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-%% $Id: pst-spirograph-doc.tex 81 2014-08-23 07:08:21Z herbert $
-\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings
- headexclude,footexclude,oneside]{pst-doc}
-\errorcontextlines=150
-\usepackage{pst-spirograph}
-\let\pstFV\fileversion
-\usepackage{pst-node,pst-plot}
-\usepackage{animate}
-
-\def\UrlFont{\small\ttfamily}
-\makeatletter
-\def\verbatim@font{\small\normalfont\ttfamily}
-\makeatother
-
-\hypersetup{pdfauthor={Manuel Luque, Herbert Voss},pdftitle={Spirograoh}}
-%
-\def\bgImage{\begin{pspicture}(-4,-4)(4,4)
-\psSpirograph[thetamax=360,Z1=36,Z2=24,m=0.15,linewidth=0.025,ap=20,
- fillstyle=solid,polarangle=150,linecolor=blue,holenumber=0,opacity=0.4]
-\end{pspicture}%
-}
-
-\lstset{basicstyle=\ttfamily\footnotesize}
-
-\addbibresource{\jobname.bib}
-
-
-\begin{document}
-\author{Manuel Luque\\Herbert Vo\ss}
-\docauthor{}
-\date{\today}
-\title{pst-spirograph \\\small v.\pstFV}
-\subtitle{A PSTricks package for drawing spirograph curves}
-\maketitle%
-
-\tableofcontents
-
-\begin{abstract}
-\vfill\noindent
-Thanks for feedback and contributions to:\\
-Uwe Ziegenhagen;
-\end{abstract}
-
-\clearpage
-
-\section{Introduction}
-
-
-\LPack{pst-spirograph} is a package to simulate the operation of a spirograph. A spirograph
-is a geometric drawing toy that produces mathematical roulette curves that are technically
-known as hypotrochoids and epitrochoids.
-The mathematician Bruno Abakanowicz invented the spirograph between 1881 and 1900.%
-\footnote{\url{http://en.wikipedia.org/wiki/Spirograph}}
-It was used to calculate an area delimited by curves.
-A hypotrochoid is generated by a fixed point on a circle rolling inside a fixed circle.%
-\footnote{\url{http://mathworld.wolfram.com/Spirograph.html}}
-It consists of a small toothed wheel rotating inside or outside a ring gear.
-The weighing tile wheel has nine drilled holes numbered from 0--8, through these small holes the tip of a
-pen or pencil can be put.
-This causes the small wheel to rotate one or more laps around the crown and draws a hypocycloid.
-
-The wheel can also turn off a first fixed gear, it is thus possible to draw epicycloids . The command is written as
-
-
-\begin{BDef}
-\Lcs{psSpirograph}\OptArgs\Largr{\CAny}\\
-\Lcs{psSpirographB}\OptArgs\Largr{\CAny}
-\end{BDef}
-
-
-and can optionally be followed by the coordinates of the point where you wish to place the
-Spirograph: \Lcs{psSpirograph}\OptArgs\Largr{x,y} which by default is centered at the origin.
-The optional parameters, including default values are indicated as following:
-
-\begin{compactenum}
-\item \LKeyset{Z1=20}: number of teeth of the wheel 1, the crown;
-\item \LKeyset{Z2=10}: number of teeth of the wheel 2;
-\item \LKeyset{m=0.5}: relative size of the gear;
-\item \LKeyset{ap=20}: pressure angle in degrees, it must be reduced if the number of teeth
- crown is large (if the path of the teeth will be incorrect), e.g. take \verb|Z1=120|;
-\item \LKeyset{holenumber=0}: active hole number;
-\item \LKeyset{polarangle=0}: polar angle in degrees to position the center of the inner/outer gear;
-of the small wheel. It is a useful parameter for an animation, then it is the starting angle..
-\item \LKeyset{thetamax=360}: the end value for the rotation of the second inside/outside gear;
-\end{compactenum}
-
-There are two Boolean values for the organisation of the two circles:
-
-\begin{compactitem}
-\item \Lkeyword{circles}: to draw circles of contact (default is \texttt{false}.
-\item \Lkeyword{inner}: the gear rotates inside of the crown (\texttt{true} --- default) or outside (\texttt{false}).
-\end{compactitem}
-
-
-In the drawing, the color selection wheel and the line of the curve is made with
-the following setting:
-
-
-\begin{compactenum}
-\item \LKeyset{color1=\{[rgb]\{0.625 0.75 1\}\}};
-\item \LKeyset{color2=\{[rgb]\{0.75 1 0.75\}\}};
-\item \Lkeyset{curvecolor=red};
-\item \LKeyset{curvewidth=1pt}: linewidth of the hypocycloid;
-\item \Lkeyset{circlescolor=red}.
-\end{compactenum}
-
-The origin of the spirograph can be set by the coordinates $(x,y)$. If the they are missing, $(0,0)$ is assumed.
-By default, the wheels are not filled with color. The color inside the wheels must be
-set by the option \Lkeyset{fillStyle=solid}.
-
-The choice of color and line thickness contour of the wheels is made with
-usual PSTricks options: \Lkeyword{linecolor} and \Lkeyword{linewidth}.
-The transparency of the small wheel is adjusted with the \Lkeyword{opacity} option of PSTricks.
-
-The last parameter is the angle \LKeyset{thetamax=360}, which represents the rotation in degrees
-the center of the small wheel around the ring, so it is a parameter to adjust,
-depending on the planned route of the hypocycloid.
-
-
-\section{Parameter}
-
-\subsection{Relative size}
-The relative size of the two gears can be set by the optional argument \Lkeyword{m},
-which can take every possible value.
-
-
-\begin{LTXexample}[pos=t]
-\psset{unit=0.75}
-\begin{pspicture}[showgrid=top,opacity=0.5](-11,-11)(11,11)
-\psframe*[linecolor=yellow!30](-11,-11)(11,11)
-\psset{thetamax=720,Z1=120,Z2=48,ap=10,linewidth=0.025,fillstyle=solid}
-\psSpirograph[inner=false,m=0.1,polarangle=200,holenumber=0,linecolor=blue,curvecolor=blue]
-\psSpirograph[m=0.1,polarangle=200,holenumber=0,linecolor=red]
-\end{pspicture}
-\end{LTXexample}
-
-
-
-
-
-\subsection{Pencil position}
-
-\noindent\begin{tabularx}{\linewidth}{@{} XX @{}}
-The holes (\Lkeyword{holenumber}) for the pencil are ordered from outside into the center of the gear with different
-polar coordinates (radius and angle) . They are numbered from 0 to 8 and the position cannot be changed. Every given number greater
-than 8 will be reset internally to 8.
-&
-\begin{pspicture}[shift=-6cm](-3.5,-3.5)(3.5,3.5)
- \pscircle*[linecolor=red!30](0,0){3}
- \psaxes[axesstyle=polar,labels=none](3,360)
- \multido{\iA=0+60,\iB=8+-1}{9}{%
- \pnode(!0.35 \iA\space DegtoRad mul \iA\space cos mul neg
- 0.35 \iA\space DegtoRad mul \iA\space sin mul){N\iB}%
- \psdot(N\iB)\uput[0](N\iB){\iB}}
- \pscurve{->}(N0)(N1)(N2)(N3)(N4)(N5)(N6)(N7)(N8)
-\end{pspicture}
-\end{tabularx}
-
-
-\begin{LTXexample}[pos=t,wide]
-\psset{unit=0.8cm}
-\begin{pspicture}[showgrid=top,opacity=0.5](-7,-7)(7,7)
-\psframe*[linecolor=yellow!30](-7,-7)(7,7)
-\psset{thetamax=720,Z1=120,Z2=48,m=0.1,ap=10,linewidth=0.025,curvewidth=1.1pt}
-\psSpirograph[holenumber=0]
-\psSpirograph[holenumber=1,curvecolor=blue] \psSpirograph[holenumber=2,curvecolor=green]
-\psSpirograph[holenumber=3,curvecolor=cyan] \psSpirograph[holenumber=4,curvecolor=magenta]
-\psSpirograph[holenumber=6,curvecolor=black] \psSpirograph[holenumber=5,curvecolor=black!50]
-\psSpirograph[holenumber=7,curvecolor=blue!50]\psSpirograph[holenumber=8,curvecolor=red!50]
-\end{pspicture}
-\end{LTXexample}
-
-
-\clearpage
-\subsection{Pressure Angle}
-
-This value defines the look of a ``teeth''. Values greater than 30 make no real sense.
-
-\psset{unit=1cm}
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top,opacity=0.5](-7,-3)(7,3)
-\psset{unit=0.4,linewidth=0.025,fillstyle=solid,polarangle=90}
-\psSpirograph[ap=0](-12,0)
-\psSpirograph[ap=20, holenumber=4](0,0)
-\psSpirograph[ap=30, holenumber=8](12,0)
-\end{pspicture}
-\end{LTXexample}
-
-\clearpage
-
-
-\section{Examples}
-
-\psset{unit=1cm}
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top](-7,-7)(7,7)
-\psframe*[linecolor=yellow!30](-7,-7)(7,7)
-\psSpirograph[thetamax=720,Z1=120,Z2=48,m=0.1,ap=10,linewidth=0.025,
- fillstyle=solid,polarangle=200,holenumber=0,opacity=0.3]
-\psSpirograph[thetamax=720,Z1=120,Z2=48,m=0.1,ap=10,linewidth=0.025,
- fillstyle=solid,polarangle=340,holenumber=3,opacity=0.3,curvecolor=blue]
-\psSpirograph[thetamax=720,Z1=120,Z2=48,m=0.1,ap=10,linewidth=0.025,
- fillstyle=solid,polarangle=90,holenumber=6,opacity=0.3,curvecolor=green]
-\end{pspicture}
-\end{LTXexample}
-
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top](-7,-7)(7,7)
-\psframe*[linecolor=yellow!30](-7,-7)(7,7)
-\psSpirograph[thetamax=720,Z1=120,Z2=48,m=0.1,ap=10,linewidth=0.025,
- fillstyle=solid,polarangle=200,holenumber=3,opacity=0.75]
-\end{pspicture}
-\end{LTXexample}
-
-
-
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top](-7,-7)(7,7)
-\psframe*[linecolor=gray!20](-7,-7)(7,7)
-\psSpirograph[thetamax=720,Z1=36,Z2=24,m=0.15,linewidth=0.025,ap=20,inner=false,
- fillstyle=solid,polarangle=150,linecolor=blue,holenumber=0,opacity=0.8]
-\end{pspicture}
-\end{LTXexample}
-
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top](-7,-7)(7,7)
-\psframe*[linecolor=yellow!30](-7,-7)(7,7)
-\psSpirograph[thetamax=1440,Z1=27,Z2=12,m=0.4,linewidth=0.025,
- curvecolor={[rgb]{0 0.25 0.5}},circles,fillstyle=solid,polarangle=30,
- linecolor=blue,holenumber=0,opacity=0.75]
-\end{pspicture}
-\end{LTXexample}
-
-
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top](-7,-7)(7,7)
-\psframe*[linecolor=yellow!30](-7,-7)(7,7)
-\psset{unit=0.5}
-\psSpirograph[thetamax=-1800,Z1=108,Z2=15,m=0.2,linewidth=0.025,ap=10,
- fillstyle=solid,polarangle=54,linecolor=blue,holenumber=0,opacity=0.75]
-\end{pspicture}
-\end{LTXexample}
-
-
-
-\begin{LTXexample}[pos=t]
-\begin{pspicture}[showgrid=top](-7,-7)(7,7)
-\psframe*[linecolor=gray!20](-7,-7)(7,7)
-\psSpirograph[thetamax=1800,Z1=36,Z2=30,m=0.15,linewidth=0.025,ap=20,inner=false,
- fillstyle=solid,polarangle=150,linecolor=blue,holenumber=4,opacity=0.8]
-\end{pspicture}
-\end{LTXexample}
-
-\clearpage
-\section{Animations}
-
-\begin{sloppypar}
-With package \LPack{animate} one can easily create animations. You get a better result with
-\verb:\multiframe{360}{iA=0+4}{...}: but that increases the file size of the PDF. To save diskspace the following
-examples use a bigger angle step than useful for a single animation.
-\end{sloppypar}
-
-
-
-%\psset{unit=0.75cm}
-\begin{LTXexample}[pos=t]
-\begin{animateinline}[
- width=0.9\linewidth,
- begin={\begin{pspicture}(-4,-4)(4,4)},
- end={\end{pspicture}},
- palindrome,controls,
-% autoplay
-]{5}
-\multiframe{80}{iA=0+10}{%
- \psSpirograph[thetamax=\iA,Z1=59,Z2=24,m=0.1,ap=10,curvewidth=1.1pt,
- linewidth=0.025,fillstyle=solid,polarangle=\iA,holenumber=5,opacity=0.5](0,0)}
-\end{animateinline}
-\end{LTXexample}
-
-
-\iffalse
-\psset{linewidth=0.1pt}
-\begin{LTXexample}[pos=t]
-\psset{unit=0.3cm}
-\begin{animateinline}[
- width=0.9\linewidth, begin={\begin{pspicture}(-11,-11)(11,11)}, end={\end{pspicture}}, palindrome,controls,]{5}
-\multiframe{109}{i=0+10}{%
-\psgrid[style=gridstyleA](-10,-10)(10,10)%
-\ifnum\i=109 \psset{gearwheels=false}\fi
-\psSpirograph[Z1=24,Z2=16,m=0.5,ap=22,TypeA=false,linewidth=0.2pt,fillstyle=solid,opacity=0.5,
- polarangle=\i,circles=false,thetamax=\i,curvecolor=blue,curvewidth=2pt,HolePos=1.1,color1=magenta]}
-\end{animateinline}
-\end{LTXexample}
-
-
-\begin{LTXexample}[pos=t]
-\psset{unit=0.5cm}
-\begin{animateinline}[
- width=0.9\linewidth,begin={\begin{pspicture}(-10,-10)(10,10)},end={\end{pspicture}},palindrome,controls]{5}
-\multiframe{721}{i=0+2}{%
-\psgrid[subgriddiv=0,gridcolor=red,unit=1.5](-10,-10)(10,10)%
-\ifnum\i=721 \psset{gearwheels=false}\fi
-\psSpirograph[Z1=24,Z2=18,m=0.5,ap=22,linewidth=0.025,TypeA=false,fillstyle=solid,opacity=0.5,polarangle=\i,circles=false,
- thetamax=\i,curvecolor=blue,curvewidth=2pt,HolePos=1.75,color1=magenta]}
-\end{animateinline}
-\end{LTXexample}
-\fi
-
-
-
-\begin{LTXexample}[pos=t]
-\psset{unit=0.6cm}
-\begin{animateinline}[
- width=0.9\linewidth,begin={\begin{pspicture}(-14,-14)(14,14)},end={\end{pspicture}},palindrome,controls]{5}
-\multiframe{181}{i=0+10}{%
- \psgrid[style=gridstyleA,unit=1.4](-10,-10)(10,10)%
- \ifnum\i=181 \psset{gearwheels=false}\fi
- \psSpirograph[Z1=50,Z2=20,m=0.2,linewidth=0.025,fillstyle=solid,opacity=0.75,polarangle=\i,circles,TypeA=false,
- thetamax=\i,curvecolor=red,curvewidth=2pt,HolePos=1.5]}
-\end{animateinline}
-\end{LTXexample}
-
-
-\iffalse
-\begin{LTXexample}[pos=t]
-\psset{unit=0.4cm}
-\begin{animateinline}[
- width=0.9\linewidth,begin={\begin{pspicture}(-18,-18)(18,18)},end={\end{pspicture}},palindrome,controls]{5}
-\multiframe{181}{i=0+10}{%
-\psgrid[style=gridstyleA]%
-\ifnum\i=181 \psset{gearwheels=false}\fi
-\psSpirograph[Z1=60,Z2=24,m=0.2,linewidth=0.025,TypeA=false,
- linecolor=blue,fillstyle=solid,opacity=0.75,polarangle=\i,circles=false,thetamax=\i,curvecolor=red,curvewidth=2pt,HolePos=1.7]}
-\end{animateinline}
-\end{LTXexample}
-
-
-
-\begin{LTXexample}[pos=t]
-\psset{unit=0.25cm}
-\begin{animateinline}[
- width=0.9\linewidth,begin={\begin{pspicture}(-20,-20)(20,20)},end={\end{pspicture}},palindrome,controls]{5}
-\multiframe{324}{i=0+10}{%
-\psgrid[subgriddiv=0,gridcolor=black!20,unit=2](-10,-10)(10,10)%
-\ifnum\i=324 \psset{gearwheels=false}\fi
-\psSpirograph[Z1=72,Z2=16,m=0.2,ap=10,TypeA=false,linewidth=0.02,linecolor={[rgb]{0.5 0 0 }},fillstyle=solid,
- opacity=0.75,polarangle=\i,circles=false,thetamax=\i,curvecolor=blue,curvewidth=3pt,
- HolePos=0.5,color1=cyan!10,color2=cyan!10,strokeopacity=0.5]%
-%\psSpirograph[Z1=72,Z2=16,m=0.2,ap=10,TypeA=false,linewidth=0.02,linecolor={[rgb]{0.5 0 0 }},fillstyle=solid,
-% opacity=0.75,polarangle=\i,circles=false,thetamax=\i,curvecolor=green,curvewidth=3pt,
-% HolePos=1.5,color1=cyan!10,color2=cyan!10,strokeopacity=0.5]
-}
-\end{animateinline}
-\end{LTXexample}
-\fi
-
-
-\clearpage
-
-\section{Connect the two gears with a rubberband}
-
-This is an adaptation with PSTricks of an idea of Alejandro Teutli which he realized with Mathematica:
-\url{https://demonstrations.wolfram.com/ParametricMovementOfARubberBand/} which is a variation of a spirograph.
-A rubber band is fixed by its ends on two gears. A pencil tied in the middle of the elastic rubberband draws the curve obtained when the gears are
-rotating. The optional argument \Lkeyword{RubberBand} must be used, if you want such a spirograph. It is only available
-in 3D.
-
-
-\begin{LTXexample}[pos=t]
-\begin{animateinline}[
- width=0.9\linewidth,
- begin={\begin{pspicture}(-6,-3)(8,6)\psframe*[linecolor=yellow,opacity=0.4](-6,-3)(8,6)},
- end={\end{pspicture}},
- palindrome,controls,
-% autoplay
-]{5}
-\multiframe{181}{iA=0+4}{%
-\psSpirograph[RubberBand,Z1=20,Z2=40,m=0.2,viewpoint=2 -5 3,arrowinset=0,arrowsize=0.2,wheelrotation=\iA,
- linewidth=0.025,color1=yellow,color2=blue!50]}
-\end{animateinline}
-\end{LTXexample}
-
-
-
-
-%There are some more examples in the documention directory of the package.
-
-\clearpage
-
-\section{List of all optional arguments for \texttt{pst-spirograph}}
-
-\xkvview{family=pst-spirograph,columns={key,type,default}}
-
-
-\bgroup
-\nocite{*}
-\raggedright
-\printbibliography
-\egroup
-
-\printindex
-
-
-
-\end{document}
-