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|
%% $Id: pst-spirograph.tex 80 2014-08-23 05:50:14Z herbert $
%%
%% This is file `pst-spirograph.tex',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pst-spirograph.tex'
%%
%% COPYRIGHT 2020- by
%% Manuel Luque <manuel.luque27@gmail.com>
%% Herbert Voss <hvoss@tug.org>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory CTAN:/macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%% `pst-spirograph' is a PSTricks package to show spirograph curves
%%
%%
\csname PSTSPIROGRAPHLoaded\endcsname
\let\PSTSPIROGRAPHLoaded\endinput
% Requires some packages
\ifx\PSTricksLoaded\endinput \else \input pstricks \fi
\ifx\PSTXKeyLoaded\endinput \else \input pst-xkey \fi
\ifx\PSTthreeDLoaded\endinput\else \input pst-3d \fi
\ifx\PSTnodesLoaded\endinput \else \input pst-node \fi
\ifx\PSTplotLoaded\endinput \else \input pst-plot \fi
\def\fileversion{0.51}
\def\filedate{2020/03/14}
\message{`PSTSPIROGRAPH' v\fileversion, \filedate\ (ml,hv)}
\edef\PstAtCode{\the\catcode`\@}
\catcode`\@=11\relax
\pst@addfams{pst-spirograph}
\pstheader{pst-spirograph.pro}
\define@key[psset]{pst-spirograph}{Z1}[20]{\def\psk@ZA{#1 }}
\psset[pst-spirograph]{Z1=20}
\define@key[psset]{pst-spirograph}{Z2}[10]{\def\psk@ZB{#1 }}
\psset[pst-spirograph]{Z2=10}
\define@key[psset]{pst-spirograph}{m}[0.5]{\def\psk@m{#1 }}
\psset[pst-spirograph]{m=0.5}
\define@key[psset]{pst-spirograph}{ap}[20]{\def\psk@ap{#1 }}
\psset[pst-spirograph]{ap=20}
\define@key[psset]{pst-spirograph}{polarangle}[0]{\def\psk@polarangle{#1 }}
\psset[pst-spirograph]{polarangle=0}
\define@key[psset]{pst-spirograph}{holenumber}[1]{\def\psk@holenumber{#1 }}
\psset[pst-spirograph]{holenumber=1}
\define@key[psset]{pst-spirograph}{thetamax}[360]{\def\psk@thetamax{#1 }}
\psset[pst-spirograph]{thetamax=360}
\define@key[psset]{pst-spirograph}{Rarct}{\def\psk@Rarct{#1 }}
\psset[pst-spirograph]{Rarct=0.1}
\define@key[psset]{pst-spirograph}{wheelrotation}{\def\psk@wheelrotation{#1 }}
\psset[pst-spirograph]{wheelrotation=0}
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{int}[true]{}
\psset[pst-spirograph]{int=false}
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{notdrawWheel}[true]{}
\psset[pst-spirograph]{notdrawWheel=false}
%
\define@key[psset]{pst-spirograph}{color1}[{[rgb]{0.625 0.75 1}}]{\pst@getcolor{#1}\pscolora}
\psset[pst-spirograph]{color1={[rgb]{0.625 0.75 1}}}
\define@key[psset]{pst-spirograph}{color2}[{[rgb]{0.75 1 0.75}}]{\pst@getcolor{#1}\pscolorb}
\psset[pst-spirograph]{color2={[rgb]{0.75 1 0.75}}}
\define@key[psset]{pst-spirograph}{circlescolor}[red]{\pst@getcolor{#1}\pscolorc}
\psset[pst-spirograph]{circlescolor=red}
\define@key[psset]{pst-spirograph}{curvecolor}[red]{\pst@getcolor{#1}\pscolord}
\psset[pst-spirograph]{curvecolor=red}
%
\newdimen\pscurvewidth
\define@key[psset]{pst-spirograph}{curvewidth}[1pt]{\pssetlength\pscurvewidth{#1}}
\psset[pst-spirograph]{curvewidth=1pt}
%% === Option pour dessiner le type d'engrenage ---------------------
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{inner}[true]{}
\psset[pst-spirograph]{inner}
%% === pour dessiner cercle de base et cercle primitif
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{circles}[true]{}
\psset[pst-spirograph]{circles=false}
%% hole position
\define@key[psset]{pst-spirograph}{HolePos}{\def\psk@HolePos{#1 }}
\psset[pst-spirograph]{HolePos=1.5} % 1<HolePos<2
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{gearwheels}[true]{}
\psset[pst-spirograph]{gearwheels}
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{TypeA}[true]{}
\psset[pst-spirograph]{TypeA}
\define@boolkey[psset]{pst-spirograph}[Pst@spirograph@]{RubberBand}[true]{}
\psset[pst-spirograph]{RubberBand=false}
\define@key[psset]{pst-spirograph}{theta1}{\def\psk@thetaA{#1}}
\define@key[psset]{pst-spirograph}{theta2}{\def\psk@thetaB{#1}}
\psset[pst-spirograph]{theta1=-90,theta2=90}
\def\psSpirograph{\def\pst@par{}\pst@object{psSpirograph}}
\def\psSpirograph@i{\@ifnextchar({\psSpirograph@ii}{\psSpirograph@ii(0,0)}}
\def\psSpirograph@ii(#1){%
\begin@SpecialObj
\ifPst@spirograph@RubberBand \psSpirograph@iv(#1)\else\psSpirograph@iii(#1)\fi
}
\def\psSpirograph@iii(#1){%
\pst@@getcoor{#1}%
\addto@pscode{
tx@spirographDict begin
\pst@coor /t@@y ED /t@@x ED
1 setlinejoin
/cm { \pst@number\psunit mul } bind def
/Z1 \psk@ZA def
/m1 \psk@m def
/Z2 \psk@ZB def
/m2 \psk@m def
/ap \psk@ap def
/polarAngle \psk@polarangle def
/setlinedash { [ \psk@dash\space ] 0 setdash } def
/ni \psk@holenumber def ni 8 gt { /ni 8 def } if
/thetamax \psk@thetamax def
%
/ifinner \ifPst@spirograph@inner true \else false \fi def
/ifcircles \ifPst@spirograph@circles true \else false \fi def
/iffill \ifx\psk@fillstyle\psfs@none false \else true \fi def
/Fill { \tx@setTransparency fill stroke } def
% on teste si le nombre de dents est pair
Z1 2 mod 1 eq { /Z1 Z1 1 sub def } if
Z2 2 mod 1 eq { /Z2 Z2 1 sub def } if
/HolePos \psk@HolePos def
HolePos 0 lt HolePos 2 ge or { /HolePos 1.5 def } if
/Fill { \psk@opacityalpha .setopacityalpha fill } def
/R1 Z1 m1 mul 2 div def
/R2 Z2 m1 mul 2 div def
/ki 1 ni 9 div sub def
/r2 m1 Z2 mul 2 div def
/qi Z1 Z2 div 1 sub def
/qi2 Z1 Z2 div 1 add def
thetamax 0 le {/pas -1 def}{/pas 1 def} ifelse
% tableau des points de l'hypocycloide
/tabSpirograph [ 0 pas thetamax {/i_ exch def [i_ coorPen]} for ] def
% tableau des points de l'epicycloide
/tabSpirograph2 [ 0 pas thetamax {/i_ exch def [i_ coorPen2]} for ] def
/nPts tabSpirograph length 1 sub def
/nPts2 tabSpirograph2 length 1 sub def
/color1 {\pst@usecolor\pscolora } def
/color2 {\pst@usecolor\pscolorb } def
/circlescolor {\pst@usecolor\pscolorc } def
/curvecolor {\pst@usecolor\pscolord } def
/linecolor {\pst@usecolor\pslinecolor} def
/fillopacity \psk@opacityalpha def
/GetCurveWidth { \pst@number\pscurvewidth } def
/SetCurveWidth { \pst@number\pscurvewidth SLW } def
%
\ifPst@spirograph@TypeA
Roue1
Roue2
\else
%%%% definition de la roue dentee %%%%%%
thetamax 0 le { /pas -1 def }{ /pas 1 def } ifelse
/tabSpirograph [ 0 pas thetamax {/i_ exch def [ i_ coorPen3 ] } for ] def
%%% Les dessins de l'engrenage %%%%%%
%%%%%%%%%% Roue N°2 %%%%%%%%%%%
%%%%%%%%%% roue fixe %%%%%%%%%%
\ifPst@spirograph@gearwheels
/wheel 2 def
gsave
m2 Z2 Datas1
Calculs
Beta_ rotate
Roue3
closepath
% \ifx\psk@fillstyle\empty\else color2 Fill \fi
iffill { color2 Fill } if
Roue3
closepath
linecolor
stroke
grestore
gsave
%% la vis de fixation de la roue sur la feuille
0 0 0.5 cm 0 360 arc
0.8 0.8 0 setrgbcolor
fill
0 setgray
0 0 0.5 cm 0 360 arc
stroke
1 setlinewidth
-0.5 cm 0 moveto 0.5 cm 0 lineto
0 -0.5 cm moveto 0 0.5 cm lineto
stroke
grestore
\ifPst@spirograph@circles Circles \fi
\fi
gsave
tabSpirograph 0 get aload pop moveto
1 1 tabSpirograph length 1 sub {/nP exch def tabSpirograph nP get aload pop lineto } for
curvecolor
\pst@number\pscurvewidth SLW
stroke
grestore
%%%%%%%%%% Roue N°1 %%%%%%%%%%%%%%%%%
%%%%%%%%%% roue tournante %%%%%%%%%%
\ifPst@spirograph@gearwheels
/wheel 1 def
gsave
m2 Z2 Datas1
Calculs
/a@ex m2 Z1 Z2 add mul 2 div cm def % entraxe engrenage exterieur
/a@in m2 Z1 Z2 sub mul 2 div cm def % entraxe engrenage interieur
a@in polarAngle cos mul a@in polarAngle sin mul translate
polarAngle Z1 Z2 sub Z1 div mul rotate
m1 Z1
Datas2
Calculs
Beta_ rotate
Roue3
COURONNE
closepath
iffill { color1 Fill } if
% \ifx\psk@fillstyle\@empty\else color1 Fill \fi
Roue3
closepath
linecolor
stroke
COURONNE
closepath
linecolor
stroke
Roue3
closepath
linecolor
stroke
plaquette
drawHole
\ifPst@spirograph@circles Circles \fi
grestore
\else
gsave
m2 Z2 Datas1
Calculs
/a@ex m2 Z1 Z2 add mul 2 div cm def % entraxe engrenage exterieur
/a@in m2 Z1 Z2 sub mul 2 div cm def % entraxe engrenage interieur
a@in polarAngle cos mul a@in polarAngle sin mul translate
polarAngle Z1 Z2 sub Z1 div mul rotate
m1 Z1
Datas2
Calculs
Beta_ rotate
Beta_ neg rotate
drawHole
grestore
\fi
\fi
end
}%
\end@SpecialObj
\ignorespaces}
%
\def\psSpirograph@iv(#1){%
\def\RA{\psCalc{\psk@ZA*\psk@m/2}}%
\def\RB{\psCalc{\psk@ZB*\psk@m/2}}% les rayons
\def\OB{\psCalc{\RA+\RB}}%
\def\RAp{\psCalc{(\RA*2-2.5*0.2)/2}}% cercles de pied
\def\RBp{\psCalc{(\RB*2-2.5*0.2)/2}}%
% la vitesse de rotation
\def\OMEGAA{-1}%
\def\OMEGAB{\psCalc{(-\OMEGAA)*\psk@ZA/\psk@ZB}}%
\def\ANGLE{\psCalc{\psk@wheelrotation}}% degrees
\def\ANGLErad{\psCalc{\ANGLE*3.14/180}}% radians
\def\nombrePoints{\psCalc{trunc(2*\ANGLE+5,0)}}%
% positionnement angulaire des 2 points de fixation de l'élastique
\def\thetaA{\psCalc{(\psk@thetaA)*3.14/180}}%
\def\thetaB{\psCalc{(\psk@thetaB)*3.14/180}}%
% les coordonnées des 2 points
\def\xA{\psCalc{0.9*\RAp*cos(\thetaA+\OMEGAA*\ANGLErad)}}%
\def\yA{\psCalc{sin(\thetaA+\OMEGAA*\ANGLErad)*\RAp*0.9}}%
\def\xB{\psCalc{cos(\thetaB+\OMEGAB*\ANGLErad)*\RBp*0.9}}%
\def\yB{\psCalc{sin(\thetaB+\OMEGAB*\ANGLErad)*\RBp*0.9+\OB}}%
% le milieu
\def\xM{\psCalc{(\xA+\xB)/2}}\def\yM{\psCalc{(\yA+\yB)/2}}%
\ThreeDput[normal=0 0 1](0,0,0){%
\psgrid[subgriddiv=0,gridlabels=0pt]%\psframe(-5,-5)(5,7)
\rput(0.05,-0.05){\psSpirographB[circles=false,polarangle=90,fillstyle=solid,color1=black,color2=black]}%
\psSpirographB[circles=false,polarangle=90,fillstyle=solid]%
\parametricplot[linecolor=red,plotpoints=\nombrePoints,algebraic,linewidth=0.1]{0}{\ANGLErad}{
(\RAp*0.9*cos(\thetaA+\OMEGAA*t)+\RBp*0.9*cos(\thetaB+\OMEGAB*t))/2|
(\RAp*0.9*sin(\thetaA+\OMEGAA*t)+\RBp*0.9*sin(\thetaB+\OMEGAB*t)+\OB)/2}%
\psline{->}(0,0)(0,1)\psline{->}(0,0)(1,0)%
% les cercles de contact
\pscircle[linestyle=dotted](0,0){\RA}\pscircle[linestyle=dotted](0,\OB){\RB}%
% les cercles de pied
%\pscircle[linestyle=dotted](0,0){\RAp}
%\pscircle[linestyle=dotted](0,\OB){\RBp}
}%
% les tiges de fixation des extrémités de l'élastique
\ThreeDput[normal=0 1 0](\xA,\yA,0){\psline[linewidth=0.1]{-*}(0,0)(0,1)\pnode(0,1){P1}}%
\ThreeDput[normal=0 1 0](\xB,\yB,0){\psline[linewidth=0.1]{-*}(0,0)(0,1)\pnode(0,1){P2}}%
% le milieu
\ThreeDput[normal=0 1 0](\xM,\yM,0){\pnodes(0,1){P3}(0,0){P4}}%
\psline[linecolor=blue](P1)(P2)%
\psline[linecolor=red]{->}(P3)(P4)%
\psdot[linecolor=blue](P3)%
\end@SpecialObj
\ignorespaces}
%
\def\psSpirographB{\def\pst@par{}\pst@object{psSpirographB}}
\def\psSpirographB@i{\@ifnextchar({\psSpirographB@ii}{\psSpirographB@ii(0,0)}}
\def\psSpirographB@ii(#1){%
\begin@SpecialObj
\pst@@getcoor{#1}%
\addto@pscode{%
\pst@coor /t@@y ED /t@@x ED
/cm {\pst@number\psunit mul } bind def
/Z1 \psk@ZA def
/m1 \psk@m def
/Z2 \psk@ZB def
/m2 \psk@m def
/ap \psk@ap def
/facteurRayonRaccord {\psk@Rarct mul} def
/polarAngle \psk@polarangle def
/color1 {\pst@usecolor\pscolora } def
/color2 {\pst@usecolor\pscolorb } def
/colorcircles {\pst@usecolor\pscolorc } def
/curvecolor {\pst@usecolor\pscolord} def
/linecolor {\pst@usecolor\pslinecolor} def
/ni \psk@holenumber def ni 8 gt { /ni 8 def } if
/thetamax \psk@thetamax def
Z1 2 mod 1 eq { /Z1 Z1 1 sub def } if
Z2 2 mod 1 eq { /Z2 Z2 1 sub def } if
/HolePos \psk@HolePos def
HolePos 0 lt HolePos 2 ge or { /HolePos 1.5 def } if
/Fill { \psk@opacityalpha .setopacityalpha fill } def
/R1 Z1 m1 mul 2 div def
/R2 Z2 m1 mul 2 div def
/ki 1 ni 9 div sub def
/r2 m1 Z2 mul 2 div def
/qi Z1 Z2 div 1 sub def
/qi2 Z1 Z2 div 1 add def
%
tx@spirographDict begin
%%%% definition de la roue dentee %%%%%%
/Roue3d {
% arc de développante
/tabArcDev [ 0 1 ThetaTdeg { /i@ exch def [i@ devCercle] } for ] def
/n@ tabArcDev length def
/tabDent [
% l'arc de developpante initial
tabArcDev aload pop
% l'arc ce cercle de tete
DeltaT 0.1 2Beta DeltaT sub {/i@ exch def [Rt cm i@ cos mul Rt cm i@ sin mul] } for
% le symetrique de l'arc de developpante par rapport a l'axe de la dent
n@ 1 sub -1 0 { /compteur exch def [tabArcDev compteur get aload pop symAxe] } for
] def
% tracé de la dent
/n2@ tabDent length def
newpath
ptC moveto
0 1 Z@ 1 sub
{ /i@ exch AngleDent mul def
\ifPst@spirograph@int
wheel 2 eq { ptA RotDent ptB RotDent Rarct arct ptB RotDent lineto }
{ ptA RotDent lineto ptB RotDent lineto } ifelse
\else
Rp Rb eq { ptA RotDent lineto ptB RotDent lineto }
{ ptA RotDent ptB RotDent Rarct arct ptB RotDent lineto } ifelse
\fi
0 1 n2@ 1 sub { /compteur exch def tabDent compteur get aload pop RotDent lineto } for
\ifPst@spirograph@int
wheel 2 eq { Rp Rb eq { ptA' RotDent lineto ptC' RotDent lineto }
{ ptA' RotDent ptC' RotDent Rarct arct ptC' RotDent lineto } ifelse }
{ ptA' RotDent lineto ptC' RotDent lineto } ifelse
\else
Rp Rb eq { ptA' RotDent lineto ptC' RotDent lineto }
{ ptA' RotDent ptC' RotDent Rarct arct ptC' RotDent lineto } ifelse
\fi
} for
} def % Roue3d
%
%%%%%%%%%%%%%%%%%5
thetamax 0 le { /pas -1 def }{ /pas 1 def } ifelse
/tabSpirograph [ 0 pas thetamax {/i_ exch def [ i_ coorPen3 ] } for ] def
% gsave
% tabSpirograph 0 get aload pop moveto
% 1 1 tabSpirograph length 1 sub {/nP exch def tabSpirograph nP get aload pop lineto } for
% curvecolor
% \pst@number\pscurvewidth SLW
% stroke
% grestore
%%%%%%%%%%%%%%%
/AngleRotation \psk@wheelrotation def
%%% Les dessins de l'engrenage %%%%%%
%%%%%%%%%% Roue N°1 %%%%%%%%%%%%%%%%%
\ifPst@spirograph@notdrawWheel
\else
/wheel 1 def
gsave
t@@x t@@y translate
m1 Z1
\ifPst@spirograph@int
Datas2 Calculs Beta_ AngleRotation sub rotate Roue3d COURONNE closepath
\ifx\psk@fillstyle\relax\else color1 fill \fi
Roue3d closepath linecolor stroke
COURONNE closepath linecolor stroke
\ifPst@spirograph@circles Circles \fi
\else
Datas1 Calculs Beta_ AngleRotation sub rotate Roue3d AXE closepath
\ifx\psk@fillstyle\relax\else color1 fill \fi
Roue3d closepath linecolor stroke
AXE closepath
\ifx\psk@fillstyle\relax\else 0.8 setgray fill \fi
AXE closepath linecolor stroke
CLAVETTE
\ifx\psk@fillstyle\relax\else 0 0.125 0.25 0.25 setcmykcolor fill \fi
CLAVETTE linecolor stroke
\ifPst@spirograph@circles Circles \fi
\fi
grestore
\fi
%%%%%%%%%% Roue N°2 %%%%%%%%%%%%%%%%%
/wheel 2 def
gsave
m2 Z2 Datas1
Calculs
/a@ex m2 Z1 Z2 add mul 2 div cm def % entraxe engrenage exterieur
/a@in m2 Z1 Z2 sub mul 2 div cm def % entraxe engrenage interieur
\ifPst@spirograph@int
a@in polarAngle cos mul t@@x add a@in polarAngle sin mul t@@y add translate
Beta_ Z1 Z2 div AngleRotation mul sub polarAngle Z1 Z2 sub Z2 div mul sub rotate
\else
a@ex polarAngle cos mul t@@x add a@ex polarAngle sin mul t@@y add translate
DeltaSdeg DeltaP add neg 180 Z2 div add 180 add Z1 Z2 div AngleRotation mul add polarAngle Z1 Z2 add Z2 div mul add rotate
\fi
Roue3d
AXE
closepath
\ifx\psk@fillstyle\relax\else color2 fill \fi
Roue3d
closepath
linecolor
stroke
AXE
closepath
\ifx\psk@fillstyle\relax\else 0.8 setgray fill \fi
AXE
closepath
linecolor
stroke
CLAVETTE
\ifx\psk@fillstyle\relax\else 0 0.125 0.25 0.25 setcmykcolor fill \fi
CLAVETTE
linecolor
stroke
\ifPst@spirograph@circles Circles \fi
grestore
end
}%
\end@SpecialObj
\ignorespaces
}% % fin de la commande PSTricks
%
\catcode`\@=\PstAtCode\relax
%
\endinput
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