Drawing a regular polygon encompassed by a circle

Question

I would like to replicate the sort of diagrams shown below - a regular polygon in dashed lines encompassed by a solid lined unit circle with vectors going from the origin to each labelled vertex in an xy-plane. How would one go about doing this in TikZ?

Answer 1

With TikZ

\def\deg{120}                   % for triangle      
\def\p{3}                       % vertices
\begin{tikzpicture}[scale=2]
\draw [<->] (-1.5,0)--(1.5,0);
\draw [<->] (0,-1.5)--(0,1.5);
\draw (0,0) circle (1);

\foreach \t/\x in {0/0*\deg,1/1*\deg, 2/2*\deg}
{\draw[thick,->] (0:0)--(\x:1) node [] (\t) at (\x:1){};
\node[anchor=center] at (\x:1.2) {$w^{\t}_\p$};}

\foreach \from/\to in {0/1,1/2,2/0}
{\draw [thin, dashed] (\from) -- (\to);}

\end{tikzpicture}

\def\deg{40}                    % for convex hull, phase angle  
\def\p{9}                       % vertices
\begin{tikzpicture}[scale=2]
\draw [<->] (-1.5,0)--(1.5,0);
\draw [<->] (0,-1.5)--(0,1.5);
\draw (0,0) circle (1);
\foreach \t/\x in {0/0*\deg, 1/1*\deg, 2/2*\deg, 3/3*\deg, 4/4*\deg, 5/5*\deg,
6/6*\deg, 7/7*\deg, 8/8*\deg}
%\foreach \t[evaluate=\t as \x using int(\t*\deg)] in {0,1,...,8} % suggested by Claudio Fiandrino
{\draw[thick,->] (0:0)--(\x:1) node[] (\t) at (\x:1) {};
\node[anchor=center] at (\x:1.2) {$w^{\t}_\p$};}
\foreach \from/\to in {0/1, 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/0}
{\draw [thin, dashed] (\from) -- (\to);}
\end{tikzpicture}

This is the result

Answer 2

Just another way with TikZ.

It is possible to use more styles and have a more flexible setup (you cannot use a or c more than once without drawing it only once). It is possible to draw ellipses by using the x radius and y radius key.

I don’t like the the implementation via \nodeRot (could just as well be a key). But that’s the easiest way to allow rotations of the polygon with the rotate key and correctly placed labeling of the corners without rotated nodes and without using PGF tricks.

Code

\documentclass[tikz]{standalone}
\tikzset{declare function={angleForPoly(\i,\n,\d)=360/\n*\i+\d;
                           x_radius              =\pgfkeysvalueof{/tikz/x radius};
                           y_radius              =\pgfkeysvalueof{/tikz/y radius};},
  d/.style={circle,fill,outer sep=1pt,inner sep=+0pt,minimum size=+3pt,#1},
  c/.style={insert path={(C) edge[#1,to path={circle[]}] ()}},
  a/.style={insert path={(C)+(left:x_radius+.5cm) edge[#1,<->] +(right:x_radius+.5cm)
                         (C)+(  up:y_radius+.5cm) edge[#1,<->] +( down:y_radius+.5cm)}}}
\def\nodeRot{0}
\newcommand*\poly[2][]{%
  \path (0,0) coordinate (C) [rotate/.append code={\def\nodeRot{##1}},#1]
  ++ ({angleForPoly(0,#2,0)}:x_radius and y_radius) coordinate[d] (c)
   \foreach \cnt[count=\Cnt from 0] in {1,...,#2} {
      (c) [late options={alias=c'}] edge [<-, thick] (C)
      coordinate[d] (c) at ({angleForPoly(\cnt,#2,0)}:x_radius and y_radius)
      (c') edge[dashed] (c)
      \ifnum\Cnt>0 node[anchor={angleForPoly(\Cnt,#2,180+\nodeRot)},circle]
        {$\omega\ifnum\Cnt>1^{\Cnt}\fi_{#2}$} \fi
   };}
\begin{document}
\begin{tikzpicture}[radius=2cm,>=latex]
\matrix {
  \poly[a,c]{3} & \poly[a=red,c,rotate=30]{4} & \poly {5} \\
  \poly[c]  {6} & \poly                   {7} & \poly {8} \\
  \poly     {9} & \poly                  {10} & \poly{11} \\
};
\end{tikzpicture}
\end{document}

Output

Answer 3

with PSTricks:

\documentclass{article}
\usepackage{pstricks-add}
\usepackage[margin=5mm]{geometry}
\pagestyle{empty}\parindent=0pt
\begin{document}

\psset{unit=2}
\multido{\iA=3+1}{20}{%
  \begin{pspicture}(-1.3,-1.3)(1.3,1.3)
  \degrees[\iA]\pscircle{1}% set unit for a circle to 3,4,5,... instead of 360
  \psaxes[labels=none,ticks=none](0,0)(-1.1,-1.1)(1.1,1.1)
  \multido{\iB=0+1,\iC=1+1}{\iA}{%
    \psline[linestyle=dashed,showpoints](1;\iB)(1;\iC)
    \psline[arrowscale=2,linewidth=1pt]{->}(1;\iB)
    \rput(1.15;\iB){$\omega_{\iA}^{\iC}$}}
  \end{pspicture} }

\end{document}

Answer 4

Just for fun with PSTricks.

\documentclass[pstricks,border=20pt]{standalone}
\usepackage{pst-node,pst-plot}

\makeatletter

\def\Atom#1{%
\begin{pspicture}(-2,-2)(2,2)
    \psaxes[labels=none,ticks=none]{->}(0,0)(-2,-2)(2,2)[$x$,0][$y$,90]
    \pscircle[dimen=medusa]{1.75}
    \degrees[#1]
    \curvepnodes[plotpoints=\numexpr#1+1]{0}{#1}{1.75 t .5 add \pst@angleunit PtoC}{P}  
    \psnline[linecolor=lightgray,linestyle=dashed](0,\Pnodecount){P}
    \multido{\i@=0+1}{\Pnodecount}{\psline[linecolor=blue]{->}(P\i@)\uput[\i@](P\i@){\scriptsize$\omega_{#1}^{\the\numexpr\i@+1}$}}
\end{pspicture}}

\makeatother

\begin{document}
    \multido{\i=3+1}{10}{\Atom{\i}}
\end{document}

Answer 5

Just for fun (some years later :-): Qrrbrbirlbel's diagram, but this time with MetaPost in a LuaLaTeX program:

\documentclass{standalone}
\usepackage{luamplib}
  \mplibsetformat{metafun}
  \mplibtextextlabel{enable}
  \everymplib{verbatimtex \leavevmode etex;

    vardef circled_polygon(expr u, n) =
      clearxy; save xmin, xmax, ymin, ymax, angl, polygon; path polygon; 
      xmax := 1.2u; xmax = ymax = -xmin = -ymin; angl := 360/n; z0 = u*right; 
      polygon = z0 for i = 1 upto n-1: hide(z[i]= z[i-1] rotated angl) -- z[i] endfor -- cycle;
      draw polygon dashed evenly; draw fullcircle scaled (2u);
      draw (xmin, 0) -- (xmax, 0); draw (0, ymin) -- (0, ymax);
      drawoptions(withpen pencircle scaled 1bp);
      drawarrow origin -- z0; label.urt("$1$", z0);
      drawarrow origin -- z1; freelabel("$\omega_{" & decimal n & "}$", z1, origin);
      for i = 2 upto n-1:
        drawarrow origin -- z[i];
        freelabel("$\omega_{" & decimal n & "}^{" & decimal i & "}$", z[i], origin);
      endfor;
      drawoptions();
    enddef;

    beginfig(0);}

  \everyendmplib{setbounds currentpicture to boundingbox currentpicture enlarged 3bp;
    endfig;}

\begin{document}
\begin{mplibcode}
  u = 2cm;
  for i= 1 upto 3:
    for j = 1 upto 3:
      draw image(circled_polygon(u, 3i+j-1)) shifted ((2u+1.5cm)*(j-1, -i+1));
    endfor;
  endfor;
\end{mplibcode}
\end{document}