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tkz-berge.sty
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% tkz-berge.sty encodage : utf8 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Créé par Alain Matthes le 08-05-2007. %
% contribution : Rafael Villarroel 2007 (RV) %
% contribution : Rafael Villarroel 2009 (RV) %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% modif Doyle form 1
% add \setkeys[GR]{edge}{#1}% in edge's macros
% remove somme bugs with pgf 2.00 cvs
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%% Objet : Création de graphes classiques
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tkz-berge}[2011/06/01 2.00 tkz-berge for named graphs]
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\RequirePackage{tkz-graph}
\def\tkzutil@empty{}
\def\tkzutil@firstofone#1{#1}
\def\tkzutil@firstoftwo#1#2{#1}
\def\tkzutil@secondoftwo#1#2{#2}
%<--------------------------------------------------------------------------–>
\long\def\tkzutil@ifundefined#1{%
\expandafter\ifx\csname#1\endcsname\relax
\expandafter\tkzutil@firstoftwo
\else
\expandafter\tkzutil@secondoftwo
\fi}
%\input{tkz-tools-arith.tex}
\tkzutil@ifundefined{pgfmath@function@isfactor}{%
\pgfmathdeclarefunction{isfactor}{2}{%
\begingroup
\c@pgfmath@counta#1\relax%
\c@pgfmath@countb#2\relax%
\c@pgfmath@countc#1\relax%
\divide\c@pgfmath@counta by\c@pgfmath@countb%
\multiply\c@pgfmath@counta by\c@pgfmath@countb%
\advance\c@pgfmath@countc by-\c@pgfmath@counta%
\ifnum\c@pgfmath@countc=0 \def\pgfmathresult{1}%
\else
\def\pgfmathresult{0}%
\fi
\pgfmath@smuggleone\pgfmathresult%
\endgroup}
}{}
\edef\tkzAtCode{\the\catcode`\@}
\catcode`\@=11\relax
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcounter{tkz@bg@cnt}
% NAMED GRAPHS
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% Graphes cls
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey [GR] {cl} {L}{}
\define@boolkey [GR] {cl} {Math}[true]{}
\define@boolkey [GR] {cl} {inv}[true]{}
\define@cmdkey [GR] {cl} {RA}{}
\define@cmdkey [GR] {cl} {RB}{}
\define@cmdkey [GR] {cl} {RC}{}
\define@cmdkey [GR] {cl} {RD}{}
\define@cmdkey [GR] {cl} {RE}{}
\define@cmdkey [GR] {cl} {RS}{}
\define@cmdkey [GR] {cl} {prefix}{}
\define@cmdkey [GR] {cl} {prefixx}{}
\define@cmdkey [GR] {cl} {prefixxx}{}
\define@cmdkey [GR] {cl} {prefixxxx}{}
\define@cmdkey [GR] {cl} {prefixxxxx}{}
\define@cmdkey [GR] {cl} {form}{}
\define@cmdkey [GR] {cl} {num}{}
\define@cmdkey [GR] {cl} {rotation}{}
\define@cmdkey [GR] {cl} {x}{}
\define@cmdkey [GR] {cl} {y}{}
\define@cmdkey [GR] {cl} {r}{}
\define@cmdkey [GR] {cl} {d}{}
\presetkeys [GR] {cl} {RA = 4,
RB = 3,
RC = 2,
RD = 1,
RE = 0.5,
RS = 0,
form = 1,
prefix = a,
prefixx = b,
prefixxx = c,
prefixxxx = d,
prefixxxxx = e,
num = {},
Math = false,
x = 0,
y = 0,
r = 0,
d = 0,
rotation = 0}{}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% Tools Graphes particuliers
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% Some tools
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grMathSep}{_}
\newcommand*{\grLabelSep}{;}
\newcommand*{\write@math}[3]{%
\Vertex[x = #1,y = #2,%
L = \cmdGR@cl@prefix\grMathSep{#3}]{\cmdGR@cl@prefix#3}}
\newcommand*{\write@nomath}[3]{%
\Vertex[x = #1,y = #2]{\cmdGR@cl@prefix#3}}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% Empty graphs
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyCycle}{\@ifstar%
\grEmptyCycleStar%
\grEmptyCycleNoStar}
\newcommand*{\grEmptyCycleNoStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@p}{#2-1}
\edef\tkz@auxctp{\thetkz@gr@p}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\pgfmathparse{360/#2*\V@x+\cmdGR@cl@rotation}
\let\tkz@angle\pgfmathresult%
\pgfmathsetmacro{\x@result}{%
\cmdGR@cl@RA*cos(\tkz@angle)+\cmdGR@cl@r*cos(\cmdGR@cl@d)}
\pgfmathsetmacro{\y@result}{%
\cmdGR@cl@RA*sin(\tkz@angle)+\cmdGR@cl@r*sin(\cmdGR@cl@d)}
\ifGR@cl@Math%
\presetkeys [GR] {vertex} {Math = true}{}%
\Vertex[x = \x@result+\cmdGR@cl@x,%
y = \y@result+\cmdGR@cl@y,%
L = \cmdGR@cl@prefix\grMathSep{\V@x}]{\cmdGR@cl@prefix\V@x}%
\else%
\Vertex[x = \x@result+\cmdGR@cl@x,%
y = \y@result+\cmdGR@cl@y]{\cmdGR@cl@prefix\V@x}%
\fi%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grEmptyCycleStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\setcounter{tkz@gr@a}{0}
\setcounter{tkz@gr@b}{0}
\foreach \V@x in {#2}{\stepcounter{tkz@gr@b}{1}}
\foreach \V@x in {#2}{%
\pgfmathsetmacro{\x@result}{%
\cmdGR@cl@RA*cos((360/\thetkz@gr@b)*\thetkz@gr@a+\cmdGR@cl@rotation)%
+\cmdGR@cl@r*cos(\cmdGR@cl@d)%
}
\pgfmathsetmacro{\y@result}{%
\cmdGR@cl@RA*sin((360/\thetkz@gr@b)*\thetkz@gr@a+\cmdGR@cl@rotation)%
+\cmdGR@cl@r*sin(\cmdGR@cl@d)%
}
\ifGR@cl@Math%
\Vertex[%
x=\x@result+\cmdGR@cl@x,
y=\y@result+\cmdGR@cl@y,
L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}%
\else%
\Vertex[%
x=\x@result+\cmdGR@cl@x,
y=\y@result+\cmdGR@cl@y,
L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}%
\fi%
\stepcounter{tkz@gr@a}%
}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grEmptyPath from (RV)
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyPath}{\@ifstar%
\grEmptyPathStar%
\grEmptyPathNoStar}
\newcommand*{\grEmptyPathNoStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\edef\tkz@auxctp{\thetkz@gr@a}
\ifcase\cmdGR@cl@form
\or
\def\tkzb@result{0}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*(\V@x)*cos(\cmdGR@cl@rotation)}
\pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*(\V@x)*sin(\cmdGR@cl@rotation)}
\pgfmathsetmacro{\x@coord}{\x@result+\cmdGR@cl@x+\cmdGR@cl@r*cos(\cmdGR@cl@d)}
\pgfmathsetmacro{\y@coord}{\y@result+\cmdGR@cl@y+
\cmdGR@cl@r*sin(\cmdGR@cl@d)+\cmdGR@cl@RS}
\ifGR@cl@Math%
\presetkeys [GR] {vertex} {Math = true}{}%
\ifthenelse{\equal{\cmdGR@cl@num}{}}{%
\write@math{\x@coord}{\y@coord}{\V@x}}{%
\write@math{\x@coord}{\y@coord}{\V@x\grLabelSep\cmdGR@cl@num}}%
\else
\ifthenelse{\equal{\cmdGR@cl@num}{}}{%
\write@nomath{\x@coord}{\y@coord}{\V@x}}{%
\write@nomath{\x@coord+\cmdGR@cl@x}{\y@coord}{%
\V@x\grLabelSep\cmdGR@cl@num}}%
\fi}%
\or
\foreach \V@x in {0,...,\tkz@auxctp}{%
\pgfmathsetmacro{\x@result}{%
\cmdGR@cl@RA*(2*\V@x-\thetkz@gr@a)*0.5*cos(\cmdGR@cl@rotation)}
\pgfmathsetmacro{\y@result}{%
\cmdGR@cl@RA*(2*\V@x-\thetkz@gr@a)*0.5*sin(\cmdGR@cl@rotation)}
\pgfmathsetmacro{\x@coord}{%
\x@result+\cmdGR@cl@x+\cmdGR@cl@r*cos(\cmdGR@cl@d)}
\pgfmathsetmacro{\y@coord}{%
\y@result+\cmdGR@cl@y+\cmdGR@cl@r*sin(\cmdGR@cl@d)+\cmdGR@cl@RS}
\ifGR@cl@Math%
\presetkeys [GR] {vertex} {Math = true}{}%
\ifthenelse{\equal{\cmdGR@cl@num}{}}{%
\write@math{\x@coord}{\y@coord}{\V@x}}{%
\write@math{\x@coord}{\y@coord}{\cmdGR@cl@num\grLabelSep\V@x}}%
\else
\ifthenelse{\equal{\cmdGR@cl@num}{}}{%
\write@nomath{\x@coord}{\y@coord}{\V@x}}{%
\write@nomath{\x@coord}{\y@coord}{\cmdGR@cl@num\grLabelSep\V@x}}%
\fi
}%
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grEmptyPathStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\setcounter{tkz@gr@a}{0}
\ifcase\cmdGR@cl@form
\or
% form 1
\foreach \V@x in {#2}{%
\pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*\value{tkz@gr@a}*cos(\cmdGR@cl@rotation)%
+\cmdGR@cl@r*cos(\cmdGR@cl@d)}%
\pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*\value{tkz@gr@a}*sin(\cmdGR@cl@rotation)%
+\cmdGR@cl@r*sin(\cmdGR@cl@d)}%
\ifGR@cl@Math%
\Vertex[%
x=\x@result+\cmdGR@cl@x,
y=\y@result+\cmdGR@cl@y,
L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}%
\else%
\Vertex[%
x=\x@result+\cmdGR@cl@x,
y=\y@result+\cmdGR@cl@y,
L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}%
\fi%
\stepcounter{tkz@gr@a}%
}%
\or
% form 2
\setcounter{tkz@gr@a}{0}
\setcounter{tkz@gr@b}{0}
\foreach \V@x in {#2}{\stepcounter{tkz@gr@b}{1}}
\foreach \V@x in {#2}{%
\pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*(2*\value{tkz@gr@a}-\value{tkz@gr@b}+1)*0.5%
*cos(\cmdGR@cl@rotation)%
+\cmdGR@cl@r*cos(\cmdGR@cl@d)%
}
\pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*(2*\value{tkz@gr@a}-\value{tkz@gr@b}+1)*0.5%
*sin(\cmdGR@cl@rotation)%
+\cmdGR@cl@r*sin(\cmdGR@cl@d)%
}
\ifGR@cl@Math%
\Vertex[%
x=\x@result+\cmdGR@cl@x,
y=\y@result+\cmdGR@cl@y,
L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}%
\else%
\Vertex[%
x=\x@result+\cmdGR@cl@x,
y=\y@result+\cmdGR@cl@y,
L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}%
\fi%
\stepcounter{tkz@gr@a}
}
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grEmptyStar
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\ifGR@cl@Math\presetkeys [GR] {vertex} {Math = true}{}%
\write@math{0}{0}{\thetkz@gr@a}%
\else
\write@nomath{0}{0}{\thetkz@gr@a}%
\fi
\grEmptyCycle[#1]{\thetkz@gr@a}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grEmptyGrid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grEmptyGrid}[3][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\edef\tkz@auxctpa{\thetkz@gr@a}
\pgfmathsetcounter{tkz@gr@b}{#3-1}
\edef\tkz@auxctpb{\thetkz@gr@b}
\foreach \V@x in {0,...,\tkz@auxctpa}{%
\foreach \V@y in {0,...,\tkz@auxctpb}{%
\ifGR@cl@Math\presetkeys [GR] {vertex} {Math = true}{}%
\write@math{\cmdGR@cl@RA*\V@x}{\cmdGR@cl@RB*\V@y}{\V@x\grLabelSep\V@y}%
\else
\write@nomath{\cmdGR@cl@RA*\V@x}{\cmdGR@cl@RB*\V@y}{\V@x\grLabelSep\V@y}%
\fi}%
}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grEmptyLadder
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyLadder}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grEmptyPath[#1,RS=0]{#2}
\edef\tkzb@ptemp{\cmdGR@cl@prefixx}
\edef\tkzb@rtemp{\cmdGR@cl@RB}
\grEmptyPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% Edges
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphFromOneToComp}[4][]{% #4
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@ta}{#3-1}
\edef\tkz@auxctp{\thetkz@gr@ta}
\foreach \cx in {0,...,\tkz@auxctp}{%
\ifthenelse{\equal{\cx}{#4}}{}{\Edge[#1](#2#4)(#2\cx)}%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeInGraphLoop loop 0--1--2.........n--0
% star 0--1--2.........n-
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphLoop}{\@ifstar%
\EdgeInGraphLoopStar%
\EdgeInGraphLoopNoStar}
\newcommand*{\EdgeInGraphLoopNoStar}[3][]{% #4
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@ta}{#3-1}
\setcounter{tkz@gr@n}{0}
\Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)
\pgfmathaddtocounter{tkz@gr@ta}{-1}
\edef\tkz@auxctp{\thetkz@gr@ta}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\stepcounter{tkz@gr@n}
\Edge[#1](#2\V@x)(#2\thetkz@gr@n)%
}%
\endgroup%
}
\newcommand*{\EdgeInGraphLoopStar}[3][]{% #4
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@ta}{#3-2}
\setcounter{tkz@gr@n}{0}
\edef\tkz@auxctp{\thetkz@gr@ta}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\stepcounter{tkz@gr@n}
\Edge[#1](#2\V@x)(#2\thetkz@gr@n)%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeInGraphMod replace nextmod
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphMod}{\@ifstar%
\EdgeInGraphModStar%
\EdgeInGraphModNoStar}
\newcommand*{\EdgeInGraphModNoStar}[4][]{% #2 order
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@ta}{#3-1}
\edef\tkz@auxctp{\thetkz@gr@ta}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\pgfmathsetcounter{tkz@gr@tb}{Mod(\V@x+#4,#3)}
\Edge[#1](#2\thetkz@gr@tb)(#2\V@x)%
}%
\endgroup%
}
%#1 prefix #2 order #3 add #4 start #5 décalage
\newcommand*{\EdgeInGraphModStar}[6][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@ta}{#5}
\whiledo{\value{tkz@gr@ta}<#3}{%
\pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@ta+#4,#3)}
\Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)
\pgfmathaddtocounter{tkz@gr@ta}{#6}%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeInGraphModLoop dep #4 add #3 mod #2 until #4
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphModLoop}[5][]{% #2 order
\begingroup%
\setkeys[GR]{edge}{#1}%
\setcounter{tkz@gr@ta}{#5}
\setcounter{tkz@gr@n}{#3}
\whiledo{\not\equal{\value{tkz@gr@n}}{#5}}{%
\pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@ta+#4,#3)}
\Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)%
\setcounter{tkz@gr@ta}{\thetkz@gr@n}
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeIdentity
% la version étoilée permet d'utliser une sélection
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeIdentity}{\@ifstar%
\EdgeIdentityStar%
\EdgeIdentityNoStar}
\newcommand*{\EdgeIdentityNoStar}[4][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@e}{#4-1}
\edef\tkz@auxctp{\thetkz@gr@e}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\Edge[#1](#2\V@x)(#3\V@x)%
}%
\endgroup%
}
\newcommand*{\EdgeIdentityStar}[4][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
\foreach \V@x in {#4}{%
\Edge[#1](#2\V@x)(#3\V@x)%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeFromOneToAll vertex #1#3 through #2 0...#2 n-1 #5 order of the graph
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToAll}[5][]{% #4 = order of the graph
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@e}{#5-1}
\edef\tkz@auxctp{\thetkz@gr@e}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\Edge[#1](#2#4)(#3\V@x)%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeFromOneToSeq vertex #1#3 through #2#4...#2#5
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToSeq}[6][]{% #4
\begingroup%
\setkeys[GR]{edge}{#1}%
\foreach \V@x in {#5,...,#6}{%
\Edge[#1](#2#4)(#3\V@x)%
}%
\endgroup%
} %<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeFromOneToSel vertex #1#3 through #2#4...#2#5
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToSel}[5][]{% #4
\begingroup%
\setkeys[GR]{edge}{#1}%
\foreach \V@x in {#5}{%
\Edge[#1](#2#4)(#3\V@x)%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeFromOneToComplement vertex #1#3 through #2#4...#2#5
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToComp}[5][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@e}{#5-1}
\edef\tkz@auxctp{\thetkz@gr@e}
\foreach \cx in {0,...,\tkz@auxctp}{%
\ifthenelse{\equal{\cx}{#4}}{}{\Edge[#1](#2#4)(#3\cx)}%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeMod replace nextmod
% identity with step like nextmod ???
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeMod}{\@ifstar%
\EdgeModStar%
\EdgeModNoStar}
\newcommand*{\EdgeModNoStar}[5][]{%#3 order #4 step
\begingroup%
\setkeys[GR]{edge}{#1}%
\pgfmathsetcounter{tkz@gr@e}{#4-1}
\edef\tkz@auxctp{\thetkz@gr@e}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\pgfmathsetcounter{tkz@gr@tb}{Mod(\V@x+#5,#4)}
\Edge[#1](#2\V@x)(#3\thetkz@gr@tb)%
}%
\endgroup%
}
%#1 prefix #2 prefix #3 order #4 order inf #5 step
\newcommand*{\EdgeModStar}[6][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
\setcounter{tkz@gr@ta}{0}
\whiledo{\value{tkz@gr@ta}<#4}{%
\pgfmathsetcounter{tkz@gr@tb}{Mod(\thetkz@gr@ta+#5,#4)}
\Edge[#1](#2\thetkz@gr@ta)(#3\thetkz@gr@tb)%
\pgfmathaddtocounter{tkz@gr@ta}{#6}}%
\endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeInGraphSeq sequence i--i+1--.....--j
% or i--i+k--...--j
% #1 options #2 graph #3 from #4 to
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphSeq}[4][]{% #4
\begingroup%
\setkeys[GR]{edge}{#1}%
\foreach \V@x in {#3,...,#4}{%
\pgfmathsetcounter{tkz@gr@n}{\V@x+1}
\Edge[#1](#2\V@x)(#2\thetkz@gr@n)}%
\endgroup%
}%
%%%%%%%%%%% NEW COMMANDS
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeSeq sequence
% #1 options #2 first graph #3 second graph #4 from #5 to
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\EdgeSequence}[5][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
\foreach \V@x in {#4,...,#5}{%
\pgfmathsetcounter{tkz@gr@n}{\V@x+1}
\Edge[#1](#2\V@x)(#3\thetkz@gr@n)}%
\endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% EdgeDoubleMod by RV
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeDoubleMod}[9]{%
\begingroup%
\foreach \V@x in {0,...,#9}{%
\pgfmathsetcounter{tkz@gr@c}{Mod(#3+(#4*\V@x),#2)}
\pgfmathsetcounter{tkz@gr@n}{Mod(#7+(#8*\V@x),#6)}
\Edge(#1\thetkz@gr@c)(#5\thetkz@gr@n)
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grPath
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grPath}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grEmptyPath[#1]{#2}
\ifthenelse{\equal{\cmdGR@cl@num}{}}{%
\ifthenelse{\equal{#2}{1}}{}{%
\EdgeInGraphLoop*{\cmdGR@cl@prefix}{#2}%
}}{%
\ifthenelse{\equal{#2}{1}}{}{%
\ifcase\cmdGR@cl@form
\or
\pgfmathsetcounter{tkz@gr@ta}{#2-2}
\setcounter{tkz@gr@n}{0}
\edef\tkz@auxctp{\thetkz@gr@ta}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\stepcounter{tkz@gr@n}
\Edge(\cmdGR@cl@prefix\V@x\grLabelSep\cmdGR@cl@num)%
(\cmdGR@cl@prefix\thetkz@gr@n\grLabelSep\cmdGR@cl@num)%
}%
\or
\EdgeInGraphLoop*{\cmdGR@cl@prefix\cmdGR@cl@num\grLabelSep}{#2}
\fi%
}}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grGrid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grGrid}[3][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grEmptyGrid[#1]{#2}{#3}
\pgfmathsetcounter{tkz@gr@a}{#2-2}
\edef\tkz@auxctpa{\thetkz@gr@a}
\pgfmathsetcounter{tkz@gr@b}{#3-2}
\edef\tkz@auxctpb{\thetkz@gr@b}
\foreach \V@x in {0,...,\tkz@auxctpa}{%
\foreach \V@y in {0,...,\tkz@auxctpb}{%
\pgfmathsetcounter{tkz@gr@c}{\V@x+1}
\pgfmathsetcounter{tkz@gr@d}{\V@y+1}
\Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)%
(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@d)
\Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)%
(\cmdGR@cl@prefix\thetkz@gr@c\grLabelSep\V@y)%
}%
}%
\pgfmathsetcounter{tkz@gr@a}{#2-2}
\pgfmathsetcounter{tkz@gr@b}{#3-1}
\edef\tkz@auxctpa{\thetkz@gr@a}
\foreach \V@x in {0,...,\tkz@auxctpa}{%
\pgfmathsetcounter{tkz@gr@c}{\V@x+1}
\Edge(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)%
(\cmdGR@cl@prefix\thetkz@gr@c\grLabelSep\thetkz@gr@b)%
}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\pgfmathsetcounter{tkz@gr@b}{#3-2}
\edef\tkz@auxctpb{\thetkz@gr@b}
\foreach \V@y in {0,...,\tkz@auxctpb}{%
\pgfmathsetcounter{tkz@gr@d}{\V@y+1}
\Edge(\cmdGR@cl@prefix\thetkz@gr@a\grLabelSep\V@y)%
(\cmdGR@cl@prefix\thetkz@gr@a\grLabelSep\thetkz@gr@d)%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grComplete
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grComplete}[2][]{% #1 options #2 ordre du graphe
\begingroup%
\setkeys[GR]{cl}{#1}%
\grEmptyCycle[#1]{#2}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\edef\tkz@auxctp{\thetkz@gr@a}
\foreach \ia in {0,...,\tkz@auxctp}%
{\foreach \ib in {\ia,...,\tkz@auxctp}
{\Edge(\cmdGR@cl@prefix\ia)(\cmdGR@cl@prefix\ib)}%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grCycle
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCycle}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}
\grEmptyCycle[#1]{#2}
\EdgeInGraphLoop{\cmdGR@cl@prefix}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grLCF
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grLCF}[3][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\setcounter{tkz@gr@a}{#3}
\setcounter{tkz@gr@b}{0}
\foreach \V@x in {#2}{\stepcounter{tkz@gr@b}}
\pgfmathsetcounter{tkz@gr@c}{\thetkz@gr@a * \thetkz@gr@b}
\setcounter{tkz@gr@b}{\thetkz@gr@c}
\grCycle[#1]{\thetkz@gr@c}
%<––––––––––––––––––––––––– End Vertex ––––––––––––––––––––––––––––––––––––>
\pgfmathsetcounter{tkz@gr@a}{#3-1}
\edef\tkz@auxctp{\thetkz@gr@a}
\setcounter{tkz@gr@e}{0}
\foreach \V@k in {0,...,\tkz@auxctp}{%
\foreach \n in {#2}{%
\ifthenelse{\n < 0}{%
\pgfmathsetcounter{tkz@gr@b}{\n+\thetkz@gr@c}}{%
\pgfmathsetcounter{tkz@gr@b}{\n}}
\pgfmathsetcounter{tkz@gr@n}%
{Mod(\thetkz@gr@e+\thetkz@gr@b,\thetkz@gr@c)}
\Edge(\cmdGR@cl@prefix\thetkz@gr@e)(\cmdGR@cl@prefix\thetkz@gr@n)
\stepcounter{tkz@gr@e}%
}%
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grStar
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grEmptyStar[#1]{#2}
\pgfmathsetcounter{tkz@gr@p}{#2-1}
\EdgeInGraphFromOneToComp{\cmdGR@cl@prefix}{#2}{\thetkz@gr@p}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grWheel
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grWheel}[2][]{
\begingroup%
\setkeys[GR]{cl}{#1}%
\grStar[#1]{#2}
\pgfmathsetcounter{tkz@gr@e}{#2-1}
\EdgeInGraphLoop{\cmdGR@cl@prefix}{\thetkz@gr@e}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grSQCircle
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grSQCycle}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grCycle[#1]{#2}%
\EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grLadder
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grLadder}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grPath[#1,RS=0]{#2}
\edef\tkzb@ptemp{\cmdGR@cl@prefixx}
\edef\tkzb@rtemp{\cmdGR@cl@RS}
\grPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2}
\EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grPrism
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grPrism}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grCycle[#1]{#2}
\edef\tkzb@rtemp{\cmdGR@cl@RB}
\edef\tkzb@ptemp{\cmdGR@cl@prefixx}
\grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{#2}
\EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grCompleteBipartite
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCompleteBipartite}[3][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\pgfmathparse{(\cmdGR@cl@RA * \thetkz@gr@a) /2}
\let\tkzRAxpos\pgfmathresult%
\pgfmathsetcounter{tkz@gr@a}{#3-1}
\pgfmathparse{(\cmdGR@cl@RB * \thetkz@gr@a) /2}
\let\tkzRBxpos\pgfmathresult%
\ifdim\tkzRBxpos pt > \tkzRAxpos pt\relax%
\pgfmathadd{\tkzRBxpos}{-\tkzRAxpos}
\let\tkzaxpos\pgfmathresult%
\def\tkzbxpos{0}
\else%
\pgfmathadd{\tkzRAxpos}{-\tkzRBxpos}
\let\tkzbxpos\pgfmathresult%
\def\tkzaxpos{0}
\fi%
\begin{scope}[xshift=\tkzaxpos cm]
\grEmptyPath[#1,RS=0]{#2}
\end{scope}
\begin{scope}[xshift=\tkzbxpos cm]
\edef\tkzb@ptemp{\cmdGR@cl@prefixx}
\edef\tkzb@rtemp{\cmdGR@cl@RS}
\edef\tkzb@stemp{\cmdGR@cl@RB}
\grEmptyPath[#1,RA=\tkzb@stemp,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#3}
\end{scope}
\pgfmathsetcounter{tkz@gr@p}{#2-1}
\pgfmathsetcounter{tkz@gr@e}{#3-1}
\edef\tkz@auxctp{\thetkz@gr@e}
\foreach \cpx in {0,...,\tkz@auxctp}{%
\EdgeFromOneToAll{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{\cpx}{#2}
}%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grTriangularGrid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grTriangularGrid}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}
\ifcase\cmdGR@cl@form
\or
%<––––––––––––––––––––– form 1 equilateral triangle ––––––––––––––––––––––––>
\pgfmathsetcounter{tkz@gr@a}{#2-1}
%\pgfmathsetcounter{tkz@gr@b}{#2}
\edef\tkz@auxctp{\thetkz@gr@a}
\foreach \lg in {0,...,\tkz@auxctp}{%
\pgfmathsetcounter{tkz@gr@b}{#2-\lg}
\setcounter{tkz@gr@b}{\thetkz@gr@b}
\edef\tkzb@rtemp{\cmdGR@cl@RA}
\edef\tkzb@ptemp{\cmdGR@cl@prefix}
\pgfmathmultiply{\cmdGR@cl@RA}{\lg}
\let\myresult\pgfmathresult
\pgfmathparse{\cmdGR@cl@RA*\lg/2}
\let\tkzaxpos\pgfmathresult
\begin{scope}[xshift=\tkzaxpos cm]
\grPath[#1,%
RA = \tkzb@rtemp,%
RS = \myresult,%
prefix = \tkzb@ptemp,%
num = \lg]{\thetkz@gr@b}%
\end{scope}%
}
\or
%<––––––––––––––––––––––––––– form 2 right triangle ––––––––––––––––––––––––>
\pgfmathsetcounter{tkz@gr@a}{#2-1}
% \pgfmathsetcounter{tkz@gr@b}{#2}
\edef\tkz@auxctp{\thetkz@gr@a}
\foreach \lg in {0,...,\tkz@auxctp}{%
\pgfmathsetcounter{tkz@gr@b}{#2-\lg}
\setcounter{tkz@gr@b}{\thetkz@gr@b}
\edef\tkzb@rtemp{\cmdGR@cl@RA}
\edef\tkzb@ptemp{\cmdGR@cl@prefix}
\pgfmathmultiply{\cmdGR@cl@RA}{\lg}
\let\myresult\pgfmathresult
\grPath[#1,%
RA = \tkzb@rtemp,%
RS = \myresult,%
prefix = \tkzb@ptemp,%
num = \lg,form=1]{\thetkz@gr@b}%
}
\or
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\pgfmathsetcounter{tkz@gr@b}{#2}
\edef\tkz@auxctp{\thetkz@gr@a}
\foreach \lg in {0,...,\tkz@auxctp}{%
\pgfmathsetcounter{tkz@gr@b}{#2-\lg}
\setcounter{tkz@gr@b}{\thetkz@gr@b}
\edef\tkzb@rtemp{\cmdGR@cl@RA}
\edef\tkzb@ptemp{\cmdGR@cl@prefix}
\pgfmathmultiply{\cmdGR@cl@RA}{\lg}
\let\myresult\pgfmathresult
\begin{scope}[xshift=\myresult cm]
\grPath[#1,%
RA = \tkzb@rtemp,%
RS = \myresult,%
prefix = \tkzb@ptemp,%
num = \lg,form=1]{\thetkz@gr@b}%
\end{scope}%
}
\fi%
\pgfmathsetcounter{tkz@gr@a}{#2-2}
\edef\tkz@auxctp{\thetkz@gr@a}
\foreach \V@x in {0,...,\tkz@auxctp}{%
\pgfmathsetcounter{tkz@gr@e}{\thetkz@gr@a-\V@x}
\edef\tkz@auxctpb{\thetkz@gr@e}
\foreach \V@y in {0,...,\tkz@auxctpb}{%
\pgfmathsetcounter{tkz@gr@b}{\V@y+1}
\Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)%
(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)
\pgfmathsetcounter{tkz@gr@p}{\V@x+1}
\Edge(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)%
(\cmdGR@cl@prefix\thetkz@gr@p\grLabelSep\V@y)
}%
}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grHeawood
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grHeawood}[1][]{% #1 options #2 ordre du graphe
\begingroup%
\setkeys[GR]{cl}{#1}%
\grCycle[#1]{14}
\EdgeInGraphMod*{\cmdGR@cl@prefix}{14}{5}{0}{2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grCirculant #1 option #2 vertex #3 add k
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCirculant}[3][]{%
\begingroup%
\setkeys[GR]{cl}{#1}
\grEmptyCycle[#1]{#2}%
\pgfmathisprime{#2}%
\ifnum\pgfmathresult=1\relax
\foreach \kci in {#3}{%
\EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{\kci}}%
\else
\foreach \kci in {#3}{%
\pgfmathisfactor{#2}{\kci}%
\ifnum\pgfmathresult=1\relax
\pgfmathsetcounter{tkz@gr@a}{\kci-1}
\edef\tkz@auxctp{\thetkz@gr@a}
\foreach \start in {0,...,\tkz@auxctp}{%
\setcounter{tkz@gr@i}{\start}%
\setcounter{tkz@gr@n}{#2}%
\whiledo{\not\equal{\value{tkz@gr@n}}{\start}}{%
\pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@i+\kci,#2)}
\Edge(\cmdGR@cl@prefix\thetkz@gr@i)%
(\cmdGR@cl@prefix\thetkz@gr@n)%
\pgfmathsetcounter{tkz@gr@i}{\thetkz@gr@n}%
}%
}%
\else
\EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{\kci}
\fi
}%
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grPetersenG
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grGeneralizedPetersen}[3][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grCycle[#1]{#2}
\edef\tkzb@rtemp{\cmdGR@cl@RB}
\edef\tkzb@pptemp{\cmdGR@cl@prefixx}
\edef\tkzb@ptemp{\cmdGR@cl@prefix}
\grCirculant[#1,RA=\tkzb@rtemp,prefix=\tkzb@pptemp]{#2}{#3}
\EdgeIdentity{\tkzb@ptemp}{\cmdGR@cl@prefixx}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grPetersen
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grStartwo}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@e}{3*#2-2}
\pgfmathsetcounter{tkz@gr@a}{3*#2-1}
\grEmptyCycle[#1]{\thetkz@gr@a}
\EdgeInGraphMod{\cmdGR@cl@prefix}{\thetkz@gr@a}{#2}%
\endgroup%
}
\newcommand*{\grPetersen}[1][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\ifcase\cmdGR@cl@form
\or
\grCycle[#1]{5}%
\edef\tkzb@rtemp{\cmdGR@cl@RB}
\edef\tkzb@ptemp{\cmdGR@cl@prefixx}
\grStartwo[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{2}
\EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{5}
\or
\grCycle[#1]{6}
\begin{scope}[rotate=30]
\edef\tkzb@rtemp{\cmdGR@cl@RB}
\edef\tkzb@ptemp{\cmdGR@cl@prefixx}
\grStar[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4}
\end{scope}
\setcounter{tkz@gr@a}{2}
\foreach \V@x in {0,...,5}{%
\ifthenelse{\equal{\thetkz@gr@a}{-1}}{%
\setcounter{tkz@gr@a}{2}}{%
}%
\Edge(\cmdGR@cl@prefix\V@x)(\cmdGR@cl@prefixx\thetkz@gr@a)
\addtocounter{tkz@gr@a}{-1}%
}%
\or
\grEmptyStar[#1]{10}
\EdgeInGraphLoop{\cmdGR@cl@prefix}{9}
\EdgeInGraphMod*{\cmdGR@cl@prefix}{9}{4}{0}{3}
\foreach \V@x in {2,5,8}{%
\Edge(\cmdGR@cl@prefix\V@x)(\cmdGR@cl@prefix 9)}%
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grPlatonic
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grTetrahedral}[1][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\begin{scope}[rotate=90]
\grWheel[#1]{4}%
\end{scope}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% grOctahedral
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grOctahedral}[1][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\grComplete[#1]{3}%
\begin{scope}[rotate=-60]