path: root/Master/texmf-dist/tex/latex/bodegraph/bodegraph.sty

% !TeX root = bodegraph.tex

\NeedsTeXFormat{LaTeX2e}[1999/01/01]
\ProvidesPackage{bodegraph}[2009/04/06]

\RequirePackage{tikz}
\RequirePackage{ifthen}
\RequirePackage{ifsym}


\usetikzlibrary{shapes,arrows,backgrounds,decorations.markings}

%macros commande schéma-blocs

\def\valpi{3.1415957}
\def\valpas{10}
\def\Unitx{}
\def\Unity{}


\newcounter{idGnuplot}

\newcommand{\OrdBode}[1]{\def\valpas{#1}}

\newcommand{\UnitedB}{
\def\Unitx{rad/s}
\def\Unity{dB}
}

\newcommand{\UniteDegre}{
\def\Unitx{rad/s}
\def\Unity{$~^\circ$}
}

\tikzset{
    ref points/.style={circle,draw, black, opacity=0.7, 
    fill, minimum size= 2pt, inner sep=0},
    gnuplot def/.style={samples=50,id=\arabic{idGnuplot},prefix=gnuplot/\jobname/},
    Bode lines/.style={very thick, blue},
    Bode lines 2/.style={Bode lines, red},
    asymp lines/.style={Bode lines,thin},
    asymp lines 2/.style={bode line 2,thin},
    semilog lines/.style={line width=0.35mm, red},
    semilog lines 2/.style={semilog lines, brown!50 },
    semilog half lines/.style={semilog lines 2, dashed },
    semilog label x/.style={semilog lines,below,font=\tiny},
    semilog label y/.style={semilog lines,right,font=\tiny},
    Black lines/.style={very thick, blue},
    Black grid/.style={ultra thin,brown},
    Black abaque mag/.style={gray,ultra thin,dashed,smooth},
    Black abaque phase/.style={gray,ultra thin,smooth},
    Black label points/.style={font=\tiny},
    Black label axes/.style={Black grid, font=\tiny},
    Nyquist lines/.style={very thick, blue},
    Nyquist grid/.style={ultra thin,brown},
    Nyquist label axes/.style={Nyquist grid,font=\tiny},
    Nyquist label points/.style={font=\tiny},
    Temp lines/.style={very thick, blue},
    Temp grid/.style={ultra thin,brown},
    Temp label axes/.style={Temp grid, font=\tiny},
    Temp label points/.style={font=\tiny},
    Abaque grid/.style={ultra thin,brown!80},
    Abaque lines/.style={thick, blue,smooth},
}


\newcommand{\semilog}{\@ifstar\semilogS\semilogNS}
\newcommand{\semilogNS}[5][]{
\pgfmathparse{int(#3-1)}\let\Xmax\pgfmathresult
\foreach \ee in{#2,...,\Xmax}{
    \foreach \x in {1,2,3,4,5,6,7,8,9}{
\draw[semilog lines 2] ({log10(\x)+\ee},#4) -- ({log10(\x)+\ee},#5);}
\draw[semilog lines] (\ee,#4)node[semilog label x]{$10^{\ee}$} -- ({\ee},#5);
};
\draw[semilog lines] ({#3},#4)node[semilog label x]{$10^{#3}$} -- ({#3},#5);
\pgfmathparse{int(#4+\valpas)}
\let\Valsuivante\pgfmathresult 
\foreach \yy in  {#4,\Valsuivante,...,#5}{
\draw[semilog lines] (#2,\yy) node[semilog label y,left]{$\yy$} -- ({#3},\yy);};
\node[semilog label y, node distance=0.3em]at (#2,#5) { \Unity};
\node[semilog label x, right,node distance=0.8em]at (#3,#4){ \Unitx};
\def\Unitx{}
\def\Unity{}
}
\newcommand{\semilogS}[5][]{
\semilog[#1]{#2}{#3}{#4}{#5}
\pgfmathparse{int(#3-1)}\let\Xmax\pgfmathresult
\foreach \ee in{#2,...,\Xmax}{
    \foreach \x in {1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5,9.5}{
\draw[semilog half lines] ({log10(\x)+\ee},#4) -- ({log10(\x)+\ee},#5);}
};
}


\newcommand{\semilogNG}[2]{
\pgfmathparse{int(#1-1)}\let\Xmax\pgfmathresult
\foreach \ee in{0,...,\Xmax}{
    \foreach \x in {1,2,3,4,5,6,7,8,9}{
\draw[semilog lines 2] ({log10(\x)+\ee},0) -- ({log10(\x)+\ee},#2);}
};
\draw[semilog lines] ({#1},0) -- ({#1},#2);
\pgfmathparse{int(0+\valpas)}
\let\Valsuivante\pgfmathresult 
\foreach \yy in  {0,\Valsuivante,...,#2}{
\draw[semilog lines] (0,\yy) -- ({#1},\yy);};
\node[semilog label y, node distance=0.3em]at (0,#2) {\tiny \Unity};
\node[semilog label x, right,node distance=0.8em]at (#1,0){\tiny \Unitx};
\def\Unitx{}
\def\Unity{}
\pgfmathparse{int(#1-1)}\let\Xmax\pgfmathresult
\foreach \ee in{0,...,\Xmax}{
    \foreach \x in {1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5,9.5}{
\draw[semilog half lines] ({log10(\x)+\ee},0) -- ({log10(\x)+\ee},#2);}
};
}


\newcommand{\KAmp}[1]{20*log10(abs(#1))}
\newcommand{\KArg}[1]{0}

\newcommand{\POAmp}[2]{20*log10(abs(#1/sqrt(1+(#2*10**t)**2)))}

\newcommand{\POAmpng}[2]{20*log10(abs(#1/sqrt(1+(#2*10^(\t))^2)))}

\newcommand{\POAmpAsymp}[2]{(t<log10(1/(#2))?20*log10(#1):+20*log10(#1/(#2))-20*log10(10**t))}
\newcommand{\POArg}[2]{-180/\valpi*atan(#2*10**t)}
\newcommand{\POArgAsymp}[2]{(t<log10(1/(#2))? 0:-90)}
\newcommand{\POAmpReel}[2]{20*log10(abs(#1/sqrt(1+(#2*t)**2)))}
\newcommand{\POArgReel}[2]{-180/\valpi*atan(#2*t)}

\newcommand{\SOAmp}[3]{20*log10(abs(#1/sqrt((1-(10**t/#3)**2)**2+(2*#2*(10**t/#3))**2)))}
\newcommand{\SOAmpAsymp}[3]{(t<log10(#3)?20*log10(#1):+20*log10(#1)+40*log10(#3)-40*log10(10**t))}
\newcommand{\SOArg}[3]{180/\valpi*(atan((#3**2-(10**t)**2)/(2*#2*#3*10**t))-\valpi/2)}
\newcommand{\SOArgAsymp}[3]{(t<log10(#3)? 0:-180)}
\newcommand{\SOAmpReel}[3]{20*log10(abs(#1/sqrt((1-(t/#3)**2)**2+(2*#2*(t/#3))**2)))}
\newcommand{\SOArgReel}[3]{180/\valpi*(atan((#3**2-(t)**2)/(2*#2*#3*t))-\valpi/2)}

\newcommand{\IntAmp}[1]{20*log10(abs(#1/(10**t)))}
\newcommand{\IntArg}[1]{-90}

%Retard R(p)=exp(-T*p)
\newcommand{\RetAmp}[1]{0}
\newcommand{\RetArg}[1]{-#1*10**t}

%Correcteur PI \PIAmp K*(1+Ti*p)/(Ti*p)
\newcommand{\PIAmp}[2]{\IntAmp{1}+20*log10(#1/#2)-\POAmp{1}{#2}}
\newcommand{\PIArg}[2]{\IntArg{1}+(\POArg{#1}{#2})*(-1)}
\newcommand{\PIAmpAsymp}[2]{\IntAmp{1}+20*log10(#1/#2)-\POAmpAsymp{1}{#2}}
\newcommand{\PIArgAsymp}[2]{\IntArg{1}+(\POArgAsymp{#1}{#2})*(-1)}

%Correcteur PID série \PIDAmp K*(1+Ti*p)/(Ti*p)(1+Td*p)
\newcommand{\PIDAmp}[3]{\IntAmp{1}+20*log10(#1/#2)-\POAmp{1}{#2}-\POAmp{1}{#3}}
\newcommand{\PIDArg}[3]{\IntArg{1}-\POArg{#1}{#2}-\POArg{1}{#3} }
\newcommand{\PIDAmpAsymp}[3]{\IntAmp{1}+20*log10(#1/#2)-\POAmpAsymp{1}{#2}-\POAmpAsymp{1}{#3}}
\newcommand{\PIDArgAsymp}[3]{\IntArg{1}-\POArgAsymp{#1}{#2}-\POArgAsymp{1}{#3} }

%Correcteur PD \PDAmp  K*(1+Td*p)
\newcommand{\PDAmp}[2]{20*log10(abs(#1*sqrt(1+(#2*10**t)**2)))}
\newcommand{\PDArg}[2]{-\POArg{(1)}{#2}}
\newcommand{\PDAmpAsymp}[2]{(t<log10(1/#2)?20*log10(#1):+20*log10(#1*#2)+20*log10(10**t))}
\newcommand{\PDArgAsymp}[2]{-\POArgAsymp{(1)}{#2}}

%Correcteur Avance de phase (Retard) C(p)=K(1+a*T1*p)/(1+T1*p)
\newcommand{\APAmp}[3]{\POAmp{#1}{#2}+\PDAmp{1}{(#3*#2)}}
\newcommand{\APArg}[3]{\POArg{#1}{#2}+\PDArg{1}{(#3*#2)}}
\newcommand{\APAmpAsymp}[3]{\POAmpAsymp{#1}{#2}+\PDAmpAsymp{1}{(#3*#2)}}
\newcommand{\APArgAsymp}[3]{\POArgAsymp{#1}{#2}+\PDArgAsymp{1}{(#3*#2)}}

%Correcteur Retard de phase (Retard) C(p)=K(1+T1*p)/(1+b*T1*p)
\newcommand{\RPAmp}[3]{\PDAmp{#1}{#2}+\POAmp{1}{(#3*#2)}}
\newcommand{\RPArg}[3]{\PDArg{#1}{#2}+\POArg{1}{(#3*#2)}}
\newcommand{\RPAmpAsymp}[3]{\PDAmpAsymp{#1}{#2}+\POAmpAsymp{1}{(#3*#2)}}
\newcommand{\RPArgAsymp}[3]{\PDArgAsymp{#1}{#2}+\POArgAsymp{1}{(#3*#2)}}

%Premier ordre généralisé C(p)=K(a1+a2*p)/(b1+b2*p)
\newcommand{\POgAmp}[5]{\POAmp{(#1*#2/#4)}{(#5/#4)}-\POAmp{1}{(#3/#2)}}
\newcommand{\POgArg}[5]{\POArg{(#1*#2/#4)}{(#5/#4)}-\POArg{1}{(#3/#2)}}
\newcommand{\POgAmpAsymp}[5]{\POAmpAsymp{(#1*#2/#4)}{(#5/#4)}-\POAmpAsymp{1}{(#3/#2)}}
\newcommand{\POgArgAsymp}[5]{\POArgAsymp{(#1*#2/#4)}{(#5/#4)}-\POArgAsymp{1}{(#3/#2)}}



\newcommand{\SOncArg}[4]{
\pgfmathparse{#1/#2}\let\ValK\pgfmathresult
\pgfmathparse{sqrt(#2/#4)}\let\ValW\pgfmathresult
\pgfmathparse{#3/#1*\ValW/2}\let\ValZ\pgfmathresult
\SOArg{\ValK}{\ValZ}{\ValW}}

\newcommand{\SOBlack}[3]{
\SOArg{#1}{#2}{3},\SOAmp{#1}{#2}{3}
}

\newcommand{\POBlack}[2]{
\POArg{#1}{#2},\POAmp{#1}{#2}
}




\def\CorpsPol{\tiny}
\def\puce{\tiny $\circ$}




\newcommand{\BodeGraph}{\@ifstar\BodeGraphText\BodeGraphNoText}
%vielles définitions
\newcommand{\BodeAmp}{\@ifstar\BodeGraphText\BodeGraphNoText}
\newcommand{\BodeArg}{\@ifstar\BodeGraphText\BodeGraphNoText}

\newcommand{\BodeGraphNoText}[3][]{
\stepcounter{idGnuplot}
\draw [Bode lines, gnuplot def,domain=#2,#1] plot[parametric,] 
function{log10(10**t),#3};}

\newcommand{\BodeGraphText}[4][]{
\stepcounter{idGnuplot}
\draw [Bode lines, gnuplot def,domain=#2,#1] plot[parametric,] 
function{log10(10**t),#3}node #4;}





\newcommand{\BodeAmpPointA}{\BodePoint}

\newcommand{\BodePoint}[3][gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\BodeGraph*[gnuplot def,#1,samples=2,,only marks,mark=.]{\LW:\LW}{#3}{[name=NBode,ref points]{}}
};
}

\newcommand{\BlackGraph}{\@ifstar\BlackGraphText\BlackGraphNoText}
\newcommand{\BlackGraphNoText}[3][Black lines,gnuplot def]{
\stepcounter{idGnuplot}
\draw [Black lines,gnuplot def,domain=#2,#1] plot[parametric,] 
function{#3};}
\newcommand{\BlackGraphText}[4][Black lines,gnuplot def]{
\stepcounter{idGnuplot}
\draw [Black lines,gnuplot def,domain=#2,#1] plot[parametric,] 
function{#3}node#4;}


\newcommand{\BlackPoint}{\@ifstar\BlackPointPos\BlackPointNoPos}
\newcommand{\BlackPointNoPos}[3][gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\BlackGraph*[Black lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{[right,Black label points]{ \W} node[name=NBlack,ref points]{}}
};
}
\newcommand{\BlackPointPos}[3][gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W/\Pos in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\BlackGraph*[Black lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{[\Pos,Black label points]{ \W} node[name=NBlack,ref points]{}}
};
}

\newcommand{\BlackText}{\@ifstar\BlackTextNoPoint\BlackTextPoint}
\newcommand{\BlackTextPoint}[3][gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W/\Pos/\Ttext in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\BlackGraph*[Black lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{[\Pos]{\CorpsPol \Ttext }node[name=NBlack,ref points]{}}
};
}
\newcommand{\BlackTextNoPoint}[3][gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W/\Pos/\Ttext in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\BlackGraph*[Black lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{[\Pos]{\CorpsPol \Ttext }node[name=NBlack]{}}
};
}


\newcommand{\NyquistGraph}{\@ifstar\NyquistGraphText\NyquistGraphNoText}
\newcommand{\NyquistGraphNoText}[4][Nyquist lines,gnuplot def]{
\stepcounter{idGnuplot}
\draw [Nyquist lines,gnuplot def,domain=#2,#1] plot[parametric,] 
function{10**((#3)/20)*cos(\valpi/180*(#4)),10**((#3)/20)*sin(\valpi/180*(#4))};}
\newcommand{\NyquistGraphText}[5][Nyquist lines,gnuplot def]{
\stepcounter{idGnuplot}
\draw [Nyquist lines,gnuplot def,domain=#2,#1] plot[parametric,] 
function{10**((#3)/20)*cos(\valpi/180*(#4)),10**((#3)/20)*sin(\valpi/180*(#4))}node#5;}

\newcommand{\NyquistPoint}{\@ifstar\NyquistPointPos\NyquistPointNoPos}
\newcommand{\NyquistPointNoPos}[4][Nyquist lines,gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\NyquistGraph*[Nyquist lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{#4}{[right,Nyquist label points]{\W} node[ref points]{}}
};
}
\newcommand{\NyquistPointPos}[4][Nyquist lines,gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W/\Pos in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\NyquistGraph*[Nyquist lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{#4}{[\Pos,Nyquist label points]{\W}node[ref points]{}}
};
}

\newcommand{\NyquistText}{\@ifstar\NyquistTextNoPoint\NyquistTextPoint}
\newcommand{\NyquistTextPoint}[4][Nyquist lines,gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W/\Pos/\Ttext in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\NyquistGraph*[Nyquist lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{#4}{[\Pos,Nyquist label points]{\Ttext}node[name=NNyquist,ref points]{}}
};
}
\newcommand{\NyquistTextNoPoint}[4][Nyquist lines,gnuplot def]{
\stepcounter{idGnuplot}
\foreach \W/\Pos/\Ttext in {#2}{
\pgfmathparse{log10(\W)}
\let\LW\pgfmathresult 
\NyquistGraph*[Nyquist lines,gnuplot def,#1,samples=2,only marks,mark=.]
{\LW:\LW}{#3}{#4}{[\Pos,Nyquist label points]{ \Ttext} node[name=NNyquist]{}}
};
}





\def\valgridNx{1cm}
\def\valgridNy{1cm}



\newcommand{\NyquistGrid}{\@ifstar\NyquistGridStar\NyquistGridNoStar}

\newcommand{\NyquistGridStar}[1][]{
\begin{pgfonlayer}{background}
\draw[xstep=\valgridNx ,ystep=\valgridNy,Nyquist grid,#1] (current bounding box.south west) grid (current bounding box.north east);
\draw[-latex,Nyquist label axes](current bounding box.west|-0,0) --(current bounding box.east|-0,0)--++(0.2,0)node[above,Nyquist label axes]{ $\mathcal{R}_e$};
\draw[-latex,,Nyquist label axes](current bounding box.south-|0,0) --(current bounding box.north-|0,0)--++(0,0.2)node[right,Nyquist label axes]{$\mathcal{I}_m$};
\end{pgfonlayer}
}
\newcommand{\NyquistGridNoStar}[1][]{
\begin{pgfonlayer}{background}
\node(PointCritique) at (-1,0){};
\draw[dotted,,Nyquist label axes,dotted] (0,0) circle (1);
\draw[xstep=\valgridNx ,ystep=\valgridNy,Nyquist grid,#1] (current bounding box.south west) grid (current
bounding box.north east);
\draw[-latex,,Nyquist label axes](current bounding box.west|-0,0) --(current bounding box.east|-0,0)--++(0.2,0)node[above,,Nyquist label axes]{$\mathcal{R}_e$};
\draw[-latex,,Nyquist label axes](current bounding box.south-|0,0) --(current bounding box.north-|0,0)--++(0,0.5)node[right,,Nyquist label axes]{$\mathcal{I}_m$};
\node[ref points](PointCritique) at (-1,0){};
\foreach \xx in {-1,1}
{\node[above,black] at (\xx,0){\tiny \xx};};
\foreach \xx in {-1,0,1}
{\node[above right,black] at (0,\xx){\tiny \xx};};
\end{pgfonlayer}
}



\def\valgridBx{45}
\def\valgridBy{10}
\def\valmaxBf{-180}

\newcommand{\BlackGrid}{\@ifstar\BlackGridStar\BlackGridNoStar}
\newcommand{\BlackGridStar}{
\begin{pgfonlayer}{background}
\coordinate (OO) at (0,0); \coordinate[right of= OO,node distance=1em] (OOt);
\draw[-latex,Black label axes](current bounding box.west|-0,0) --(OOt)node[above]{\tiny $~^\circ$};
\draw[-latex,Black label axes](current bounding box.south-|0,0) --(current bounding box.north-|0,0)coordinate[name=finaxe,pos=1.01]--(finaxe)node[right]{\tiny dB};
\draw[xstep=\valgridBx ,ystep=\valgridBy,Black grid] (current bounding box.south west) grid (current
bounding box.north east);
\end{pgfonlayer}
}
\newcommand{\BlackGridNoStar}{
\begin{pgfonlayer}{background}
\node(PointCritique) at (-180,0){};
\node(Pointzero) at (-0,0){};
\node(Pointmax) at (\valmaxBf,0){};
\coordinate (OO) at (0,0); \coordinate[right of= OO,node distance=1em] (OOt);
\draw[xstep=\valgridBx ,ystep=\valgridBy,Black grid] (current bounding box.south west) grid (current
bounding box.north east);
\draw[-latex,Black label axes](current bounding box.west|-0,0) --(OOt)node[above]{\tiny $~^\circ$};
\draw[-latex,Black label axes](current bounding box.south-|0,0) --(current bounding box.north-|0,0)node[right]{\tiny dB};

\node[ref points](PointCritique) at (-180,0){};

\foreach \xx in {0,-\valgridBx,...,\valmaxBf}{\node[below,Black label axes] at (\xx,0){\tiny \xx};};
\foreach \xx in {-\valgridBy,+\valgridBy}{\node[right,Black label axes] at (0,\xx){\tiny \xx};};
\end{pgfonlayer}
}

\newcommand{\RepTemp}{\@ifstar\RepTempText\RepTempNoText}

\newcommand{\RepTempNoText}[3][Temp lines,gnuplot def]{
\stepcounter{idGnuplot}
\draw [Temp lines,gnuplot def,domain=#2,#1] plot function{#3};
}
\newcommand{\RepTempText}[4][Temp lines,gnuplot def]{
\stepcounter{idGnuplot}
\draw [Temp lines, gnuplot def,domain=#2,#1] plot function{#3}node #4;
}

\def\valgridx{1}
\def\valmaxx{1}
\def\valgridy{1}
\def\valmaxy{1}
\def\UnitS{s}


\newcommand{\TempGrid}{\@ifstar\TempGridStar\TempGridNoStar}
\newcommand{\TempGridNoStar}[1][]{
\begin{pgfonlayer}{background}
\node(Pointzero) at (-0,0){};
\draw[xstep=\valgridx ,ystep=\valgridy,Temp grid,#1] (current bounding box.south west) grid (current
bounding box.north east);
\draw[-latex,Temp label axes](current bounding box.west|-0,0) --(current bounding box.east|-0,0)coordinate[name=finaxe,pos=1.01]--(finaxe)node[above]{\tiny $t$};
\draw[-latex,Temp label axes](current bounding box.south-|0,0) --(current bounding box.north-|0,0)node[right]{\tiny \UnitS};
\foreach \xx in {0,\valgridx,...,\valmaxx}
{\node[below,Temp label axes] at (\xx,0){\tiny \xx};};
\foreach \xx in {0,\valgridy,...,\valmaxy}
{\node[left,Temp label axes] at (0,\xx){\tiny \xx};};
\end{pgfonlayer}
}
\newcommand{\TempGridStar}[1][]{
\begin{pgfonlayer}{background}
\node(Pointzero) at (-0,0){};
\draw[-latex,Temp label axes](current bounding box.west|-0,0) --(current bounding box.east|-0,0)coordinate[name=finaxe,pos=1.01]--(finaxe);
\draw[-latex,Temp label axes](current bounding box.south-|0,0) --(current bounding box.north-|0,0);
\end{pgfonlayer}
}



\newcommand{\AbaqueBlack}{\@ifstar\AbaqueBlackStar\AbaqueBlackNoStar}
\newcommand{\AbaqueBlackNoStar}{
\begin{pgfonlayer}{background}
\IsoModule
\IsoArgument
\end{pgfonlayer}
}
\newcommand{\AbaqueBlackStar}{
\IsoModule
\IsoArgument
}

\tikzstyle{styleIsoM}=[Black abaque mag]
\newcommand{\StyleIsoM}[1][Black abaque mag]{
\tikzstyle{styleIsoM}=[#1]
}

\tikzstyle{styleIsoA}=[Black abaque phase]
\newcommand{\StyleIsoA}[1][Black abaque phase]{
\tikzstyle{styleIsoA}=[#1]
}

\newcommand{\IsoModule}[1][-30,-25,-20,-15,-12,-10,-8,-6,-5,-4,-3,-2,-1,-0.5,-0.2,0,0.2,0.5,1,2,2.3,3,4,5,6,8,10]{
\foreach \dbi in {#1}{
\draw[Black abaque mag,styleIsoM] plot coordinates {\csname ISOM\dbi \endcsname } node{\tiny $\dbi\mathrm{dB}$};
};
}

\newcommand{\IsoArgument}[1][359,357,354,350,345,340,330,315,300,285,270,255,240,225,210,195,%
190,170,165,150,135,120,105,90,75,60,45,30,20,15,10,6,3,1]{
\foreach \di in {#1}{
\draw[Black abaque phase,styleIsoA] plot coordinates {\csname ISOA-\di \endcsname } node{\tiny $-\di^\circ$};
};
}







%============Abaque temps de réponse 2nd ordre==========

\newcommand{\AbaqueTRsecond}{
\begin{scope}[Abaque grid]
\foreach \x/\xtext in {0.01/0.01,0.05/0.05,0.1/0.1,0.5/0.5,0.7/0.7,1/1,5/5,10/10,50/50}
{\draw ({log10(\x)},2.5) -- ({log10(\x)},0) node[below,rotate=45,left]{\tiny \xtext};};

\foreach \y/\ytext in{3/3,5/5,10/10,30/30,50/50,100/100,300/300}{
\draw (-2.2,{log10(\y)})node[left]{\tiny \ytext} -- (1.7,{log10(\y)});
};
\draw[-latex] (-2.2,0) -- (1.8,0)node[above]{\small$z$};
\draw[-latex] (-2.2,0) -- (-2.2,2.6)node[right]{\small $T_r\cdot\omega_n$};
\end{scope}

\draw[Abaque lines] plot coordinates {(-2.145, 2.459) (-2.135, 2.454) (-2.125, 2.450) (-2.115, 2.445) (-2.105, 2.440) (-2.095, 2.435) (-2.085, 2.430) (-2.075, 2.425) (-2.065, 2.420) (-2.055, 2.414) (-2.045, 2.409) (-2.035, 2.404) (-2.025, 2.398) (-2.015, 2.393) (-2.005, 2.388) (-1.995, 2.382) (-1.985, 2.376) (-1.975, 2.371) (-1.965, 2.365) (-1.955, 2.359) (-1.945, 2.353) (-1.935, 2.347) (-1.925, 2.341) (-1.915, 2.334) (-1.905, 2.328) (-1.895, 2.322) (-1.885, 2.315) (-1.875, 2.309) (-1.865, 2.302) (-1.855, 2.295) (-1.845, 2.288) (-1.835, 2.281) (-1.825, 2.274) (-1.815, 2.267) (-1.805, 2.259) (-1.795, 2.252) (-1.785, 2.244) (-1.775, 2.237) (-1.765, 2.229) (-1.755, 2.221) (-1.745, 2.212) (-1.735, 2.204) (-1.725, 2.195) (-1.715, 2.187) (-1.705, 2.178) (-1.695, 2.169) (-1.685, 2.160) (-1.675, 2.150) (-1.665, 2.140) (-1.655, 2.130) (-1.645, 2.120) (-1.635, 2.111) (-1.625, 2.100) (-1.615, 2.089) (-1.605, 2.078) (-1.595, 2.067) (-1.585, 2.055) (-1.575, 2.043) (-1.565, 2.041) (-1.555, 2.029) 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}


\newcommand{\AbaqueDepassement}{

\begin{scope}[Abaque grid]
\foreach \x in{0.01,0.05,0.1,0.3,0.5,0.7,1}{
\draw ({log10(\x)},0) -- ({log10(\x)},-2)node[below,rotate=45,left]{\tiny \x};};
\foreach \x in{0.01,0.05,0.1,0.3,0.5,0.7,1}{
\draw (0,{log10(\x)}) -- (-2,{log10(\x)})node[left]{\tiny \x};};
\coordinate (coinbas) at (0,{log10(0.01)});
\coordinate (coinhaut) at ({log10(0.01)},0);
\coordinate[right of=coinbas, node distance=1em] (coinbt);
\coordinate[above of=coinhaut, node distance=1em] (coinht);
\draw[-latex] ({log10(0.01)},{log10(0.01)}) -- (coinbt) node[above]{z};
\draw[-latex] ({log10(0.01)},{log10(0.01)}) -- (coinht) node[right]{D};
\end{scope}
\begin{scope}
\clip (0,0) rectangle (-2,-2);
\foreach \NN in {1,2,3,4,5,6,7,8}{
\draw[Abaque lines,domain=0.01:0.99] plot ({log10(\x)},{log10(exp(-\NN*\valpi*\x/(sqrt(1-(\x)^2))))});
\node at({log10(0.08)},{log10(exp(-\NN*\valpi*0.08/(sqrt(1-(0.08)^2))))}){\tiny$D_\NN$};
};
\end{scope}

\begin{scope}[shift={(-1.95,-1.95)}]
\node[above right,fill=white]{
\begin{tikzpicture}[xscale=1/8,yscale=1.8]
\draw[,color=red,domain=0:20,samples=200,smooth] plot
(\x,{1-1.02*exp(-0.2*\x)*sin((0.979*\x+1.369) r)});
\draw[-latex] (0,0) -- (20,0);
\draw[-latex] (0,0) -- (0,1.55);
\draw (0,1)node[left]{\tiny 1} -- (20,1);
\foreach \NN in {1,2,3,4}{
\pgfmathsetmacro{\tmm}{\NN*\valpi/(sqrt(1-0.2^2))}
\draw (\tmm,1) -- node[right]{\tiny$ D_\NN$}(\tmm,{1-1.02*exp(-0.2*\tmm)*sin((0.979*\tmm+1.369) r)});
};
\end{tikzpicture}

};
\end{scope}
}



%========================= Courbes de Black================
%les lignes ci dessous contiennent les commandes \ISOMxx et \ISOAxx appelées dans le tracé des courbes isomodules et isoargument 

%====Iso Module==============
%\input{isom.txt}

\expandafter\def\csname ISOM-30\endcsname {(-350., -29.7250) (-340., -29.7374) (-330., -29.7576) (-320., -29.7850) (-310., -29.8190) (-300., -29.8582) (-290., -29.9016) (-280., -29.9478) (-270., -29.9956) (-260., -30.0432) (-250., -30.0896) (-240., -30.1330) (-230., -30.1722) (-220., -30.2060) (-210., -30.2336) (-200., -30.2538) (-190., -30.2662) (-180., -30.2704) (-170., -30.2662) (-160., -30.2538) (-150., -30.2336) (-140., -30.2060) (-130., -30.1722) (-120., -30.1330) (-110., -30.0896) (-100., -30.0432) (-90., -29.9956) (-80., -29.9478) (-70., -29.9016) (-60., -29.8582) (-50., -29.8190) (-40., -29.7850) (-30., -29.7576) (-20., -29.7374) (-10., -29.7250)}

 \expandafter\def\csname ISOM-25\endcsname {(-350., -24.5046) (-340., -24.5268) (-330., -24.5626) (-320., -24.6116) (-310., -24.6718) (-300., -24.7416) (-290., -24.8190) (-280., -24.9012) (-270., -24.9862) (-260., -25.0712) (-250., -25.1536) (-240., -25.2308) (-230., -25.3006) (-220., -25.3608) (-210., -25.4098) (-200., -25.4456) (-190., -25.4678) (-180., -25.4752) (-170., -25.4678) (-160., -25.4456) (-150., -25.4098) (-140., -25.3608) (-130., -25.3006) (-120., -25.2308) (-110., -25.1536) (-100., -25.0712) (-90., -24.9862) (-80., -24.9012) (-70., -24.8190) (-60., -24.7416) (-50., -24.6718) (-40., -24.6116) (-30., -24.5626) (-20., -24.5268) (-10., -24.5046)}

 \expandafter\def\csname ISOM-20\endcsname {(-350., -19.0980) (-340., -19.1372) (-330., -19.2012) (-320., -19.2883) (-310., -19.3956) (-300., -19.5199) (-290., -19.6578) (-280., -19.8047) (-270., -19.9563) (-260., -20.1078) (-250., -20.2548) (-240., -20.3926) (-230., -20.5170) (-220., -20.6244) (-210., -20.7114) (-200., -20.7754) (-190., -20.8146) (-180., -20.8278) (-170., -20.8146) (-160., -20.7754) (-150., -20.7114) (-140., -20.6244) (-130., -20.5170) (-120., -20.3926) (-110., -20.2548) (-100., -20.1078) (-90., -19.9563) (-80., -19.8047) (-70., -19.6578) (-60., -19.5199) (-50., -19.3956) (-40., -19.2883) (-30., -19.2012) (-20., -19.1372) (-10., -19.0980)}

 \expandafter\def\csname ISOM-15\endcsname {(-350., -13.3227) (-340., -13.3925) (-330., -13.5066) (-320., -13.6617) (-310., -13.8537) (-300., -14.0767) (-290., -14.3239) (-280., -14.5879) (-270., -14.8604) (-260., -15.1330) (-250., -15.3969) (-240., -15.6440) (-230., -15.8671) (-220., -16.0590) (-210., -16.2142) (-200., -16.3284) (-190., -16.3981) (-180., -16.4216) (-170., -16.3981) (-160., -16.3284) (-150., -16.2142) (-140., -16.0590) (-130., -15.8671) (-120., -15.6440) (-110., -15.3969) (-100., -15.1330) (-90., -14.8604) (-80., -14.5879) (-70., -14.3239) (-60., -14.0767) (-50., -13.8537) (-40., -13.6617) (-30., -13.5066) (-20., -13.3925) (-10., -13.3227)}

 \expandafter\def\csname ISOM-12\endcsname {(-350., -9.52058) (-340., -9.61916) (-330., -9.78090) (-320., -10.0013) (-310., -10.2747) (-300., -10.5930) (-290., -10.9470) (-280., -11.3256) (-270., -11.7169) (-260., -12.1082) (-250., -12.4868) (-240., -12.8408) (-230., -13.1592) (-220., -13.4324) (-210., -13.6529) (-200., -13.8145) (-190., -13.9132) (-180., -13.9465) (-170., -13.9132) (-160., -13.8145) (-150., -13.6529) (-140., -13.4324) (-130., -13.1592) (-120., -12.8408) (-110., -12.4868) (-100., -12.1082) (-90., -11.7169) (-80., -11.3256) (-70., -10.9470) (-60., -10.5930) (-50., -10.2747) (-40., -10.0013) (-30., -9.78090) (-20., -9.61916) (-10., -9.52058)}

 \expandafter\def\csname ISOM-10\endcsname {(-350., -6.73998) (-340., -6.86436) (-330., -7.06858) (-320., -7.34790) (-310., -7.69530) (-300., -8.10138) (-290., -8.55428) (-280., -9.03990) (-270., -9.54238) (-260., -10.0449) (-250., -10.5305) (-240., -10.9835) (-230., -11.3895) (-220., -11.7369) (-210., -12.0162) (-200., -12.2204) (-190., -12.3448) (-180., -12.3866) (-170., -12.3448) (-160., -12.2204) (-150., -12.0162) (-140., -11.7369) (-130., -11.3895) (-120., -10.9835) (-110., -10.5305) (-100., -10.0449) (-90., -9.54238) (-80., -9.03990) (-70., -8.55428) (-60., -8.10138) (-50., -7.69530) (-40., -7.34790) (-30., -7.06858) (-20., -6.86436) (-10., -6.73998)}

 \expandafter\def\csname ISOM-8\endcsname {(-350., -3.64298) (-340., -3.79992) (-330., -4.05844) (-320., -4.41368) (-310., -4.85798) (-300., -5.38034) (-290., -5.96602) (-280., -6.59660) (-270., -7.25060) (-260., -7.90454) (-250., -8.53518) (-240., -9.12086) (-230., -9.64322) (-220., -10.0875) (-210., -10.4428) (-200., -10.7013) (-190., -10.8581) (-180., -10.9108) (-170., -10.8581) (-160., -10.7013) (-150., -10.4428) (-140., -10.0875) (-130., -9.64322) (-120., -9.12086) (-110., -8.53518) (-100., -7.90454) (-90., -7.25060) (-80., -6.59660) (-70., -5.96602) (-60., -5.38034) (-50., -4.85798) (-40., -4.41368) (-30., -4.05844) (-20., -3.79992) (-10., -3.64298)}

 \expandafter\def\csname ISOM-6\endcsname {(-350., -.249992e-1) (-340., -.223240) (-330., -.551664) (-320., -1.00638) (-310., -1.58045) (-300., -2.26226) (-290., -3.03418) (-280., -3.87164) (-270., -4.74370) (-260., -5.61586) (-250., -6.45328) (-240., -7.22516) (-230., -7.90702) (-220., -8.48108) (-210., -8.93576) (-200., -9.26418) (-190., -9.46238) (-180., -9.52866) (-170., -9.46238) (-160., -9.26418) (-150., -8.93576) (-140., -8.48108) (-130., -7.90702) (-120., -7.22516) (-110., -6.45328) (-100., -5.61586) (-90., -4.74370) (-80., -3.87164) (-70., -3.03418) (-60., -2.26226) (-50., -1.58045) (-40., -1.00638) (-30., -.551664) (-20., -.223240) (-10., -.249992e-1)}

 \expandafter\def\csname ISOM-5\endcsname {(-350., 2.10292) (-340., 1.87991) (-330., 1.50911) (-320., .992734) (-310., .336154) (-300., -.449816) (-290., -1.34661) (-280., -2.32572) (-270., -3.34910) (-260., -4.37246) (-250., -5.35162) (-240., -6.24840) (-230., -7.03436) (-220., -7.69098) (-210., -8.20734) (-200., -8.57810) (-190., -8.80114) (-180., -8.87548) (-170., -8.80114) (-160., -8.57810) (-150., -8.20734) (-140., -7.69098) (-130., -7.03436) (-120., -6.24840) (-110., -5.35162) (-100., -4.37246) (-90., -3.34910) (-80., -2.32572) (-70., -1.34661) (-60., -.449816) (-50., .336154) (-40., .992734) (-30., 1.50911) (-20., 1.87991) (-10., 2.10292)}

 \expandafter\def\csname ISOM-4\endcsname {(-350., 4.57498) (-340., 4.32394) (-330., 3.90448) (-320., 3.31604) (-310., 2.56062) (-300., 1.64608) (-290., .590758) (-280., -.572580) (-270., -1.79519) (-260., -3.01788) (-250., -4.18114) (-240., -5.23648) (-230., -6.15096) (-220., -6.90644) (-210., -7.49486) (-200., -7.91432) (-190., -8.16538) (-180., -8.24884) (-170., -8.16538) (-160., -7.91432) (-150., -7.49486) (-140., -6.90644) (-130., -6.15096) (-120., -5.23648) (-110., -4.18114) (-100., -3.01788) (-90., -1.79519) (-80., -.572580) (-70., .590758) (-60., 1.64608) (-50., 2.56062) (-40., 3.31604) (-30., 3.90448) (-20., 4.32394) (-10., 4.57498)}

 \expandafter\def\csname ISOM-3\endcsname {(-350., 7.59694) (-340., 7.31420) (-330., 6.83864) (-320., 6.16484) (-310., 5.28818) (-300., 4.20962) (-290., 2.94300) (-280., 1.52493) (-270., .206478e-1) (-260., -1.48378) (-250., -2.90170) (-240., -4.16834) (-230., -5.24688) (-220., -6.12356) (-210., -6.79734) (-200., -7.27296) (-190., -7.55560) (-180., -7.64944) (-170., -7.55560) (-160., -7.27296) (-150., -6.79734) (-140., -6.12356) (-130., -5.24688) (-120., -4.16834) (-110., -2.90170) (-100., -1.48378) (-90., .206478e-1) (-80., 1.52493) (-70., 2.94300) (-60., 4.20962) (-50., 5.28818) (-40., 6.16484) (-30., 6.83864) (-20., 7.31420) (-10., 7.59694)}

 \expandafter\def\csname ISOM-2\endcsname {(-350., 11.6312) (-340., 11.3123) (-330., 10.7715) (-320., 9.99484) (-310., 8.96494) (-300., 7.66574) (-290., 6.09462) (-280., 4.28488) (-270., 2.32922) (-260., .373594) (-250., -1.43615) (-240., -3.00730) (-230., -4.30646) (-220., -5.33644) (-210., -6.11302) (-200., -6.65386) (-190., -6.97276) (-180., -7.07802) (-170., -6.97276) (-160., -6.65386) (-150., -6.11302) (-140., -5.33644) (-130., -4.30646) (-120., -3.00730) (-110., -1.43615) (-100., .373594) (-90., 2.32922) (-80., 4.28488) (-70., 6.09462) (-60., 7.66574) (-50., 8.96494) (-40., 9.99484) (-30., 10.7715) (-20., 11.3123) (-10., 11.6312)}

 \expandafter\def\csname ISOM-1\endcsname {(-350., 18.1531) (-340., 17.7931) (-330., 17.1755) (-320., 16.2720) (-310., 15.0390) (-300., 13.4165) (-290., 11.3378) (-280., 8.77768) (-270., 5.86826) (-260., 2.95872) (-250., .398766) (-240., -1.68001) (-230., -3.30242) (-220., -4.53566) (-210., -5.43912) (-200., -6.05656) (-190., -6.41658) (-180., -6.53496) (-170., -6.41658) (-160., -6.05656) (-150., -5.43912) (-140., -4.53566) (-130., -3.30242) (-120., -1.68001) (-110., .398766) (-100., 2.95872) (-90., 5.86826) (-80., 8.77768) (-70., 11.3378) (-60., 13.4165) (-50., 15.0390) (-40., 16.2720) (-30., 17.1755) (-20., 17.7931) (-10., 18.1531)}

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%==== ISo Argument============

%\input{isoa.txt}
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 \expandafter\def\csname ISOA-300\endcsname {(-182.4, .199974) (-184.8, .380746) (-184.8, .380746) (-187.2, .542668) (-189.6, .686712) (-189.6, .686712) (-192., .813548) (-194.4, .923342) (-199.2, 1.09418) (-204., 1.20164) (-208.8, 1.24750) (-213.6, 1.23221) (-218.4, 1.15568) (-223.2, 1.01679) (-228., .813548) (-232.8, .542748) (-237.6, .200060) (-242.4, -.220496) (-247.2, -.726508) (-252., -1.32916) (-256.8, -2.04262) (-261.6, -2.88662) (-266.4, -3.88986) (-271.2, -5.09422) (-276., -6.56396) (-280.8, -8.41006) (-285.6, -10.8377) (-290.3, -14.2191) (-290.4, -14.3075) (-292.7, -16.6696) (-295.1, -20.1180) (-295.2, -20.2980) (-297.5, -25.9580) (-299.9, -30)}

 \expandafter\def\csname ISOA-285\endcsname {(-182.1, .791144e-1) (-184.2, .145906) (-184.2, .145906) (-186.3, .200568) (-188.4, .243410) (-188.4, .243410) (-190.5, .274266) (-192.6, .293518) (-196.8, .296876) (-201., .253370) (-205.2, .162716) (-209.4, .238534e-1) (-213.6, -.164867) (-217.8, -.405536) (-222., -.701236) (-226.2, -1.05591) (-230.4, -1.47440) (-234.6, -1.96322) (-238.8, -2.53108) (-243., -3.18868) (-247.2, -3.95086) (-251.4, -4.83830) (-255.6, -5.87898) (-259.8, -7.11494) (-264., -8.61260) (-268.2, -10.4799) (-272.4, -12.9235) (-276.5, -16.3047) (-276.6, -16.4075) (-278.6, -18.7562) (-280.7, -22.1982) (-280.8, -22.4040) (-282.8, -28.0134) (-284.9, -31)}

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 \expandafter\def\csname ISOA-195\endcsname {(-180.3, -.171942) (-180.6, -.346264) (-180.6, -.346264) (-180.9, -.525808) (-181.2, -.709064) (-181.2, -.709064) (-181.5, -.895782) (-181.8, -1.08794) (-182.4, -1.48469) (-183., -1.90266) (-183.6, -2.34150) (-184.2, -2.80466) (-184.8, -3.29686) (-185.4, -3.81760) (-186., -4.37262) (-186.6, -4.96822) (-187.2, -5.60696) (-187.8, -6.29798) (-188.4, -7.05146) (-189., -7.87500) (-189.6, -8.78610) (-190.2, -9.80808) (-190.8, -10.9653) (-191.4, -12.3006) (-192., -13.8851) (-192.6, -15.8198) (-193.2, -18.3138) (-193.7, -21.1428) (-193.8, -21.8446) (-194.0, -23.4234) (-194.3, -26.5098) (-194.4, -27.8592) (-194.6, -31.3678) (-194.9, -37)}

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 \expandafter\def\csname ISOA-45\endcsname {(-177.3, .390550) (-174.6, .745898) (-174.6, .745898) (-171.9, 1.06863) (-169.2, 1.36127) (-169.2, 1.36127) (-166.5, 1.62558) (-163.8, 1.86339) (-158.4, 2.26482) (-153., 2.57438) (-147.6, 2.79852) (-142.2, 2.94152) (-136.8, 3.00592) (-131.4, 2.99312) (-126., 2.90262) (-120.6, 2.73300) (-115.2, 2.48094) (-109.8, 2.14154) (-104.4, 1.70766) (-99., 1.16935) (-93.60, .512752) (-88.20, -.281694) (-82.80, -1.24187) (-77.40, -2.40934) (-72., -3.84880) (-66.60, -5.66978) (-61.20, -8.07798) (-55.90, -11.4561) (-55.80, -11.5354) (-53.20, -13.9056) (-50.50, -17.3582) (-50.40, -17.5171) (-47.80, -23.2126) (-45.1, -29)}

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 \expandafter\def\csname ISOA-20\endcsname {(-176.8, 1.22769) (-173.6, 2.27912) (-173.6, 2.27912) (-170.4, 3.19248) (-167.2, 3.99428) (-167.2, 3.99428) (-164., 4.70334) (-160.8, 5.33370) (-154.4, 6.39868) (-148., 7.24968) (-141.6, 7.92498) (-135.2, 8.45030) (-128.8, 8.84274) (-122.4, 9.11400) (-116., 9.27130) (-109.6, 9.31872) (-103.2, 9.25766) (-96.80, 9.08638) (-90.40, 8.80052) (-84., 8.39220) (-77.60, 7.84916) (-71.20, 7.15346) (-64.80, 6.27826) (-58.40, 5.18288) (-52., 3.80320) (-45.60, 2.03034) (-39.20, -.340598) (-32.90, -3.70510) (-32.80, -3.77164) (-29.70, -6.14956) (-26.50, -9.60380) (-26.40, -9.73772) (-23.30, -15.4780) (-20.1, -27)}

 \expandafter\def\csname ISOA-15\endcsname {(-176.7, 1.67836) (-173.4, 3.06000) (-173.4, 3.06000) (-170.1, 4.22658) (-166.8, 5.22900) (-166.8, 5.22900) (-163.5, 6.10180) (-160.2, 6.86840) (-153.6, 8.14824) (-147., 9.16150) (-140.4, 9.96460) (-133.8, 10.5932) (-127.2, 11.0711) (-120.6, 11.4140) (-114., 11.6325) (-107.4, 11.7324) (-100.8, 11.7167) (-94.20, 11.5849) (-87.60, 11.3332) (-81., 10.9547) (-74.40, 10.4375) (-67.80, 9.76404) (-61.20, 8.90788) (-54.60, 7.82860) (-48., 6.46222) (-41.40, 4.70016) (-34.80, 2.33732) (-28.30, -1.02352) (-28.20, -1.08786) (-25.00, -3.46652) (-21.70, -6.92058) (-21.60, -7.05070) (-18.40, -12.7979) (-15.1, -26)}

 \expandafter\def\csname ISOA-10\endcsname {(-176.6, 2.50696) (-173.2, 4.42546) (-173.2, 4.42546) (-169.8, 5.97046) (-166.4, 7.25556) (-166.4, 7.25556) (-163., 8.34748) (-159.6, 9.29024) (-152.8, 10.8360) (-146., 12.0420) (-139.2, 12.9920) (-132.4, 13.7368) (-125.6, 14.3091) (-118.8, 14.7304) (-112., 15.0147) (-105.2, 15.1707) (-98.40, 15.2031) (-91.60, 15.1129) (-84.80, 14.8973) (-78., 14.5499) (-71.20, 14.0597) (-64.40, 13.4094) (-57.60, 12.5731) (-50.80, 11.5104) (-44., 10.1578) (-37.20, 8.40678) (-30.40, 6.05244) (-23.70, 2.69572) (-23.60, 2.63314) (-20.30, .254046) (-16.90, -3.19986) (-16.80, -3.32614) (-13.50, -9.07978) (-10.1, -25)}

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 \expandafter\def\csname ISOA-3\endcsname {(-176.5, 6.70160) (-172.9, 10.5032) (-172.9, 10.5032) (-169.4, 13.0509) (-165.8, 15.0414) (-165.8, 15.0414) (-162.3, 16.5911) (-158.8, 17.8780) (-151.7, 19.9361) (-144.6, 21.4878) (-137.5, 22.6888) (-130.4, 23.6248) (-123.4, 24.3392) (-116.3, 24.8850) (-109.2, 25.2720) (-102.1, 25.5138) (-95.04, 25.6184) (-87.96, 25.5904) (-80.88, 25.4282) (-73.80, 25.1268) (-66.72, 24.6762) (-59.64, 24.0600) (-52.56, 23.2526) (-45.48, 22.2142) (-38.40, 20.8818) (-31.32, 19.1468) (-24.24, 16.8047) (-17.26, 13.4541) (-17.16, 13.3942) (-13.72, 11.0146) (-10.18, 7.56132) (-10.08, 7.44006) (-6.640, 1.67786) (-3.1, -23)}

 \expandafter\def\csname ISOA-1\endcsname {(-176.4, 13.2463) (-172.8, 18.2469) (-172.8, 18.2469) (-169.3, 21.3038) (-165.7, 23.5908) (-165.7, 23.5908) (-162.1, 25.3716) (-158.5, 26.8196) (-151.4, 29.0364) (-144.2, 30.7118) (-137.0, 31.9982) (-129.9, 32.9852) (-122.7, 33.7594) (-115.6, 34.3364) (-108.4, 34.7560) (-101.2, 35.0244) (-94.08, 35.1502) (-86.92, 35.1408) (-79.76, 34.9946) (-72.60, 34.7070) (-65.44, 34.2682) (-58.28, 33.6620) (-51.12, 32.8632) (-43.96, 31.8320) (-36.80, 30.5054) (-29.64, 28.7750) (-22.48, 26.4366) (-15.42, 23.0878) (-15.32, 23.0286) (-11.84, 20.6490) (-8.260, 17.1959) (-8.160, 17.0760) (-4.680, 11.3113) (-1.1, -20)}