%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %                                                               %
    %     tkz-base.sty         encodage : utf8                      %
    %                                                               %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %                                                               %
    %           Créé par Alain Matthes le 07-07-2007.               %
    %                                                               %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 15/09/2007
%% Objet :  Outils pour la création de graphiques géométriquesss

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% v2 modif de grid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tkz-base}[2008/02/17 v3.14 tkz-base]

\RequirePackage{etex}
\RequirePackage{xkeyval}[2005/11/25]
\RequirePackage{tikz}[2007/06/07]
\RequirePackage{fp,calc,tkz-arith}%\RequirePackage{ifthen}
\RequirePackage[np,autolanguage]{numprint}
\FPmessagesfalse%
   
\newcounter{cmdTKZ@tkzf@fct} 
\newcounter{tkz@tok}% il faut modifier
\newcounter{tkz@tempc}
\newcounter{tkz@cnt}% ???? utile
\newcounter{tkz@leg} 
\newcounter{tkz@nb@gon} 
\newlength{\tkz@tmplen}
\newlength{\tkzmathLen}  
\newdimen\tkz@ax
\newdimen\tkz@ay
\newdimen\tkz@bx
\newdimen\tkz@by
\newdimen\tkz@cx
\newdimen\tkz@cy
\newdimen\tkz@dx
\newdimen\tkz@dy  

\newdimen\tkz@Rapt
\newdimen\tkz@Rbpt
\newdimen\tkzpt@xa 
\newdimen\tkzpt@ya
\newdimen\tkz@tempdim
\newif\if@tkz@visible%
\@tkz@visiblefalse
\def\tkzmathresult{}

\def\nameedef#1{\expandafter\edef\csname #1\endcsname}
\def\nameuse#1{\csname #1\endcsname}
% % %<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% % %             sign of #1 
% % %<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% % 
% % \newdimen\tkz@dim
% % \newcommand*{\tkz@findsign}[1]{%
% % \tkz@dim=#1 pt\relax%
% % \ifdim\tkz@dim<0pt\relax%
% %   \edef\tkz@sign{0}\relax%%
% %   \else%
% %   \edef\tkz@sign{1}\relax%%
% %   \fi%
% % }%
% 

%<––––––––––––––––––––––––––––– autres tools ––––––––––––––––––––––––––––––––>   
\newcommand*\getdecimal[1]{%
  \expandafter\@getdecimal#1.\@nil
}

\def\@getdecimal#1.#2\@nil{%
  \ifx\empty#2\empty
    % Si #2 est vide, c'est qu'il n'y avait pas de point
    % dans la chaîne initiale
    \setcounter{tkz@tok}{0}%
   \global\def\decpart{}%
  \else
    % sinon c'est la chaîne qui suit le point décimal...
    \CountToken{#2}%
    % ... y compris le point en trop ajouté par \getdecimal  :-)
    \addtocounter{tkz@tok}{-1}%
    \@@getdecimal#2\@nil
  \fi
}
\def\@@getdecimal#1.\@nil{\global\def\decpart{#1}}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% code from JCC modifi
\newcommand\CountToken[1]{%
 \setcounter{tkz@tok}{0}%
  \expandafter\C@untToken#1\@nil
%modifi ajout du expandafter
}
\newcommand\C@untToken{%
  \afterassignment\C@untT@ken\let\CurrT@ken=
}
\newcommand\C@untT@ken{%
 \ifx\CurrT@ken\@nil \else
   \stepcounter{tkz@tok}%
   \expandafter\C@untToken
 \fi
}
% end code from JCC   
\newboolean{@twopt} \setboolean{@twopt}{false} 
\newcommand*{\twoptoff}{\ifnum \catcode`\:=13 \catcode`\:=12 \setboolean{@twopt}{true} \fi}
\newcommand*{\twopton}{\if@twopt \catcode`\:=13 \setboolean{@twopt}{false}  \fi}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>


%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                initialisation  des styles points et lignes
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               Setup   axe
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey [TKZ] {SUA} {gradsize}{}
\define@cmdkey [TKZ] {SUA} {lw}{}
\define@cmdkey [TKZ] {SUA} {tickwd}{}
\define@cmdkey [TKZ] {SUA} {tickb}{}
\define@cmdkey [TKZ] {SUA} {ticka}{}
\presetkeys    [TKZ] {SUA} {gradsize = \textstyle,%
                            lw       = 0.4pt,%
                            tickwd   = 0.8pt,%
                            tickb    = 2pt,%
                            ticka    = 2pt}{}

\newcommand*{\SetUpAxis}[1][]{\tkz@SetUpAxe[#1]}%
\def\tkz@SetUpAxe[#1]{%
\setkeys[TKZ]{SUA}{#1}% 
\presetkeys[TKZ]{tkzX}{gradsize = \cmdTKZ@SUA@gradsize,%
                       lw       = \cmdTKZ@SUA@lw,%
                       tickwd   = \cmdTKZ@SUA@tickwd,%
                       tickup   = \cmdTKZ@SUA@ticka,%
                       tickdn   = \cmdTKZ@SUA@tickb}{}
\presetkeys[TKZ]{tkzY}{gradsize = \cmdTKZ@SUA@gradsize,%
                       lw       = \cmdTKZ@SUA@lw,%
                       tickwd   = \cmdTKZ@SUA@tickwd,%
                       tickrt   = \cmdTKZ@SUA@ticka,%
                       ticklt   = \cmdTKZ@SUA@tickb}{}
}   
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               Setup   Segment todo !!!
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%  INITIALISATION
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\gdef\xgrad{1}
\gdef\ygrad{1}
\gdef\tkz@xa{0}
\gdef\tkz@xb{10}
\gdef\tkz@ya{0}
\gdef\tkz@yb{10}
\define@cmdkey [TKZ] {tkzInit} {xmin}{}
\define@cmdkey [TKZ] {tkzInit} {xmax}{}
\define@cmdkey [TKZ] {tkzInit} {xstep}{}
\define@cmdkey [TKZ] {tkzInit} {ymin}{}
\define@cmdkey [TKZ] {tkzInit} {ymax}{}
\define@cmdkey [TKZ] {tkzInit} {ystep}{}
\define@boolkey[TKZ] {tkzInit} {NO}[true]{}% interne
\presetkeys    [TKZ] {tkzInit} {%
                        xmin    = 0,%
                        xmax    = 10,%
                        xstep   = 1,%
                        ymin    = 0,%
                        ymax    = 10,%
                        ystep   = 1,%
                        NO      = false}{}
\newcommand*{\tkzInit}[1][]{\@tkzInit[#1]}% 
\def\@tkzInit[#1]{%
   \setkeys[TKZ]{tkzInit}{#1}%
   \setcounter{cmdTKZ@tkzf@fct}{0}
   \xdef\cmdTKZ@tkzInit@xorigine{0}
   \xdef\cmdTKZ@tkzInit@yorigine{0}
   \FPsgn\@xsgmin{\cmdTKZ@tkzInit@xmin}
   \FPsgn\@xsgmax{\cmdTKZ@tkzInit@xmax}
   \FPsgn\@ysgmin{\cmdTKZ@tkzInit@ymin}
   \FPsgn\@ysgmax{\cmdTKZ@tkzInit@ymax}
   \global\let\@xa\cmdTKZ@tkzInit@xmin
   \global\let\@xb\cmdTKZ@tkzInit@xmax
   \global\let\@ya\cmdTKZ@tkzInit@ymin
   \global\let\@yb\cmdTKZ@tkzInit@ymax
   \ifthenelse{%
      \(\equal{\@xsgmin}{\@xsgmax}\) \or \(\equal{\@ysgmin}{\@ysgmax}\)}{%
      \TKZ@tkzInit@NOtrue}{%
      \TKZ@tkzInit@NOfalse}%

   \ifTKZ@tkzInit@NO%
   \ifthenelse{%
      \equal{\@xsgmin}{\@xsgmax}}{%
   \FPadd{\cmdTKZ@tkzInit@xmax}{\cmdTKZ@tkzInit@xmax}{-\cmdTKZ@tkzInit@xmin}%
     \edef\cmdTKZ@tkzInit@xorigine{\cmdTKZ@tkzInit@xmin}
     \edef\cmdTKZ@tkzInit@xmin{0}}%
     {}%
   \ifthenelse{%
      \equal{\@ysgmin}{\@ysgmax}}{%
    \FPadd{\cmdTKZ@tkzInit@ymax}{\cmdTKZ@tkzInit@ymax}{-\cmdTKZ@tkzInit@ymin}%
     \edef\cmdTKZ@tkzInit@yorigine{\cmdTKZ@tkzInit@ymin}
     \edef\cmdTKZ@tkzInit@ymin{0}}%
     {}%
   \fi%
   \FPdiv{\tkz@xa}{\cmdTKZ@tkzInit@xmin}{\cmdTKZ@tkzInit@xstep}
   \FPdiv{\tkz@xb}{\cmdTKZ@tkzInit@xmax}{\cmdTKZ@tkzInit@xstep}
   \FPdiv{\tkz@ya}{\cmdTKZ@tkzInit@ymin}{\cmdTKZ@tkzInit@ystep}
   \FPdiv{\tkz@yb}{\cmdTKZ@tkzInit@ymax}{\cmdTKZ@tkzInit@ystep}
   \getdecimal{\cmdTKZ@tkzInit@xstep} % amélioration nb dec et integer
   \global\edef\cmdTKZ@tkzInit@xdec{\thetkz@tok}
   \getdecimal{\cmdTKZ@tkzInit@ystep}
   \global\edef\cmdTKZ@tkzInit@ydec{\thetkz@tok}
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey [TKZ] {CLI} {space}{}
\presetkeys    [TKZ] {CLI} {space = {}}{} 

\newcommand*{\tkzClip}[1][]{\tkz@Clip[#1]}%
\def\tkz@Clip[#1]{%
    \setkeys [TKZ]{CLI}{#1}% 
    \ifthenelse{\equal{\cmdTKZ@CLI@space}{}}{%   
        \clip (\tkz@xa,\tkz@ya) rectangle (\tkz@xb,\tkz@yb);}{% 
        \FPadd{\tkz@xxa}{\tkz@xa}{-\cmdTKZ@CLI@space}
        \FPadd{\tkz@yya}{\tkz@ya}{-\cmdTKZ@CLI@space}
        \FPadd{\tkz@xxb}{\tkz@xb}{\cmdTKZ@CLI@space}
        \FPadd{\tkz@yyb}{\tkz@yb}{\cmdTKZ@CLI@space} 
        \clip (\tkz@xxa,\tkz@yya)%
        rectangle (\tkz@xxb,\tkz@yyb);
}} 
%todo add options 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               Setup   point
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@boolkey[TKZ] {SUP} {noname}[true]{}
\define@boolkey[TKZ] {SUP} {nomark}[true]{}
\define@cmdkey [TKZ] {SUP} {mark}{}
\define@cmdkey [TKZ] {SUP} {size}{}
\define@cmdkey [TKZ] {SUP} {color}{}
\define@cmdkey [TKZ] {SUP} {style}{}
\define@cmdkey [TKZ] {SUP} {pos}{} 
\define@cmdkey [TKZ] {SUP} {posxlabel}{}
\define@cmdkey [TKZ] {SUP} {posylabel}{}
\define@boolkey[TKZ] {SUP} {label}[true]{}  
\presetkeys    [TKZ] {SUP} {%
               noname    = false,%
               nomark    = false,% 
               mark      = *,% 
               size      = 1pt,%
               color     = black,%
               label     = false,% 
               pos       = below right,%
               posxlabel = 3pt,%
               posylabel = 3pt}{} 
\newcommand*{\SetUpPoint}[1][]{\tkz@SetUpPt[#1]}%
\def\tkz@SetUpPt[#1]{%
\setkeys       [TKZ]{SUP}{#1}% 
\presetkeys    [TKZ]{pt}{%
               mark      = \cmdTKZ@SUP@mark,% 
               size      = \cmdTKZ@SUP@size,%
               color     = \cmdTKZ@SUP@color,% 
               pos       = \cmdTKZ@SUP@pos,% 
               posxlabel = \cmdTKZ@SUP@posxlabel,%
               posylabel = \cmdTKZ@SUP@posylabel}{}
\ifTKZ@SUP@noname%
    \presetkeys[TKZ]{pt}{noname = true}{}%
\else%
     \presetkeys[TKZ]{pt}{noname = false}{}%
\fi}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                       tkzPoint
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\tikzstyle{StyleMark}=[]
  
\define@boolkey [TKZ] {pt} {noname}[true]{}
\define@boolkey [TKZ] {pt} {nomark}[true]{}
\define@cmdkey  [TKZ] {pt} {name}{}
\define@cmdkey  [TKZ] {pt} {pos}{}
\define@cmdkey  [TKZ] {pt} {posxlabel}{}
\define@cmdkey  [TKZ] {pt} {posylabel}{}
\define@cmdkey  [TKZ] {pt} {mark}{}
\define@cmdkey  [TKZ] {pt} {color}{}
\define@cmdkey  [TKZ] {pt} {namecolor}{}
\define@cmdkey  [TKZ] {pt} {size}{}
\define@cmdkey  [TKZ] {pt} {k}{}
\define@boolkey [TKZ] {pt} {coord}[true]{}
\define@boolkey [TKZ] {pt} {label}[true]{}
\define@cmdkey  [TKZ] {pt} {xlabel}{}
\define@cmdkey  [TKZ] {pt} {ylabel}{}

\presetkeys[TKZ]{pt}{noname    = false,%
                     nomark    = false,% 
                     name      = {},%
                     coord     = false,%
                     label     = false,%
                     color     = black,%
                     namecolor = black,%
                     pos       = below right,%
                     posxlabel = 3pt,%
                     posylabel = 3pt,% 
                     xlabel    = {},%
                     ylabel    = {},%
                     size      = 1pt,%
                     k         = 1,%
                     mark      = *}{} 
% \@ifnextchar(%
% {\tkz@@ptNoStar[#1]}{}}%
% 
% \def\tkz@whatnode#1{\global\def\tkz@node{#1}}
\def\tkz@drawnode#1{\path[coordinate](\ptxa,\ptya) coordinate(#1);
\tkz@DrawPoint{#1}}
  
\newcommand*{\tkzPoint}{\@ifstar\tkzptStar\tkzptNoStar}
\newcommand*{\tkzptNoStar}[1][]{\tkz@ptNoStar[#1]}% 

\def\tkz@ptNoStar[#1](#2,#3)#{%  
    \setkeys[TKZ]{pt}{#1}%
    \FPeval\tkz@x{(#2)}
    \FPeval\tkz@y{(#3)}
    \FPadd{\ptxa}{\tkz@x}{-\cmdTKZ@tkzInit@xorigine}
    \FPadd{\ptya}{\tkz@y}{-\cmdTKZ@tkzInit@yorigine}
    \FPdiv{\ptxa}{\ptxa}{\cmdTKZ@tkzInit@xstep}
    \FPdiv{\ptya}{\ptya}{\cmdTKZ@tkzInit@ystep}
    \tkz@drawnode
}

\def\tkz@node#1{\path[coordinate](\ptxa,\ptya) coordinate(#1);
}   

\newcommand*{\tkzptStar}{\tkz@ptStar}%

\def\tkz@ptStar(#1,#2)#{%
    \FPeval\tkz@x{(#1)}
    \FPeval\tkz@y{(#2)}
    \FPadd{\ptxa}{\tkz@x}{-\cmdTKZ@tkzInit@xorigine}
    \FPadd{\ptya}{\tkz@y}{-\cmdTKZ@tkzInit@yorigine}
    \FPdiv{\ptxa}{\ptxa}{\cmdTKZ@tkzInit@xstep}
    \FPdiv{\ptya}{\ptya}{\cmdTKZ@tkzInit@ystep}
    \tkz@node
}
% dessin du point  nomark
% 	\node [circle,fill=red,inner sep=2pt]
\def\tkz@DrawPoint#1{%
\draw plot[mark size    = \cmdTKZ@pt@size,%
           mark         = \cmdTKZ@pt@mark,%
           mark options = {color=\cmdTKZ@pt@color},
           StyleMark] coordinates {(#1)};

% traitement du label
  \ifTKZ@pt@noname%pas de nom rien
  \else% si name={} alors on prend le nom du node sinon name
     \ifthenelse{\equal{\cmdTKZ@pt@name}{}}{%
     \def\cmdTKZ@pt@name{$#1$}}{}%
     \protected@edef\tkz@temp{%
        \noexpand \node[\cmdTKZ@pt@pos]}\tkz@temp at (#1)%
        {\textcolor{\cmdTKZ@pt@namecolor} {\cmdTKZ@pt@name}};%
   \fi
% traitement si coord 
  \ifTKZ@pt@coord%
     \ifthenelse{\equal{\cmdTKZ@pt@xlabel}{}}{%
        \TKZ@pt@labelfalse}{%
        \TKZ@pt@labeltrue}
        % \draw[fill=white,color=white,line width=1pt]%
        %       (#1)--(#1 |- xline);
         \draw[color=black,line width=.8pt,dashed,>=latex',->]%
               (#1)--(#1 |- xline)
         \ifTKZ@pt@label node[fill      = white,%
                              below     = \cmdTKZ@pt@posxlabel]%
                        {\cmdTKZ@pt@xlabel}%
          \fi;%
     \ifthenelse{\equal{\cmdTKZ@pt@ylabel}{}}{%
         \TKZ@pt@labelfalse}{%
         \TKZ@pt@labeltrue}
         % \draw[fill=white,color=white,line width=1pt]%
         %       (#1)--(#1 -| yline);
         \draw[color=black,line width=.8pt,dashed,>=latex',->]%
             (#1)--(#1 -| yline)
        \ifTKZ@pt@label node[fill    = white,%
                             left    = \cmdTKZ@pt@posylabel]%
                             {\cmdTKZ@pt@ylabel}%
         \fi;% 
% on retrace ???  ici ou après le fi
\draw plot[
          mark size    = \cmdTKZ@pt@size,%
          mark         = \cmdTKZ@pt@mark,%
          mark options = {color=\cmdTKZ@pt@color},
          StyleMark] coordinates {(#1)};
\fi%  end of coord
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                  Points   
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand*{\tkzPoints}{\@ifstar%
                         \tkzPointsStar%
                         \tkzPointsNoStar}

\newcommand*{\tkzPointsNoStar}[1][]{\tkz@PointsNoStar[#1]}% 
\def\tkz@PointsNoStar[#1](#2){%
    \setkeys[TKZ]{pt}{#1}%
\begingroup%
   \foreach \ptx/\pty/\name in {#2}{%
             \tkzPoint[#1](\ptx,\pty){\name}%
   }
\endgroup%
}
  
\newcommand*{\tkzPointsStar}{\tkz@PointsStar}%
\def\tkz@PointsStar(#1){%
\begingroup%
    \foreach \ptx/\pty/\name in {#1}{%
             \tkzPoint*(\ptx,\pty){\name}}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                     Draw Point   
% todo liste
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\tkzDrawPoint}[1][]{\tkz@drawpt[#1]}%
\def\tkz@drawpt[#1](#2){%
  \setkeys[TKZ]{pt}{#1}%
  \foreach \point in {#2}{%
       \tkz@DrawPoint{\point}}
} 

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                              SetOfPoints
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\tkzSetOfPoints}[1][]{\tkz@SetOfPoints[#1]}%
\def\tkz@SetOfPoints[#1](#2){%  
    \setkeys[TKZ]{pt}{#1}
    \setcounter{tkz@cnt}{1}
    \foreach \x/\y in {#2}{%
         \tkzPoint[#1,noname](\x,\y){tkzPt\thetkz@cnt}
         \stepcounter{tkz@cnt}}
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% macro d'affichage  % 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\tkz@showgrad}[1]{%
\FPifint{#1}\FPtrunc\tkz@result{#1}{0}\else\FPset\tkz@result{#1}\fi%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                 tkzX      todo améliorer les unités
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\tikzstyle{LabelXStyle}=[]
\tikzstyle{TicksXStyle}=[]
\tikzstyle{AxeXStyle}=[>=latex,->]

\define@cmdkey [TKZ] {tkzX} {pos}{}
\define@cmdkey [TKZ] {tkzX} {trig}{}
\define@cmdkey [TKZ] {tkzX} {lw}{}
\define@cmdkey [TKZ] {tkzX} {color}{}
\define@cmdkey [TKZ] {tkzX} {label}{}
\define@cmdkey [TKZ] {tkzX} {poslabel}{}
\define@boolkey[TKZ] {tkzX} {noticks}[true]{} 
\define@cmdkey [TKZ] {tkzX} {tickwd}{} 
\define@cmdkey [TKZ] {tkzX} {tickup}{} 
\define@cmdkey [TKZ] {tkzX} {tickdn}{}   
\define@boolkey[TKZ] {tkzX} {nograd}[true]{}
\define@cmdkey [TKZ] {tkzX} {gradsize}{} 
\define@boolkey[TKZ] {tkzX} {orig}[true]{}
\define@boolkey[TKZ] {tkzX} {unit}[true]{}
\presetkeys    [TKZ] {tkzX} {trig     = 0,%
                             lw       = 0.4 pt,
                             orig     = false,%
                             unit     = false,%
                             noticks  = false,%
                             nograd   = false,% 
                             gradsize = \textstyle,%  
                             pos      = {below = 3pt},%
                             color    = black,%
                             label    = $x$,%
                             poslabel = {below = 3pt},%
                             tickwd   = 0.8pt,%
                             tickup   = 1pt,%
                             tickdn   = 1pt}{}
\newcommand*{\tkzX}[1][]{\@tkzX[#1]}%
\def\@tkzX[#1]{%
   \setkeys[TKZ]{tkzX}{#1}% 
   \FPtrunc\posmax{\tkz@xb}{\cmdTKZ@tkzInit@xdec}%
   \FPtrunc\posmin{\tkz@xa}{\cmdTKZ@tkzInit@xdec}%
   \FPadd\tkz@xbsup{\tkz@xb}{.5}
   \path (\tkz@xa,0)--(\tkz@xb,0) node(xline){};%
   \protected@edef\tkz@temp{%
   \noexpand% 
   \draw[line width = \cmdTKZ@tkzX@lw,%
         color      = \cmdTKZ@tkzX@color,AxeXStyle]%
        (\tkz@xa,0)--(\tkz@xbsup,0)%
         node[\cmdTKZ@tkzX@poslabel,LabelXStyle]}\tkz@temp%
         {\cmdTKZ@tkzX@label};%
   \FPtrunc\xtkzero{0.0000000}{\cmdTKZ@tkzInit@xdec}% 
   \ifTKZ@tkzX@noticks%
   \else% 
    \ifnum\cmdTKZ@tkzX@trig=0%
   \FPtrunc\posmax{\posmax}{\cmdTKZ@tkzInit@xdec}% 
   \foreach \pos in {\posmin,...,\posmax}{%
       \FPtrunc\tkz@pos{\pos}{\cmdTKZ@tkzInit@xdec}%
       \protected@edef\tkz@temp{%
          \noexpand% 
          \draw[line width = \cmdTKZ@tkzX@tickwd,%
                shift      = {(\pos,0)}]%
                (0pt,\cmdTKZ@tkzX@tickup)--(0pt,-\cmdTKZ@tkzX@tickdn)%
                node[\cmdTKZ@tkzX@pos,inner sep = 0pt]%%
          }\tkz@temp%
          {\FPmul{\xgrad}{\pos}{\cmdTKZ@tkzInit@xstep}%
           \FPadd{\xgrad}{\xgrad}{\cmdTKZ@tkzInit@xorigine}%
           \FPtrunc\xgrad{\xgrad}{\cmdTKZ@tkzInit@xdec}%
           \ifTKZ@tkzX@orig% 
              \ifTKZ@tkzX@nograd\else\tkz@showgrad{\xgrad}%
                      $\cmdTKZ@tkzX@gradsize{\np{\tkz@result}}$%
              \fi\else%
              \ifTKZ@tkzInit@NO% 
                  \ifthenelse{\equal{\tkz@pos}{\posmin}}%
                   {}{\tkz@showgrad{\xgrad}%
                      $\cmdTKZ@tkzX@gradsize{\np{\tkz@result}}$}%
               \else%
                   \ifthenelse{\equal{\tkz@pos}{\xtkzero}}%
                    {\ifTKZ@tkzX@unit\tkz@showgrad{\xgrad}%
                      $\cmdTKZ@tkzX@gradsize{\np{\tkz@result}}$\fi}%
                    {\ifTKZ@tkzX@nograd%
                     \else\tkz@showgrad{\xgrad}%
                      $\cmdTKZ@tkzX@gradsize{\np{\tkz@result}}$\fi}%
                \fi%
           \fi%
          };%  end of draw
   }% end foreach
   \else% trig affichage
       \FPadd{\posmin}{\posmin}{0.5}%
       \FPdiv\nbtrigticksmax{\posmax}{\FPpi}%
       \FPdiv\nbtrigticksmin{\posmin}{\FPpi}%
       \FPmul\nbtrigticksmax{\nbtrigticksmax}{\cmdTKZ@tkzX@trig}%
       \FPmul\nbtrigticksmin{\nbtrigticksmin}{\cmdTKZ@tkzX@trig}%
       \FPround\nbtrigticksmin{\nbtrigticksmin}{0}% 
       \foreach \pos in {\nbtrigticksmin,...,\nbtrigticksmax}{%
            \FPmul\pospi{\pos}{\FPpi}\FPdiv\pospi{\pospi}{\cmdTKZ@tkzX@trig}%
                     \protected@edef\tkz@temp{%
          \noexpand\draw[line width = \cmdTKZ@tkzX@tickwd,%
                         shift      = {(\pospi,0)}]%
                      (0pt,\cmdTKZ@tkzX@tickup)--(0pt,-\cmdTKZ@tkzX@tickup)%
                      node[\cmdTKZ@tkzX@pos,%
                           text height = 8pt,%
                           inner sep   = 1pt]}\tkz@temp%
                {\tkz@reducfrac{\pos}{\cmdTKZ@tkzX@trig}\tkz@rfrac%
};%  end of draw
}% end foreach                              
\fi\fi% end ticks  
\ifTKZ@tkzInit@NO\else\ifTKZ@tkzX@unit%
%  on n'est à l'origine doc on peut placer l'unité 
          \draw[line width = \cmdTKZ@tkzX@tickwd,%
                inner sep  = 1pt] (0,0) -- (1,0)%
                node[below=3pt]%
                {$\cmdTKZ@tkzX@gradsize{\np{\cmdTKZ@tkzInit@xstep}}$};
           \draw[line width = \cmdTKZ@tkzX@tickwd,%
                 shift      = {(1,0)}]%
                (0pt,\cmdTKZ@tkzX@tickup)--(0pt,-\cmdTKZ@tkzX@tickdn);%
          \fi%  
   \fi%
}% todo macro pour l'affichage 

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 tkzY
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\tikzstyle{LabelYStyle}=[]
\tikzstyle{TicksYStyle}=[]
\tikzstyle{AxeYStyle}=[>=latex,->]

\define@cmdkey  [TKZ]{tkzY} {pos}{}
\define@cmdkey  [TKZ]{tkzY} {lw}{}
\define@cmdkey  [TKZ]{tkzY} {color}{}
\define@cmdkey  [TKZ]{tkzY} {label}{}
\define@cmdkey  [TKZ]{tkzY} {poslabel}{}
\define@boolkey [TKZ]{tkzY} {noticks}[true]{}
\define@cmdkey  [TKZ]{tkzY} {tickwd}{} 
\define@cmdkey  [TKZ]{tkzY} {tickrt}{} 
\define@cmdkey  [TKZ]{tkzY} {ticklt}{} 
\define@boolkey [TKZ]{tkzY} {nograd}[true]{}
\define@cmdkey  [TKZ]{tkzY} {gradsize}{}
\define@boolkey [TKZ]{tkzY} {orig}[true]{}
\define@boolkey [TKZ]{tkzY} {unit}[true]{}
\presetkeys     [TKZ]{tkzY} {lw       = 0.4 pt,
                             orig     = false,%
                             unit     = false,%
                             noticks  = false,%
                             nograd   = false,%
                             gradsize = \textstyle,% 
                             pos      = {left = 3pt},%
                             label    = $y$,%
                             color    = black,%
                             poslabel = {left = 3pt},%
                             tickwd   = 0.8pt,%
                             ticklt   = 1pt,%
                             tickrt   = 1pt}{}
\newcommand*{\tkzY}[1][]{\@tkzY[#1]}%
\def\@tkzY[#1]{%
   \setkeys[TKZ]{tkzY}{#1}% 
   \FPtrunc\posmax{\tkz@yb}{\cmdTKZ@tkzInit@ydec}%
   \FPtrunc\posmin{\tkz@ya}{\cmdTKZ@tkzInit@ydec}%
   \path (0,\tkz@ya)--(0,\tkz@yb) node(yline){};%
   \FPadd\tkz@ybsup{\tkz@yb}{.5}   
   \protected@edef\tkz@temp{%
   \noexpand% 
   \draw[line width = \cmdTKZ@tkzY@lw,%
         color      = \cmdTKZ@tkzY@color,AxeYStyle]%
        (0,\tkz@ya)--(0,\tkz@ybsup)%
        node[\cmdTKZ@tkzY@poslabel,LabelYStyle]}\tkz@temp%
        {\cmdTKZ@tkzY@label};%
   \FPtrunc\ytkzero{0.000000}{\cmdTKZ@tkzInit@ydec}%
   \ifTKZ@tkzY@noticks%
   \else%
   \foreach \pos in {\posmin,...,\posmax}{%
       \FPtrunc\tkz@pos{\pos}{\cmdTKZ@tkzInit@ydec}%
       \protected@edef\tkz@temp{%
       \noexpand% 
       \draw[line width = \cmdTKZ@tkzY@tickwd,%
            shift       = {(0,\pos)}]%
            (\cmdTKZ@tkzY@tickrt,0pt)--(-\cmdTKZ@tkzY@ticklt,0pt)%
            node[\cmdTKZ@tkzY@pos,inner sep = 0pt]}\tkz@temp%
         {\FPmul{\ygrad}{\pos}{\cmdTKZ@tkzInit@ystep}%
          \FPadd{\ygrad}{\ygrad}{\cmdTKZ@tkzInit@yorigine}
          \FPtrunc\ygrad{\ygrad}{\cmdTKZ@tkzInit@ydec}%
          \ifTKZ@tkzY@orig% 
              \ifTKZ@tkzY@nograd\else\tkz@showgrad{\ygrad}%
                         $\cmdTKZ@tkzY@gradsize{\np{\tkz@result}}$\fi%
          \else%
           \ifTKZ@tkzInit@NO% 
             \ifthenelse{\equal{\tkz@pos}{\posmin}}%
            {}{\tkz@showgrad{\ygrad}%
                 $\cmdTKZ@tkzY@gradsize{\np{\tkz@result}}$}%
        \else% 
          \ifthenelse{\equal{\tkz@pos}{\ytkzero}}%
            {\ifTKZ@tkzY@unit\tkz@showgrad{\ygrad}%
               $\cmdTKZ@tkzY@gradsize{\np{\tkz@result}}$\fi}%
            {\ifTKZ@tkzY@nograd%
             \else \tkz@showgrad{\ygrad}%
              $\cmdTKZ@tkzY@gradsize{\np{\tkz@result}}$\fi}%
        \fi%
    \fi%
   };%
  }%
\fi%
\ifTKZ@tkzInit@NO\else\ifTKZ@tkzY@unit%
  \draw[line width = 1pt,%
        inner sep  = 1pt] (0,0) -- (0,1)%
        node[left=3pt]%
       {$\cmdTKZ@tkzY@gradsize{\np{\cmdTKZ@tkzInit@ystep}}$};% 
  \draw[line width = \cmdTKZ@tkzY@tickwd,%
        shift      = {(0,1)}]%
      (\cmdTKZ@tkzY@tickrt,0pt)--(-\cmdTKZ@tkzY@ticklt,0pt);%
  \fi\fi%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                grid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey [TKZ]{tkzg} {color}{}
\define@cmdkey [TKZ]{tkzg} {subcolor}{}
\define@boolkey[TKZ]{tkzg} {sub}[true]{}
\define@cmdkey [TKZ]{tkzg} {subxstep}{}
\define@cmdkey [TKZ]{tkzg} {subystep}{}
\define@cmdkey [TKZ]{tkzg} {lw}{} 
\define@cmdkey [TKZ]{tkzg} {sublw}{} 
\presetkeys    [TKZ]{tkzg} {sub      = false,%
                            color    = darkgray,% 
                            subcolor = lightgray,% 
                            subxstep = 0.2,%
                            subystep = 0.2,%
                            lw       = .4 pt,%
                            sublw    = .3 pt}{}
\newcommand*{\tkzGrid}[1][]{\tkz@grid[#1]}%
\def\tkz@grid[#1]{%
\@ifnextchar(%
{\tkz@@grid[#1]}
{\tkz@@grid[#1](\@xa,\@ya)(\@xb,\@yb)}}
\def\tkz@@grid[#1](#2,#3)(#4,#5){%
    \setkeys[TKZ]{tkzg}{#1}% 
    \begingroup%
    \FPadd{\tkz@gxa}{#2}{-\cmdTKZ@tkzInit@xorigine}
    \FPadd{\tkz@gxb}{#4}{-\cmdTKZ@tkzInit@xorigine}
    \FPadd{\tkz@gya}{#3}{-\cmdTKZ@tkzInit@yorigine}
    \FPadd{\tkz@gyb}{#5}{-\cmdTKZ@tkzInit@yorigine}
    \FPdiv{\tkz@gxa}{\tkz@gxa}{\cmdTKZ@tkzInit@xstep}
    \FPdiv{\tkz@gya}{\tkz@gya}{\cmdTKZ@tkzInit@ystep}
    \FPdiv{\tkz@gxb}{\tkz@gxb}{\cmdTKZ@tkzInit@xstep}
    \FPdiv{\tkz@gyb}{\tkz@gyb}{\cmdTKZ@tkzInit@ystep}
    \ifTKZ@tkzg@sub%
      \FPdiv{\@subxstep}{\cmdTKZ@tkzg@subxstep}{\cmdTKZ@tkzInit@xstep}%
      \FPdiv{\@subystep}{\cmdTKZ@tkzg@subystep}{\cmdTKZ@tkzInit@ystep}%
      \draw [xstep      = \@subxstep cm,%
             ystep      = \@subystep cm,%
             color      = \cmdTKZ@tkzg@subcolor,%
             line width = \cmdTKZ@tkzg@sublw]%
             (\tkz@gxa,\tkz@gya) grid (\tkz@gxb,\tkz@gyb);%
    \fi%
    \draw [xstep      = 1 cm,%
           ystep      = 1 cm,%
           color      = \cmdTKZ@tkzg@color,%
           line width = \cmdTKZ@tkzg@lw]%
           (\tkz@gxa,\tkz@gya) grid (\tkz@gxb,\tkz@gyb);%
    \endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                repère
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\tikzstyle{RepStyle}=[->,>=latex]

\define@cmdkey[TKZ]{Rep}{lw}{}
\define@cmdkey[TKZ]{Rep}{xlabel}{}
\define@cmdkey[TKZ]{Rep}{ylabel}{}
\define@cmdkey[TKZ]{Rep}{poslabel}{}
\define@cmdkey[TKZ]{Rep}{xnorm}{}
\define@cmdkey[TKZ]{Rep}{ynorm}{}
\define@cmdkey[TKZ]{Rep}{color}{}
\define@cmdkey[TKZ]{Rep}{colorlabel}{}
\define@boolkey[TKZ]{Rep}{orig}[false]{}
\define@cmdkey[TKZ]{Rep}{LO}{}
\presetkeys[TKZ]{Rep}{%
                 lw          = 0.8pt,%
                 xlabel      = $\vec{\imath}$,%
                 ylabel      = $\vec{\jmath}$,%
                 poslabel    = 2pt,%
                 xnorm       = 1,%
                 ynorm       = 1,%
                 color       = black,%
                 colorlabel  = black,%
                 orig        = true,%
                 LO          = $O$}{}

\newcommand*{\tkzRep}[1][]{\tkz@Rep[#1]}%
\def\tkz@Rep[#1]{%
  \setkeys[TKZ]{Rep}{#1}%
  \begingroup%
  \draw [line width=\cmdTKZ@Rep@lw,RepStyle,%
  color=\cmdTKZ@Rep@color]%
         (0,0) to node[left  = \cmdTKZ@Rep@poslabel,%
                       color = \cmdTKZ@Rep@colorlabel]%
         {\cmdTKZ@Rep@ylabel}%
         (0,\cmdTKZ@Rep@ynorm);
  \draw [line width=\cmdTKZ@Rep@lw,RepStyle,%
  color=\cmdTKZ@Rep@color]%
        (0,0) to  node[below = \cmdTKZ@Rep@poslabel,%
                       color = \cmdTKZ@Rep@colorlabel]%
         {\cmdTKZ@Rep@xlabel}%
         (\cmdTKZ@Rep@xnorm,0);  
   \ifTKZ@Rep@orig%
     \node[below left] at (0,0) {\cmdTKZ@Rep@LO};%
   \fi%
   \endgroup% 
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               Setup   Segment
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\define@cmdkey [TKZ] {SUS} {color}{}
\define@cmdkey [TKZ] {SUS} {style}{}
\define@cmdkey [TKZ] {SUS} {lw}{}
\define@cmdkey [TKZ] {SUS} {symbol}{}
\define@cmdkey [TKZ] {SUS} {colorsymbol}{}
\define@cmdkey [TKZ] {SUS} {poslabel}{}
\define@cmdkey [TKZ] {SUS} {colorlabel}{}
\define@cmdkey [TKZ] {SUS} {time}{}
\presetkeys    [TKZ] {SUS} {%
                            color       = black,%
                            style       = solid,%
                            lw          = 0.4pt,%
                            symbol      = {},%  
                            colorsymbol = black,%
                            colorlabel  = black,%
                            poslabel    = 1pt,%
                            time        = .5}{}
\newcommand*{\SetUpSegment}[1][]{\tkz@SetUpSegment[#1]}%
\def\tkz@SetUpSegment[#1]{%
  \setkeys       [TKZ] {SUS} {#1}%
  \presetkeys    [TKZ] {seg} {%
                                color       = \cmdTKZ@SUS@color,%
                                style       = \cmdTKZ@SUS@style,%
                                lw          = \cmdTKZ@SUS@lw,%
                                symbol      = \cmdTKZ@SUS@symbol,%
                                colorsymbol = \cmdTKZ@SUS@colorsymbol,%
                                poslabel    = \cmdTKZ@SUS@poslabel,%
                                colorlabel  = \cmdTKZ@SUS@colorlabel}{}
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                   segment  (s)
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey [TKZ] {seg} {color}{}
\define@cmdkey [TKZ] {seg} {style}{}
\define@cmdkey [TKZ] {seg} {lw}{}
\define@cmdkey [TKZ] {seg} {symbol}{}
\define@cmdkey [TKZ] {seg} {colorsymbol}{}
\define@cmdkey [TKZ] {seg} {colorlabel}{}
\define@cmdkey [TKZ] {seg} {poslabel}{}
\define@cmdkey [TKZ] {seg} {label}{}
\define@cmdkey [TKZ] {seg} {time}{} 


\presetkeys[TKZ]{seg}{%
                            color       = black,%
                            style       = solid,%
                            lw          = 0.4pt,%
                            label       = {},%
                            symbol      = {},%  
                            colorsymbol = black,%
                            colorlabel  = black,%
                            poslabel    = 1pt,%
                            time        = .5}{}
\newcommand*{\tkzSegment}{\@ifstar\tkzSegmentStar\tkzSegmentNoStar}
\newcommand*{\tkzSegmentNoStar}[1][]{\tkz@SegmentNoStar[#1]}% 
\def\tkz@SegmentNoStar[#1](#2){% 
    \setkeys[TKZ]{seg}{#1}% 
    \begingroup%
    \foreach \deb/\fin in {#2}{%
       \ifthenelse{\equal{\cmdTKZ@seg@symbol}{}}
       {\draw[line width = \cmdTKZ@seg@lw,%
              color      = \cmdTKZ@seg@color,
                           \cmdTKZ@seg@style]%
             (\deb.center)--(\fin.center);}%
       {\protected@edef\tkz@temp{%
          \noexpand \draw[line width = \cmdTKZ@seg@lw,%
                          color      = \cmdTKZ@seg@color,%
                                       \cmdTKZ@seg@style]}\tkz@temp
          (\deb.center) to node[pos=\cmdTKZ@seg@time,sloped]%
            {\textcolor{\cmdTKZ@seg@colorsymbol}{\cmdTKZ@seg@symbol}}%
          (\fin.center);}%
      \ifthenelse{\equal{\cmdTKZ@seg@label}{}}{}{%
    \path (\deb.center) to  node[pos=\cmdTKZ@seg@time,above=\cmdTKZ@seg@poslabel,sloped]%
     {\textcolor{\cmdTKZ@seg@colorlabel}{\cmdTKZ@seg@label}} (\fin.center);}%
    }%
  \endgroup%
} 

\newcommand*{\tkzSegmentStar}[1][]{\tkz@SegmentStar[#1]}% 
\def\tkz@SegmentStar[#1](#2,#3)(#4,#5){%
  \setkeys[TKZ]{seg}{#1}% 
  \begingroup%
  \tkzPoint*(#2,#3){tkz@deb}
  \tkzPoint*(#4,#5){tkz@fin}
  \tkz@SegmentNoStar[#1](tkz@deb/tkz@fin)%
  \endgroup%
} 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                           Mark on        segment  (s)
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\tkzSegmentMark}[1][]{\@tkzSegM[#1]}%
\def\@tkzSegM[#1](#2){% 
    \setkeys[TKZ]{seg}{#1}% 
    \begingroup%
    \foreach \deb/\fin in {#2}{%
       \ifthenelse{\equal{\cmdTKZ@seg@symbol}{}}{}%
          {\protected@edef\tkz@temp{%
          \noexpand \path (\deb.center) to node[sloped]}\tkz@temp%
          {\textcolor{\cmdTKZ@seg@colorsymbol}{\cmdTKZ@seg@symbol}}%
           (\fin.center);}%
       \ifthenelse{\equal{\cmdTKZ@seg@label}{}}{}{%
         \path (\deb.center) to  node[above=\cmdTKZ@seg@poslabel,sloped]%
        {\textcolor{\cmdTKZ@seg@colorlabel}{\cmdTKZ@seg@label}} (\fin.center);}%
   }% end foreach
   \endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                 tkzXH
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
 \define@cmdkey [TKZ] {tkzXh} {left}{}
 \define@cmdkey [TKZ] {tkzXh} {right}{}
 \define@cmdkey [TKZ] {tkzXh} {posgrad}{}
 \presetkeys    [TKZ] {tkzXh} {%
                posgrad     = 6 pt,%
                left        = {},%
                right       = {}}{}

\newcommand*{\tkzXH}[1][]{\tkzX@h[#1]}%
\def\tkzX@h[#1]#2{%
\setkeys[TKZ]{tkzXh}{#1}%
   \begingroup%
   \foreach \xA/\RA/\sA/\xB/\RB/\sB in {#2}{%
       \tkzPoint*(\xA,0){deb}\tkzPoint*(\xB,0){fin}
       \begin{scope}[segment amplitude=8pt,segment length=4pt]
         \draw[snake=border,segment angle=60,red,thick,raise snake=-3.5pt] (deb) -- (fin);
         \node at (deb) {\Large\textbf{\sA}};\node at (fin) {\Large\textbf{\sB}};
         \ifthenelse{\equal{\RA}{T}}{
         \node[below=\cmdTKZ@tkzXh@posgrad] at (deb)%
         {\tkz@showgrad{\xA}$\cmdTKZ@tkzX@gradsize{\np{\tkz@result}}$};}{}%
         \ifthenelse{\equal{\RB}{T}}{\node[below=\cmdTKZ@tkzXh@posgrad]%
          at (fin)  {\tkz@showgrad{\xB}$\cmdTKZ@tkzX@gradsize{\np{\tkz@result}}$};}{}%
         \node[below=\cmdTKZ@tkzXh@posgrad] at (\tkz@xa,0) {\cmdTKZ@tkzXh@left};%
         \node[below=\cmdTKZ@tkzXh@posgrad] at (\tkz@xb,0) {\cmdTKZ@tkzXh@right};
       \end{scope}
       }%
   \endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                         tkzText
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\define@cmdkey[TKZ]{tkzText}{color}{}
\define@cmdkey[TKZ]{tkzText}{opacity}{}
\define@cmdkey[TKZ]{tkzText}{bkgcolor}{}
\define@cmdkey[TKZ]{tkzText}{style}{}
\define@cmdkey[TKZ]{tkzText}{name}{}
\presetkeys[TKZ]{tkzText}{color    = black,%
                          bkgcolor = white,%
                          opacity  = 1,%
                          name     = {},%
                          style    = {}}{}
\newcommand*{\tkzText}[1][]{\tkz@Text[#1]}%
\def\tkz@Text[#1](#2,#3)#4{%
    \setkeys[TKZ]{tkzText}{#1}%
    \begingroup%
    \FPadd{\ptxa}{#2}{-\cmdTKZ@tkzInit@xorigine}
    \FPadd{\ptya}{#3}{-\cmdTKZ@tkzInit@yorigine}
    \FPdiv{\ptxa}{\ptxa}{\cmdTKZ@tkzInit@xstep}
    \FPdiv{\ptya}{\ptya}{\cmdTKZ@tkzInit@ystep}
    \protected@edef\tkz@temp{%
       \noexpand%
       \node[         \cmdTKZ@tkzText@style,%
            fill    = \cmdTKZ@tkzText@bkgcolor,%
            opacity = \cmdTKZ@tkzText@opacity]}\tkz@temp (\cmdTKZ@tkzText@name) at (\ptxa,\ptya)%
      {\textcolor{\cmdTKZ@tkzText@color}{#4}};%
   \endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                    légende
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey[TKZ]{legend}{color}{}
\define@cmdkey[TKZ]{legend}{lw}{}
\define@boolkey[TKZ]{legend}{line}[true]{}
\presetkeys[TKZ]{legend}{color=white,line=false,lw=.8pt}{}

\newcommand{\tkzLegend}[1][]{\tkz@Legend[#1]}%
\def\tkz@Legend[#1](#2,#3)#4{
    \setkeys[TKZ]{legend}{#1}% 
    \begingroup%
    \setcounter{tkz@leg}{0}
    \FPadd{\ptxa}{#2}{-\cmdTKZ@tkzInit@xorigine}
    \FPadd{\ptya}{#3}{-\cmdTKZ@tkzInit@yorigine}
    \FPdiv{\ptxa}{\ptxa}{\cmdTKZ@tkzInit@xstep}
    \FPdiv{\ptya}{\ptya}{\cmdTKZ@tkzInit@ystep}
    \node[draw,%
          fill       = \cmdTKZ@legend@color,%
          line width = \cmdTKZ@legend@lw]%
          at (\ptxa,\ptya) {%
    \begin{tikzpicture}
       \foreach \motif/\size/\col/\mtext in {#4}{%
           \ifTKZ@legend@line
              \draw[color=\motif,line width=1pt,\size]%
              (0cm ,\thetkz@leg ex)--(1cm,\thetkz@leg ex)
           \else%
              \draw plot[mark size    = \size,%
                         mark         = \motif,%
                         mark options = {color=\col}]%
               coordinates{(0 ex,\thetkz@leg ex)}%
           \fi%
           node[right=1ex] {\mtext};
           \addtocounter{tkz@leg}{3}
           }%
    \end{tikzpicture}%
    };% 
  \endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 hline 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey [TKZ] {line} {lw}{}
\define@cmdkey [TKZ] {line} {color}{}
\define@cmdkey [TKZ] {line} {style}{}
\presetkeys    [TKZ] {line} {color = black,%
                      style = {dashed},%
                      lw    = 0.6 pt}{}

\newcommand*{\tkzHLine}[1][]{\tkz@hline[#1]}%
\def\tkz@hline[#1]#2{%
    \setkeys[TKZ]{line}{#1}%
    \begingroup%
    \foreach \tkzY in {#2}{%
       \FPeval{\tkzYy}{\tkzY}%
       \FPadd{\ptya}{\tkzYy}{-\cmdTKZ@tkzInit@yorigine}
       \FPdiv{\ptya}{\ptya}{\cmdTKZ@tkzInit@ystep}
       \draw[             \cmdTKZ@line@style,%
             line width = \cmdTKZ@line@lw,%
             color      = \cmdTKZ@line@color]%
        (\tkz@xa,\ptya)--(\tkz@xb,\ptya);%
     }%
   \endgroup%
}
%<--------------------------------------------------------------------------->
%                                      vline
%<--------------------------------------------------------------------------->
\newcommand*{\tkzVLine}[1][]{\tkz@vline[#1]}%
\def\tkz@vline[#1]#2{%
    \setkeys[TKZ]{line}{#1}%
    \begingroup%
    \foreach \tkzX in {#2}{%
      \FPeval\tkzXx{\tkzX}%
      \FPadd{\ptxa}{\tkzXx}{-\cmdTKZ@tkzInit@xorigine}
      \FPdiv{\ptxa}{\ptxa}{\cmdTKZ@tkzInit@xstep}
      \draw[line width = \cmdTKZ@line@lw,%
            color      = \cmdTKZ@line@color,%
                         \cmdTKZ@line@style]%
           (\ptxa,\tkz@ya)--(\ptxa,\tkz@yb);}
    \endgroup%
}

%<--------------------------------------------------------------------------->
%                    distance entre deux nodes en pt  
%<--------------------------------------------------------------------------->
\newcommand*{\tkzMathLength}{\tkz@MathLength}
\let\tkzMathLength\tkzMathLength
\def\tkz@MathLength(#1,#2){%
\begingroup%
\pgfpointdiff{\pgfpointanchor{#1}{center}}%
             {\pgfpointanchor{#2}{center}}%
\tkz@ax=\pgf@x%
\tkz@ay=\pgf@y%
\pgfmathveclen{\pgfmath@tonumber{\tkz@ax}}%
              {\pgfmath@tonumber{\tkz@ay}}
\global\edef\tkzMathLen{\pgfmathresult}
\global\let\tkzmathLen\tkzMathLen 
\endgroup%
}%

\newcommand*{\tkzpttocm}{\tkz@pttocm}
\def\tkz@pttocm#1{% 
    \pgfmathdivide@{#1/28.4528}
     \global\let\tkzmathresult\pgfmathresult
}%

\endinput
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>