) arc (5:#3:\circrad);
    \node at (#3/2:1.4*\circrad){\scriptsize#3\degree};
    \draw[-{Triangle[angle=60:3pt]}] (185:\circrad) arc (185:180+#3:\circrad);
}}

\begin{document}

\polyrot{3}{120}\quad\polyrot{4}{90}\quad\polyrot{4}{180}\quad\polyrot{4}{-90}\quad\polyrot{5}{144}

\end{document}

Answer 2

We can measure the polygon node (or any other node when arcs around/anchor is set to a proper anchor) and use that measurement for the drawing of a few arcs around it.

The \ifnum in edge node makes sure that we only put the angle once in our diagram. With the value key arcs around/test you can specify one angle that shortens the arcs a bit.

The value of arcs around/sep will be added to the measured radius.

They main keys are arcs around/a (the list of start angles) and arcs around/d the delta angle.

Code

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,shapes.geometric,matrix,arrows.meta,bending}
\begin{document}
\begin{tikzpicture}[
  arcs around/.code=\pgfqkeys{/tikz/arcs around}{#1},
  arcs around={
    .search also=/tikz,
    a/.initial=0,
    d/.initial=180,
    test/.initial=180,
    sep/.initial=1pt,
    anchor/.initial=corner 1,
    node/.style={
      shape=rectangle, inner sep=+.1666em, auto, swap,
      font=\scriptsize, node contents={$\pgfmathprintnumber{#1}^\circ$}
    },
    arc/.style n args={3}{
      % #1 = counter, #2 = start angle, #3 = delta angle
      ->, draw, to path={arc[start angle=#2]\tikztonodes},
      edge node/.expand once={\ifnum#1=1 node[arcs around/node=#3]\fi}
    }
  },
  arcs around node/.style={
    % #1 = list of start angles, #2 = delta angle (and text), #3 = mand. options
    append after command={
      % calculate radius of that circle
      [arcs around={#1}]
      let \p{circle} = ($(\tikzlastnode.\pgfkeysvalueof
                         {/tikz/arcs around/anchor})-(\tikzlastnode.center)$),
          \n{radius} =
                  {veclen(\p{circle})+\pgfkeysvalueof{/tikz/arcs around/sep}},
          \n{delta} = {\pgfkeysvalueof{/tikz/arcs around/d}} in % shortcut
      % common values
      [radius=\n{radius},
       delta angle={\n{delta}-sign(\n{delta})*(abs(\n{delta})==
                                  \pgfkeysvalueof{/tikz/arcs around/test}?4:0)}]
      % draw arc for every angle in #1
      foreach \stangle[
        expand list,
        count=\inlineiconcounter,
        evaluate={\stAngle=\stangle+sign(\n{delta})*(abs(\n{delta})==
                                 \pgfkeysvalueof{/tikz/arcs around/test}?2:0);}
      ] in {\pgfkeysvalueof{/tikz/arcs around/a}}{
          ([shift=(\stAngle:\n{radius})]\tikzlastnode.center)
            edge[arcs around/arc={\inlineiconcounter}{\stAngle}{\n{delta}}]()
      }
    }
  },
  poly shape/.style={
    shape=regular polygon, regular polygon sides={#1}, at={(0,0)},
    fill={rgb:red,0;green,149;blue,182}, minimum size=+1cm, draw=none},
  trans matrix/.style={
    matrix of nodes,
    nodes in empty cells,
    row sep=.2em,
    column sep=.4em,
    % counteract any cells={nodes={<styles>}}
    arcs around/node/.append style={draw=none, fill=none, minimum size=+1pt}
  },
  >={Stealth[scale=.8,round,bend]},
]
\matrix (m4) [
  trans matrix,
  arcs around/a={0,180},
  cells={nodes={poly shape=4}}]{
  & |[arcs around node={d= 90}]|
  & |[arcs around node={d=180}]|
  & |[arcs around node={d=-90, swap}]| \\
    |[arcs around node={d= 90}]|
  & |[arcs around node={d=180}]|
  & |[arcs around node={d=-90, swap}]|
  & \\
};

\matrix at (m4.south west) [
  trans matrix,
  anchor=north west,
  yshift=-1.2em,
  % triangle setup:
  cells={nodes={poly shape=3}},
  arcs around={
    test=120,
    a={0,120,240}
  }
]{
  & |[arcs around node={d=120}]|
  & |[arcs around node={a={0,240,120}, d=240,
      arc/.append style={
        shift={(##2:##1*2pt)},
        radius/.expanded=\pgfkeysvalueof{/tikz/x radius}+##1*2pt
      }}]|
  & |[arcs around node={d=-120, swap}]| \\
};
\end{tikzpicture}
\end{document}

Output

Answer 3

The concept node of TikZ is great! but we should not abuse node. That is an extreme use. In fact, node is just a path (with anchors).

Here is my suggestion!

\documentclass[tikz,border=2mm]{standalone}
\pagecolor{black}
\begin{document}
\begin{tikzpicture}[declare function={a=.5;startangle=-20;endangle=160;}, 
truncated arrow/.style={->,white,thick,shorten >=1pt,shorten <=1pt}
]
\fill[cyan] (a,a) rectangle (-a,-a);
\draw[truncated arrow] (startangle:{1.7*a}) arc(startangle:endangle:{1.7*a}) node[midway,above]{$180^{\circ}$};
\draw[truncated arrow] (endangle:{1.7*a}) arc(endangle:startangle+360:{1.7*a});
\end{tikzpicture}
\end{document}

Answer 4

Something like this?

\documentclass[border=10mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

\newcommand{\polyrot}[3][1ex]{%
    \tikz[baseline=-3pt, inner sep=0pt] {%
        \node[draw,
              regular polygon,
              regular polygon sides=#2,
              minimum size={2 * #1},
              line width=1pt] 
              at (0,0) (p) {};
        \pgfmathparse{360/#3}
        \foreach \a in {1,...,\pgfmathresult} {
            \draw[->] ({(\a - 1) * #3}:{2 * #1}) 
                arc ({(\a - 1) * #3}:{\a * #3}:{2 * #1});
        }
    }}

\begin{document}

abc \polyrot{4}{180} def \polyrot{3}{90} ghi \polyrot{5}{120} jkl

\end{document}

If you want a gap between the start and the end of the arrows, you could subtract (or add) a few degrees from (or to) the start (or end) points of the arcs (I also added the labels in this example):

\documentclass[border=10mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

\newcommand{\polyrot}[3][1ex]{%
    \tikz[baseline=-3pt, inner sep=0pt] {%
        \node[draw,
              regular polygon,
              regular polygon sides=#2,
              minimum size={2 * #1},
              line width=1pt] 
              at (0,0) {};
        \pgfmathparse{360/#3}
        \foreach \a in {1,...,\pgfmathresult} {
            \draw[->] ({(\a - 1) * #3 + 5}:{2 * #1}) 
                arc ({(\a - 1) * #3 + 5}:{\a * #3 - 5}:{2 * #1});
            \ifnum\a=1
                \node[anchor=south west, overlay] at ({min((\a * #3 * 0.5),90)}:{2.5 * #1}) {\tiny$#3^{\circ}$};
            \fi
        }
    }}

\begin{document}

abc \polyrot{4}{180} def \polyrot{3}{90} ghi \polyrot{5}{120} jkl

\end{document}

You could also try using the option shorten > or shorten < on the arrows, which will shorten the path by the respective amount stated.