%% 
%%  Ein Beispiel der DANTE-Edition
%%  
%%  7. Auflage
%% 
%%  Beispiel 05-05-2 auf Seite 81.
%% 
%%  Copyright (C) 2016 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1
%% 
%% 
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{352.81416pt}
\setlength\parindent{0pt}
%StartShownPreambleCommands
\usepackage{pst-plot,pst-xkey,multido}
\makeatletter
\pst@addfams{demo}% add family demo to the list
\define@boolkey[psset]{demo}[Pst@]{showcircles}[true]{}% prefix is \Pst@
\define@boolkey[psset]{demo}[Pst@]{hypocycloid}[true]{}%  "    "   "
\define@key[psset]{demo}{nAngle}{\pst@getint{#1}\psk@nAngle}
\define@key[psset]{demo}{dAngle}{\pst@getangle{#1}\psk@dAngle}
%
\psset[demo]{showcircles=false,nAngle=6,dAngle=60,hypocycloid=false}
\newpsstyle{cycloid}{linecolor=black,linewidth=0.2\pslinewidth}
%
\def\psCycloid{\pst@object{psCycloid}}
% A pstricks object reads a star and the optional arguments
% and then cintinues with <name>@i
% we use (#1), but will test, if we have another (#2,#3),
% otherwise we use the default (0,720)
\def\psCycloid@i(#1){%
  \@ifnextchar({\psCycloid@ii(#1)}{\psCycloid@ii(#1)(0,360)}}
% (#1)   : origin
% (#2,#3): start and end angle for the parametrix plot
% #4     : radius R of the big circle
% #5     : radius r of the small circle
% #6     : radius A of the rotatetd point
\def\psCycloid@ii(#1)(#2,#3)#4#5#6{%
  \pst@killglue % no whitespace
  \begingroup% % hold all local
  \addbefore@par{plotpoints=500}% can be overwritten by a following user set
  \use@par% % set the optional arguments
  \pst@getlength{#4}\pst@tempB% get the radius in pt (screen coors)
  \pst@getlength{#5}\pst@tempC% get the 2nd radius in pt
  \pst@getlength{#6}\pst@tempD% get the distance for a in pt
  \pstVerb{ % define it only once (in user coors!!!)
/R \pst@tempB \pst@number\psunit div def
    /r \pst@tempC \pst@number\psunit div def
    /A \pst@tempD \pst@number\psunit div def
    /Rr R r \ifPst@hypocycloid sub \else add \fi def  % R +- r
    /RDivr R r div def  % R/r
    /RrDivr RDivr 1 \ifPst@hypocycloid sub \else add \fi def % (R+-r)/r
  }%
  \if@star\psset{fillstyle=eofill,fillcolor=\pslinecolor}\fi%
  \parametricplot{#2}{#3}{%
      Rr t cos mul t RrDivr mul cos A mul sub  % x(t)
      Rr t sin mul t RrDivr mul sin A mul
      \ifPst@hypocycloid add \else sub \fi }% y(t)
  \ifPst@showcircles%
    \psset{style=cycloid}%
    \pscircle(#1){#4}%
    \multido{\rA=0.0+\psk@dAngle}{\psk@nAngle}{%
     \rput(!#4 #5 \ifPst@hypocycloid sub \else add \fi dup
       \rA\space cos mul exch \rA\space sin mul){% user coors!!
        \pscircle{#5}\psline[linecolor=blue]{*-o}(!%
          \rA\space RrDivr mul dup % the angle
          cos A mul neg
          exch sin A mul \ifPst@hypocycloid\else neg \fi)%
    }}%
    \psarc[arrowscale=2]{->}(#1){0.5cm}{0}{270}
  \fi%
  \endgroup% end of local macro
  \ignorespacesafterend% no whitespace at the end
}
\makeatother

\def\oneShot#1{%
\begin{pspicture}(-3,-3)(3,3)
  \psCycloid[linecolor=red,linewidth=1.5pt,showcircles,
     dAngle=10,nAngle=1][#1](0,0){2}{0.5}{0.6}
\end{pspicture}}

%StopShownPreambleCommands
\begin{document}
\begin{pspicture}(-3,-3)(3,3)
  \psCycloid[hypocycloid,linecolor=red,linewidth=1.5pt](0,0){2}{0.25}{0.6}
\end{pspicture}
%
\begin{pspicture}(-4,-3)(4,3)
  \psCycloid[hypocycloid,linecolor=red,linewidth=1.5pt,showcircles,
     dAngle=20,nAngle=18](0,0){2}{0.25}{0.6}
\end{pspicture}
\end{document}