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+% Copyright 2019 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/generic/pgf/licenses/LICENSE for more details.
+
+\ProvidesPackageRCS{tikz.code.tex}
+
+
+\def\tikzerror#1{\pgfutil@packageerror{tikz}{#1}{}}
+
+% Always-present libraries (|\usepgflibrary| defined in
+% \file{pgfutil-common.tex}).
+\usepgflibrary{plothandlers}
+
+\newdimen\tikz@lastx
+\newdimen\tikz@lasty
+\newdimen\tikz@lastxsaved
+\newdimen\tikz@lastysaved
+\newdimen\tikz@lastmovetox
+\newdimen\tikz@lastmovetoy
+
+\newdimen\tikzleveldistance
+\newdimen\tikzsiblingdistance
+
+\newbox\tikz@figbox
+\newbox\tikz@figbox@bg
+\newbox\tikz@tempbox
+\newbox\tikz@tempbox@bg
+
+\newcount\tikztreelevel
+\newcount\tikznumberofchildren
+\newcount\tikznumberofcurrentchild
+
+\newcount\tikz@fig@count
+
+\newif\iftikz@node@is@a@label
+\newif\iftikz@snaked
+\newif\iftikz@decoratepath
+
+\let\tikz@options\pgfutil@empty
+% |\tikz@addoption| adds \texttt{#1} at the end of the replacement
+% text of |\tikz@options| without expansion.
+\def\tikz@addoption#1{%
+ \expandafter\def\expandafter\tikz@options\expandafter{\tikz@options#1}}%
+% Same as |tikz@addoption| for |\tikz@mode|. Note that |\tikz@mode| is
+% initially let to |\pgfutil@empty| later (see path usage options).
+\def\tikz@addmode#1{%
+ \expandafter\def\expandafter\tikz@mode\expandafter{\tikz@mode#1}}%
+% Same as |tikz@addoption| for |\tikz@transform|. Works even if
+% |\tikz@transform| is not defined. In that case, nothing is added to
+% |\tikz@transform|: \texttt{#1} is expanded.
+\def\tikz@addtransform#1{%
+ \ifx\tikz@transform\relax
+ #1%
+ \else
+ \expandafter\def\expandafter\tikz@transform\expandafter{\tikz@transform#1}%
+ \fi
+}%
+
+
+% TikZ options management.
+
+% Setting up the tikz key family (key management needs
+% \file{pgfkeys.code.tex});
+\pgfkeys{/tikz/.is family}%
+
+% |\tikzset| is a shortcut to set keys that belongs to the tikz
+% family.
+\def\tikzset{\pgfqkeys{/tikz}}%
+
+% Note: |\tikzoption| is supported for compatibility only. |\tikzset|
+% should be used instead.
+\def\tikzoption#1{%
+ \pgfutil@ifnextchar[%]
+ {\tikzoption@opt{#1}}{\tikzoption@noopt{#1}}}%
+\def\tikzoption@opt#1[#2]#3{%
+ \pgfkeysdef{/tikz/#1}{#3}%
+ \pgfkeyssetvalue{/tikz/#1/.@def}{#2}}%
+\def\tikzoption@noopt#1#2{%
+ \pgfkeysdef{/tikz/#1}{#2}%
+ \pgfkeyssetvalue{/tikz/#1/.@def}{\pgfkeysvaluerequired}}%
+
+% Baseline options
+\tikzoption{baseline}[0pt]{%
+ \pgfutil@ifnextchar(%)
+ {\tikz@baseline@coordinate}{\tikz@baseline@simple}#1\@nil}%
+\def\tikz@baseline@simple#1\@nil{\pgfsetbaseline{#1}}%
+\def\tikz@baseline@coordinate#1\@nil{%
+ \pgfsetbaselinepointlater{\tikz@scan@one@point\pgfutil@firstofone#1}}%
+
+\tikzoption{trim left}[0pt]{\pgfutil@ifnextchar({\tikz@trim@coordinate{left}}{\tikz@trim@simple{left}}#1\@nil}%)%
+\tikzoption{trim right}{\pgfutil@ifnextchar({\tikz@trim@coordinate{right}}{\tikz@trim@simple{right}}#1\@nil}%)%
+\def\tikz@trim@simple#1#2\@nil{\csname pgfsettrim#1\endcsname{#2}}%
+\def\tikz@trim@coordinate#1#2\@nil{\csname pgfsettrim#1pointlater\endcsname{\tikz@scan@one@point\pgfutil@firstofone#2}}%
+
+% Draw options
+\tikzoption{line width}{\tikz@semiaddlinewidth{#1}}%
+
+\def\tikz@semiaddlinewidth#1{\tikz@addoption{\pgfsetlinewidth{#1}}\pgfmathsetlength\pgflinewidth{#1}}%
+
+\tikzoption{cap}{\tikz@addoption{\csname pgfset#1cap\endcsname}}%
+\tikzoption{join}{\tikz@addoption{\csname pgfset#1join\endcsname}}%
+\tikzoption{line cap}{\tikz@addoption{\csname pgfset#1cap\endcsname}}%
+\tikzoption{line join}{\tikz@addoption{\csname pgfset#1join\endcsname}}%
+\tikzoption{miter limit}{\tikz@addoption{\pgfsetmiterlimit{#1}}}%
+
+\tikzoption{dash pattern}{% syntax: on 2pt off 3pt on 4pt ...
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\pgfutil@empty%
+ \def\tikz@dashpattern{}%
+ \tikz@addoption{\pgfsetdash{}{0pt}}%
+ \else%
+ \def\tikz@dashpattern{}%
+ \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil%
+ \edef\tikz@temp{{\tikz@dashpattern}{\noexpand\tikz@dashphase}}%
+ \expandafter\tikz@addoption\expandafter{\expandafter\pgfsetdash\tikz@temp}%
+ \fi}%
+\tikzoption{dash phase}{%
+ \def\tikz@dashphase{#1}%
+ \edef\tikz@temp{{\tikz@dashpattern}{\noexpand\tikz@dashphase}}%
+ \expandafter\tikz@addoption\expandafter{\expandafter\pgfsetdash\tikz@temp}%
+}%
+\tikzoption{dash}{\tikz@parse@full@dash#1\pgf@stop}%
+\def\tikz@parse@full@dash#1phase#2\pgf@stop{%
+ \def\tikz@dashphase{#2}%
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\pgfutil@empty%
+ \def\tikz@dashpattern{}%
+ \tikz@addoption{\pgfsetdash{}{0pt}}%
+ \else%
+ \def\tikz@dashpattern{}%
+ \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil%
+ \edef\tikz@temp{{\tikz@dashpattern}{\noexpand\tikz@dashphase}}%
+ \expandafter\tikz@addoption\expandafter{\expandafter\pgfsetdash\tikz@temp}%
+ \fi%
+}%
+\def\tikz@dashphase{0pt}%
+\def\tikz@dashpattern{}%
+
+\def\tikz@scandashon n#1o{%
+ \expandafter\def\expandafter\tikz@dashpattern\expandafter{\tikz@dashpattern{#1}}%
+ \pgfutil@ifnextchar\@nil{\pgfutil@gobble}{\tikz@scandashoff}}%
+\def\tikz@scandashoff ff#1o{%
+ \expandafter\def\expandafter\tikz@dashpattern\expandafter{\tikz@dashpattern{#1}}%
+ \pgfutil@ifnextchar\@nil{\pgfutil@gobble}{\tikz@scandashon}}%
+
+% use a decoration to expand the `off' section of a dash pattern.
+% https://tex.stackexchange.com/a/133357
+\tikzset{
+ dash expand off/.code={%
+ \ifcsname tikz@library@decorations@loaded\endcsname\else
+ \tikzerror{You need \string\usetikzlibrary{decorations} for ``dash expand off''}%
+ \fi
+ \tikz@addoption{%
+ \pgfgetpath\currentpath
+ \pgfprocessround{\currentpath}{\currentpath}%
+ \pgf@decorate@parsesoftpath{\currentpath}{\currentpath}%
+ % All of \on, \off, \dashphase, \rest, and \onoff are unit-free.
+ % Parse \on and \off from the current path
+ \pgfmathsetmacro\on{\expandafter\pgfutil@firstoftwo\tikz@dashpattern}%
+ \pgfmathsetmacro\off{\expandafter\pgfutil@secondoftwo\tikz@dashpattern}%
+ % \dashphase = max(\on - \dashphase, 0)
+ \pgfmathsetmacro\tikz@dashphase{\tikz@dashphase}%
+ \pgfmathsubtract@{\on}{\tikz@dashphase}%
+ \pgfmathmax@{\pgfmathresult,0}%
+ \let\dashphase=\pgfmathresult
+ % \rest = \pgf@decorate@totalpathlength - \on + 2\dashphase
+ \edef\rest{\pgf@sys@tonumber\dimexpr\pgf@decorate@totalpathlength - \on pt + 2\dimexpr\dashphase pt\relax\relax}%
+ % \onoff = \on + \off
+ \edef\onoff{\pgf@sys@tonumber\dimexpr\on pt+\off pt\relax}%
+ % \nfullonoff = max(floor(\rest/\onoff), 1)
+ \pgfmathdivide@{\rest}{\onoff}%
+ \pgfmathfloor@{\pgfmathresult}%
+ \pgfmathmax@{\pgfmathresult,1}%
+ % \offexpand = max(\rest/\nfullonoff - \on, \off)
+ \pgfmathdivide@{\rest}{\pgfmathresult}%
+ \pgfmathsubtract@{\pgfmathresult}{\on}%
+ \pgfmathmax@{\pgfmathresult,\off}%
+ \edef\tikz@marshal{\noexpand\pgfsetdash{{+\on pt}{+\pgfmathresult pt}}{+\dashphase pt}}%
+ \tikz@marshal
+ }%
+ }
+}
+
+\tikzoption{draw opacity}{\tikz@addoption{\pgfsetstrokeopacity{#1}}}%
+
+% Double draw options
+\tikzoption{double}[]{%
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\tikz@nonetext%
+ \tikz@addmode{\tikz@mode@doublefalse}%
+ \else%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else%
+ \pgfsetinnerstrokecolor{#1}%
+ \fi%
+ \tikz@addmode{\tikz@mode@doubletrue}%
+ \tikzset{every double/.try}%
+ \fi}%
+\tikzoption{double distance}{%
+ \pgfmathsetlength{\pgf@x}{#1}%
+ \edef\tikz@double@setup{%
+ \pgf@x=\the\pgf@x%
+ \advance\pgf@x by2\pgflinewidth%
+ \pgflinewidth=\pgf@x%
+ \noexpand\pgfsetlinewidth{\pgflinewidth}%
+ \noexpand\pgfsetinnerlinewidth{\the\pgf@x}%
+ }%
+ \tikzset{double}}%
+\def\tikz@double@setup{%
+ \pgf@x=2\pgflinewidth%
+ \advance\pgf@x by0.6pt%
+ \pgflinewidth=\pgf@x%
+ \pgfsetlinewidth{\pgflinewidth}%
+ \pgfsetinnerlinewidth{0.6pt}%
+}%
+\tikzset{double distance between line centers/.code={
+ \pgfmathsetlength{\pgf@x}{#1}%
+ \edef\tikz@double@setup{%
+ \pgf@x=\pgflinewidth%
+ \pgf@xa=\the\pgf@x%
+ \advance\pgf@x by\pgf@xa%
+ \advance\pgf@xa by-\pgflinewidth%
+ \pgflinewidth=\pgf@x%
+ \noexpand\pgfsetlinewidth{\pgflinewidth}%
+ \noexpand\pgfsetinnerlinewidth{\pgf@xa}%
+ }%
+ \tikzset{double}}}%
+\tikzset{double equal sign distance/.style={double distance between line centers=0.45ex}}%
+
+
+
+
+% Fill options
+
+\tikzoption{even odd rule}[]{\tikz@addoption{\pgfseteorule}}%
+\tikzoption{nonzero rule}[]{\tikz@addoption{\pgfsetnonzerorule}}%
+
+\tikzoption{fill opacity}{\tikz@addoption{\pgfsetfillopacity{#1}}}%
+
+
+% Joined fill/draw options
+
+\tikzoption{opacity}{\tikz@addoption{\pgfsetstrokeopacity{#1}\pgfsetfillopacity{#1}}}%
+
+
+% Blend mode
+
+\tikzset{blend mode/.code={\tikz@addoption{\pgfsetblendmode{#1}}}}%
+
+
+% Main color options
+\tikzoption{color}{%
+ \tikz@addoption{%
+ \ifx\tikz@fillcolor\pgfutil@empty%
+ \ifx\tikz@strokecolor\pgfutil@empty%
+ \else%
+ \pgfsys@color@reset@inorderfalse%
+ \let\tikz@strokecolor\pgfutil@empty%
+ \let\tikz@fillcolor\pgfutil@empty%
+ \fi%
+ \else%
+ \pgfsys@color@reset@inorderfalse%
+ \let\tikz@strokecolor\pgfutil@empty%
+ \let\tikz@fillcolor\pgfutil@empty%
+ \fi%
+ \pgfutil@colorlet{tikz@color}{#1}%
+ \pgfutil@colorlet{.}{tikz@color}%
+ %
+ \pgfsetcolor{.}%
+ \pgfsys@color@reset@inordertrue%
+ }%
+ \def\tikz@textcolor{#1}}%
+
+
+
+% Rounding options
+\tikzoption{rounded corners}[4pt]{\pgfsetcornersarced{\pgfpoint{#1}{#1}}}%
+\tikzoption{sharp corners}[]{\pgfsetcornersarced{\pgfpointorigin}}%
+
+% Radii and arc options
+\tikzset{x radius/.initial=0pt}%
+\tikzset{y radius/.initial=0pt}%
+\tikzset{%
+ radius/.code={%
+ \pgfmathparse{#1}%
+ \ifpgfmathunitsdeclared
+ \pgfkeyssetevalue{/tikz/x radius}{\pgfmathresult pt}%
+ \pgfkeyssetevalue{/tikz/y radius}{\pgfmathresult pt}%
+ \else
+ \pgfkeyssetevalue{/tikz/x radius}{\pgfmathresult}%
+ \pgfkeyssetevalue{/tikz/y radius}{\pgfmathresult}%
+ \fi
+ }%
+}%
+\tikzset{start angle/.initial=}%
+\tikzset{end angle/.initial=}%
+\tikzset{delta angle/.initial=}%
+
+
+% Coordinate options
+\tikzoption{x}{\tikz@handle@vec{\pgfsetxvec}{\tikz@handle@x}#1\relax}%
+\tikzoption{y}{\tikz@handle@vec{\pgfsetyvec}{\tikz@handle@y}#1\relax}%
+\tikzoption{z}{\tikz@handle@vec{\pgfsetzvec}{\tikz@handle@z}#1\relax}%
+
+\def\tikz@handle@vec#1#2{\pgfutil@ifnextchar({\tikz@handle@coordinate#1}{\tikz@handle@single#2}}%
+\def\tikz@handle@coordinate#1{\tikz@scan@one@point#1}%
+\def\tikz@handle@single#1#2\relax{#1{#2}}%
+\def\tikz@handle@x#1{\pgfsetxvec{\pgfpoint{#1}{0pt}}}%
+\def\tikz@handle@y#1{\pgfsetyvec{\pgfpoint{0pt}{#1}}}%
+\def\tikz@handle@z#1{\pgfsetzvec{\pgfpoint{#1}{#1}}}%
+
+
+% Transformation options
+\tikzoption{scale}{\tikz@addtransform{\pgftransformscale{#1}}}%
+\tikzoption{scale around}{\tikz@addtransform{\def\tikz@aroundaction{\pgftransformscale}\tikz@doaround{#1}}}%
+\tikzoption{xscale}{\tikz@addtransform{\pgftransformxscale{#1}}}%
+\tikzoption{xslant}{\tikz@addtransform{\pgftransformxslant{#1}}}%
+\tikzoption{yscale}{\tikz@addtransform{\pgftransformyscale{#1}}}%
+\tikzoption{yslant}{\tikz@addtransform{\pgftransformyslant{#1}}}%
+\tikzoption{rotate}{\tikz@addtransform{\pgftransformrotate{#1}}}%
+\tikzoption{rotate around}{\tikz@addtransform{\def\tikz@aroundaction{\pgftransformrotate}\tikz@doaround{#1}}}%
+\def\tikz@doaround#1{%
+ \edef\tikz@temp{#1}% get rid of active stuff
+ \expandafter\tikz@doparseA\tikz@temp%
+}%
+\def\tikz@doparseA#1:{%
+ \def\tikz@temp@rot{#1}%
+ \tikz@scan@one@point\tikz@doparseB%
+}%
+\def\tikz@doparseB#1{%
+ \pgf@process{#1}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgftransformshift{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ \tikz@aroundaction{\tikz@temp@rot}%
+ \pgftransformshift{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}%
+}%
+
+\tikzoption{shift}{\tikz@addtransform{\tikz@scan@one@point\pgftransformshift#1\relax}}%
+\tikzoption{xshift}{\tikz@addtransform{\pgftransformxshift{#1}}}%
+\tikzoption{yshift}{\tikz@addtransform{\pgftransformyshift{#1}}}%
+\tikzoption{cm}{\tikz@addtransform{\tikz@parse@cm#1\relax}}%
+\tikzoption{reset cm}[]{\tikz@addtransform{\pgftransformreset}}%
+\tikzoption{shift only}[]{\tikz@addtransform{\pgftransformresetnontranslations}}%
+
+\def\tikz@parse@cm#1,#2,#3,#4,{%
+ \def\tikz@p@cm{{#1}{#2}{#3}{#4}}%
+ \tikz@scan@one@point\tikz@parse@cmA}%
+\def\tikz@parse@cmA#1{%
+ \expandafter\pgftransformcm\tikz@p@cm{#1}%
+}%
+
+\tikzset{transform canvas/.code=%
+ {%
+ \tikz@addoption
+ {%
+ {%
+ \pgftransformreset%
+ \let\tikz@transform=\relax%
+ \tikzset{#1}%
+ \pgflowlevelsynccm%
+ }%
+ \pgf@relevantforpicturesizefalse%
+ }%
+ }%
+}%
+
+\tikzset{turn/.code={%
+ \pgf@x=0pt%
+ \pgf@y\pgf@x%
+ \pgf@process{\tikz@tangent}%
+ \advance\pgf@x by-\tikz@lastx%
+ \advance\pgf@y by-\tikz@lasty%
+ \pgfpointnormalised{}% x/y = normalised vector
+ \pgf@x=-\pgf@x%
+ \pgf@ya=-\pgf@y%
+ \pgftransformcm%
+ {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@ya}}%
+ {\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@x}}{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}%
+ }%
+}%
+
+\def\tikz@tangent@lookup{%
+ \pgfgetpath\tikz@temp%
+ \pgfprocesspathextractpoints\tikz@temp%
+ \pgfpointsecondlastonpath%
+}%
+
+% Code for rotating the xyz coordinate system
+% around the x, y, or z vector.
+%
+\def\tikz@xyz@rotate@let{%
+ \let\pgf@z=\pgf@yc%
+ \let\pgf@za=\pgf@xc%
+}%
+
+\def\tikz@xyz@rotate@xyz@xaxis#1#2#3#4{%
+ \tikz@xyz@rotate@let%
+ \pgf@x=#1\relax%
+ \pgf@ya=#2\relax%
+ \pgf@za=#3\relax%
+ \pgfmathsin@{#4}\let\tikz@xyz@sin=\pgfmathresult%
+ \pgfmathcos@{#4}\let\tikz@xyz@cos=\pgfmathresult%
+ \pgf@y=\tikz@xyz@cos\pgf@ya%
+ \advance\pgf@y by-\tikz@xyz@sin\pgf@za%
+ \pgf@z=\tikz@xyz@sin\pgf@ya%
+ \advance\pgf@z by\tikz@xyz@cos\pgf@za%
+}%
+
+\def\tikz@xyz@rotate@xyz@yaxis#1#2#3#4{%
+ \tikz@xyz@rotate@let%
+ \pgf@xa=#1\relax%
+ \pgf@y=#2\relax%
+ \pgf@za=#3\relax%
+ \pgfmathsin@{#4}\let\tikz@xyz@sin=\pgfmathresult%
+ \pgfmathcos@{#4}\let\tikz@xyz@cos=\pgfmathresult%
+ \pgf@x=\tikz@xyz@cos\pgf@xa%
+ \advance\pgf@x by\tikz@xyz@sin\pgf@za%
+ \pgf@z=-\tikz@xyz@sin\pgf@xa%
+ \advance\pgf@z by\tikz@xyz@cos\pgf@za%
+}%
+
+\def\tikz@xyz@rotate@xyz@zaxis#1#2#3#4{%
+ \tikz@xyz@rotate@let%
+ \pgf@xa=#1\relax%
+ \pgf@ya=#2\relax%
+ \pgf@z=#3\relax%
+ \pgfmathsin@{#4}\let\tikz@xyz@sin=\pgfmathresult%
+ \pgfmathcos@{#4}\let\tikz@xyz@cos=\pgfmathresult%
+ \pgf@x=\tikz@xyz@cos\pgf@xa%
+ \advance\pgf@x by-\tikz@xyz@sin\pgf@ya%
+ \pgf@y=\tikz@xyz@sin\pgf@xa%
+ \advance\pgf@y by\tikz@xyz@cos\pgf@ya%
+}%
+
+\tikzset{rotate around x/.code={%
+ \tikz@xyz@rotate@let%
+ \pgfmathparse{#1}\let\tikz@xyz@angle=\pgfmathresult%
+ \tikz@xyz@rotate@xyz@xaxis{0pt}{1pt}{0pt}{\tikz@xyz@angle}%
+ \pgfextract@process\tikz@xyz@rotate@yvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}%
+ \tikz@xyz@rotate@xyz@xaxis{0pt}{0pt}{1pt}{\tikz@xyz@angle}%
+ \pgfsetzvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}%
+ \pgfsetyvec{\tikz@xyz@rotate@yvec}%
+ },
+ rotate around y/.code={%
+ \tikz@xyz@rotate@let%
+ \pgfmathparse{#1}\let\tikz@xyz@angle=\pgfmathresult%
+ \tikz@xyz@rotate@xyz@yaxis{1pt}{0pt}{0pt}{\tikz@xyz@angle}%
+ \pgfextract@process\tikz@xyz@rotate@xvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}%
+ \tikz@xyz@rotate@xyz@yaxis{0pt}{0pt}{1pt}{\tikz@xyz@angle}%
+ \pgfsetzvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}%
+ \pgfsetxvec{\tikz@xyz@rotate@xvec}%
+ },
+ rotate around z/.code={%
+ \tikz@xyz@rotate@let%
+ \pgfmathparse{#1}\let\tikz@xyz@angle=\pgfmathresult%
+ \tikz@xyz@rotate@xyz@zaxis{1pt}{0pt}{0pt}{\tikz@xyz@angle}%
+ \pgfextract@process\tikz@xyz@rotate@xvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}%
+ \tikz@xyz@rotate@xyz@zaxis{0pt}{1pt}{0pt}{\tikz@xyz@angle}%
+ \pgfsetyvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}%
+ \pgfsetxvec{\tikz@xyz@rotate@xvec}%
+ },
+}%
+
+% Grid options
+\tikzoption{xstep}{\def\tikz@grid@x{#1}}%
+\tikzoption{ystep}{\def\tikz@grid@y{#1}}%
+\tikzoption{step}{\tikz@handle@vec{\tikz@step@point}{\tikz@step@single}#1\relax}%
+\def\tikz@step@single#1{\def\tikz@grid@x{#1}\def\tikz@grid@y{#1}}%
+\def\tikz@step@point#1{\pgf@process{#1}\edef\tikz@grid@x{\the\pgf@x}\edef\tikz@grid@y{\the\pgf@y}}%
+
+\def\tikz@grid@x{1cm}%
+\def\tikz@grid@y{1cm}%
+
+
+% Current point updates
+\newif\iftikz@current@point@local
+\tikzset{current point is local/.is if=tikz@current@point@local}%
+
+% Path usage options
+\newif\iftikz@mode@double
+\newif\iftikz@mode@fill
+\newif\iftikz@mode@draw
+\newif\iftikz@mode@clip
+\newif\iftikz@mode@boundary
+\newif\iftikz@mode@shade
+\newif\iftikz@mode@fade@path
+\newif\iftikz@mode@fade@scope
+\let\tikz@mode=\pgfutil@empty
+
+\def\tikz@nonetext{none}%
+
+\tikzoption{path only}[]{\let\tikz@mode=\pgfutil@empty}%
+\tikzset{
+ shade/.is choice,
+ shade/.default=true,
+ shade/true/.code=\tikz@addmode{\tikz@mode@shadetrue},
+ shade/false/.code=\tikz@addmode{\tikz@mode@shadefalse},
+ shade/none/.code=\tikz@addmode{\tikz@mode@shadefalse},
+}%
+
+\tikzoption{fill}[]{%
+ \edef\tikz@temp{#1}%
+ \ifx\tikz@temp\tikz@nonetext%
+ \tikz@addmode{\tikz@mode@fillfalse}%
+ \else%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else%
+ \tikz@addoption{\pgfsetfillcolor{#1}}%
+ \def\tikz@fillcolor{#1}%
+ \fi%
+ \tikz@addmode{\tikz@mode@filltrue}%
+ \fi%
+}%
+\tikzoption{draw}[]{%
+ \edef\tikz@temp{#1}%
+ \ifx\tikz@temp\tikz@nonetext%
+ \tikz@addmode{\tikz@mode@drawfalse}%
+ \else%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else%
+ \tikz@addoption{\pgfsetstrokecolor{#1}}%
+ \def\tikz@strokecolor{#1}%
+ \fi%
+ \tikz@addmode{\tikz@mode@drawtrue}%
+ \fi%
+}%
+\tikzoption{clip}[]{\tikz@addmode{\tikz@mode@cliptrue}}%
+\tikzoption{use as bounding box}[]{\tikz@addmode{\tikz@mode@boundarytrue}}%
+
+\tikzoption{save path}{\tikz@addmode{\pgfsyssoftpath@getcurrentpath#1\global\let#1=#1}}%
+\tikzoption{use path}{\tikz@addmode{\pgfsyssoftpath@setcurrentpath#1}}%
+
+\let\tikz@fillcolor=\pgfutil@empty
+\let\tikz@strokecolor=\pgfutil@empty
+
+% Insert a path using an option
+\tikzset{insert path/.code=\tikz@scan@next@command#1\pgf@stop}%
+
+% Pattern options
+\tikzset{pattern/.code=\tikzerror{You need to say \string\usetikzlibrary{patterns}},
+ pattern color/.style=pattern}%
+
+% Path pictures
+\tikzset{path picture/.code=\tikz@addmode{\def\tikz@path@picture{#1}}}%
+
+% Fading options
+\tikzset{path fading/.code={
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\tikz@nonetext%
+ \tikz@addmode{\tikz@mode@fade@pathfalse}%
+ \else%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else%
+ \def\tikz@path@fading{#1}%
+ \fi%
+ \tikz@addmode{\tikz@mode@fade@pathtrue}%
+ \fi%
+ },
+ path fading/.default=,
+ scope fading/.code={
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\tikz@nonetext%
+ \tikz@addmode{\tikz@mode@fade@scopefalse}%
+ \else%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else%
+ \def\tikz@scope@fading{#1}%
+ \fi%
+ \tikz@addmode{\tikz@mode@fade@scopetrue}%
+ \fi%
+ },
+ scope fading/.default=}%
+\tikzset{fit fading/.is if=tikz@fade@adjust}%
+\tikzset{fading transform/.store in=\tikz@fade@transform}%
+\tikzset{fading angle/.style={fading transform={rotate={#1}}}}%
+
+\newif\iftikz@fade@adjust%
+\tikz@fade@adjusttrue%
+\let\tikz@fade@transform\pgfutil@empty%
+
+\pgfutil@colorlet{transparent}{pgftransparent}%
+\def\tikz@do@fade@transform{\let\tikz@transform=\relax\expandafter\tikzset\expandafter{\tikz@fade@transform}}%
+
+
+
+% Transparency groups
+\newif\iftikz@transparency@group%
+\tikzset{/tikz/transparency group/.code=\tikz@transparency@grouptrue\def\tikz@transparency@group@options{isolated=true,#1}\let\tikz@blend@group\pgfutil@empty}%
+\tikzset{/tikz/blend group/.code=\tikz@transparency@grouptrue\def\tikz@transparency@group@options{isolated=true}\def\tikz@blend@group{\pgfsetblendmode{#1}}}%
+
+\let\tikz@blend@group\pgfutil@empty
+
+% Shading options
+\tikzoption{shading}{\def\tikz@shading{#1}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{shading angle}{\def\tikz@shade@angle{#1}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{top color}{%
+ \pgfutil@colorlet{tikz@axis@top}{#1}%
+ \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}%
+ \def\tikz@shading{axis}\def\tikz@shade@angle{0}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{bottom color}{%
+ \pgfutil@colorlet{tikz@axis@bottom}{#1}%
+ \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}%
+ \def\tikz@shading{axis}\def\tikz@shade@angle{0}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{middle color}{%
+ \pgfutil@colorlet{tikz@axis@middle}{#1}%
+ \def\tikz@shading{axis}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{left color}{%
+ \pgfutil@colorlet{tikz@axis@top}{#1}%
+ \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}%
+ \def\tikz@shading{axis}\def\tikz@shade@angle{90}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{right color}{%
+ \pgfutil@colorlet{tikz@axis@bottom}{#1}%
+ \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}%
+ \def\tikz@shading{axis}\def\tikz@shade@angle{90}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{ball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{ball}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{inner color}{\pgfutil@colorlet{tikz@radial@inner}{#1}\def\tikz@shading{radial}\tikz@addmode{\tikz@mode@shadetrue}}%
+\tikzoption{outer color}{\pgfutil@colorlet{tikz@radial@outer}{#1}\def\tikz@shading{radial}\tikz@addmode{\tikz@mode@shadetrue}}%
+
+\def\tikz@shading{axis}%
+\def\tikz@shade@angle{0}%
+
+\pgfdeclareverticalshading[tikz@axis@top,tikz@axis@middle,tikz@axis@bottom]{axis}{100bp}{%
+ color(0bp)=(tikz@axis@bottom);
+ color(25bp)=(tikz@axis@bottom);
+ color(50bp)=(tikz@axis@middle);
+ color(75bp)=(tikz@axis@top);
+ color(100bp)=(tikz@axis@top)}%
+
+\pgfutil@colorlet{tikz@axis@top}{gray}%
+\pgfutil@colorlet{tikz@axis@middle}{gray!50!white}%
+\pgfutil@colorlet{tikz@axis@bottom}{white}%
+
+\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{-10bp}{10bp}}{%
+ color(0bp)=(tikz@ball!15!white);
+ color(9bp)=(tikz@ball!75!white);
+ color(18bp)=(tikz@ball!70!black);
+ color(25bp)=(tikz@ball!50!black);
+ color(50bp)=(black)}%
+
+\pgfutil@colorlet{tikz@ball}{blue}%
+
+\pgfdeclareradialshading[tikz@radial@inner,tikz@radial@outer]{radial}{\pgfpointorigin}{%
+ color(0bp)=(tikz@radial@inner);
+ color(25bp)=(tikz@radial@outer);
+ color(50bp)=(tikz@radial@outer)}%
+
+\pgfutil@colorlet{tikz@radial@inner}{gray}%
+\pgfutil@colorlet{tikz@radial@outer}{white}%
+
+
+% Pin options
+\tikzset{
+ pin distance/.store in=\tikz@pin@distance,
+ pin distance=3ex,
+ pin position/.store in=\tikz@pin@default@pos,
+ pin position=above,
+ pin edge/.store in=\tikz@pin@edge@style,
+ pin edge={},
+ tikz@pin@post/.code={\global\let\tikz@pin@edge@style@smuggle=\tikz@pin@edge@style},
+ tikz@pre@pin@edge/.code={%
+ \toks0=\expandafter{\tikz@pin@edge@style@smuggle}%
+ \edef\pgf@marshal{\noexpand\tikzset{tikz@pin@options/.style={\the\toks0}}}%
+ \pgf@marshal
+ },%
+}%
+
+\tikzset{%
+ pin/.code={%
+ \begingroup
+ \ifnum\the\catcode`\:=\active\relax
+ \def\tikz@next{%
+ \endgroup
+ \tikz@parse@pin@active@i{#1}}%
+ \else
+ \def\tikz@next{%
+ \endgroup
+ \pgfutil@ifnextchar[%]
+ {\tikz@parse@pin@nonactive}
+ {\tikz@parse@pin@nonactive[]}#1:\pgf@nil}%
+ \fi
+ \tikz@next}}%
+
+\begingroup
+ \catcode`\:=\active\relax
+
+ \gdef\tikz@parse@pin@active@i#1{%
+ \pgfutil@ifnextchar[%]
+ {\tikz@parse@pin@active}
+ {\tikz@parse@pin@active[]}#1:\pgf@nil}%
+
+ \long\gdef\tikz@parse@pin@active[#1]#2:#3\pgf@nil{%
+ \def\tikz@temp{#3}%
+ \ifx\tikz@temp\pgfutil@empty
+ % no position, use default
+ \tikz@@parse@pin@active[#1]\tikz@pin@default@pos:#2:\pgf@nil%
+ \else
+ \tikz@@parse@pin@active[#1]#2:#3\pgf@nil%
+ \fi}%
+
+ \long\gdef\tikz@@parse@pin@active[#1]#2:#3:\pgf@nil{%
+ \tikzset{%
+ append after command = {%
+ \bgroup
+ [current point is local = true]
+ \pgfextra{\let\tikz@save@last@node=\tikzlastnode\tikz@node@is@a@labelfalse}%
+ node [tikz@label@angle = #2,
+ anchor=@auto,
+ every pin,
+ #1,
+ append after command = {%
+ (\tikz@save@last@node)
+ edge [every pin edge,
+ tikz@pre@pin@edge,
+ tikz@pin@options]
+ (\tikzlastnode)},
+ tikz@label@post = \tikz@pin@distance,
+ tikz@pin@post] {#3}
+ \egroup}}}%
+\endgroup
+
+\long\def\tikz@parse@pin@nonactive[#1]#2:#3\pgf@nil{%
+ \def\tikz@temp{#3}%
+ \ifx\tikz@temp\pgfutil@empty
+ % no position, use default
+ \tikz@@parse@pin@nonactive[#1]\tikz@pin@default@pos:#2:\pgf@nil%
+ \else
+ \tikz@@parse@pin@nonactive[#1]#2:#3\pgf@nil%
+ \fi}%
+
+\long\def\tikz@@parse@pin@nonactive[#1]#2:#3:\pgf@nil{%
+ \tikzset{%
+ append after command = {%
+ \bgroup
+ [current point is local = true]
+ \pgfextra{\let\tikz@save@last@node=\tikzlastnode\tikz@node@is@a@labelfalse}%
+ node [tikz@label@angle = #2,
+ anchor=@auto,
+ every pin,
+ #1,
+ append after command = {%
+ (\tikz@save@last@node)
+ edge [every pin edge,
+ tikz@pre@pin@edge,
+ tikz@pin@options]
+ (\tikzlastnode)},
+ tikz@label@post = \tikz@pin@distance,
+ tikz@pin@post] {#3}
+ \egroup}}}%
+
+% Label and pin options
+
+\tikzset{
+ label distance/.store in=\tikz@label@distance,
+ label distance=0pt,
+ label position/.store in=\tikz@label@default@pos,
+ label position=above,
+ absolute/.is if=tikz@absolute,
+ tikz@label@angle/.store in=\tikz@label@angle
+}%
+
+\newif\iftikz@absolute
+\def\tikz@on@text{center}%
+
+\tikzset{tikz@label@post/.code 2 args={
+ \edef\tikz@label@angle{\tikz@label@angle}%
+ \expandafter\pgfkeys@spdef\expandafter\tikz@label@angle\expandafter{\tikz@label@angle}%
+ \csname tikz@label@angle@is@\tikz@label@angle\endcsname
+ \ifx\tikz@label@angle\tikz@on@text%
+ \def\tikz@node@at{\pgfpointanchor{\tikzlastnode}{center}}%
+ \def\tikz@anchor{center}%
+ \else%
+ \iftikz@absolute%
+ \pgftransformreset%
+ \pgf@process{%
+ \pgfpointshapeborder{\tikzlastnode}%
+ {\pgfpointadd{\pgfpointanchor{\tikzlastnode}{center}}{\pgfpointpolar{\tikz@label@angle}{1pt}}}}%
+ \edef\tikz@node@at{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+ \tikz@compute@direction{\tikz@label@angle}%
+ \tikz@addtransform{\pgftransformshift{\pgfpointpolar{\tikz@label@angle}{#1}}}%
+ \else%
+ \pgf@process{\pgfpointanchor{\tikzlastnode}{\tikz@label@angle}}%
+ \edef\tikz@node@at{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgf@process{\pgfpointanchor{\tikzlastnode}{center}}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \tikz@label@simplefalse%
+ \ifdim\pgf@xc=\pgf@xb\relax%
+ \ifdim\pgf@yc=\pgf@yb\relax%
+ \tikz@label@simpletrue%
+ \fi%
+ \fi%
+ \iftikz@label@simple%
+ \tikz@compute@direction{\tikz@label@angle}%
+ \tikz@addtransform{\pgftransformshift{\pgfpointpolar{\tikz@label@angle}{#1}}}%
+ \else%
+ \pgf@process{\pgfpointnormalised{%
+ \pgfpointdiff{\pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}}{\pgfpointtransformed{\pgfqpoint{\pgf@xb}{\pgf@yb}}}}}%
+ \edef\pgf@marshal{%
+ \noexpand\tikz@addtransform{\noexpand\pgftransformshift{\noexpand\pgfpointscale{#1}{
+ \noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}}}%
+ \pgf@marshal%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@x=\pgf@yc%
+ \pgf@y=-\pgf@xc%
+ \ifx\tikz@anchor\tikz@auto@text%
+ \tikz@auto@anchor%
+ \fi%
+ \fi%
+ \fi%
+ \fi}
+}%
+
+\newif\iftikz@label@simple%
+
+\tikzset{%
+ label/.code={%
+ \begingroup
+ \ifnum\the\catcode`\:=\active\relax
+ \def\tikz@next{%
+ \endgroup
+ \tikz@parse@label@active@i{#1}}%
+ \else
+ \def\tikz@next{%
+ \endgroup
+ \pgfutil@ifnextchar[%]
+ {\tikz@parse@label@nonactive}
+ {\tikz@parse@label@nonactive[]}#1:\pgf@nil}%
+ \fi
+ \tikz@next}}%
+
+\begingroup
+ \catcode`\:=\active\relax
+
+ \gdef\tikz@parse@label@active@i#1{%
+ \pgfutil@ifnextchar[%]
+ {\tikz@parse@label@active}
+ {\tikz@parse@label@active[]}#1:\pgf@nil}%
+
+ \gdef\tikz@parse@label@active[#1]#2:#3\pgf@nil{%
+ \def\tikz@temp{#3}%
+ \ifx\tikz@temp\pgfutil@empty
+ % no position, use default
+ \tikz@@parse@label@active[#1]\tikz@label@default@pos:#2:\pgf@nil%
+ \else
+ \def\tikz@temp{#2}%
+ \ifx\tikz@temp\pgfutil@empty
+ \tikz@@parse@label@active[#1]\tikz@label@default@pos:#3\pgf@nil%
+ \else
+ \tikz@@parse@label@active[#1]#2:#3\pgf@nil%
+ \fi
+ \fi
+ }%
+
+ \gdef\tikz@@parse@label@active[#1]#2:#3:\pgf@nil{%
+ \tikzset{%
+ append after command = {%
+ \bgroup
+ [current point is local=true]
+ \pgfextra{\let\tikz@save@last@fig@name=\tikz@last@fig@name\tikz@node@is@a@labelfalse}
+ node [tikz@label@angle = #2,
+ anchor=@auto,
+ every label,
+ #1,
+ tikz@label@post = \tikz@label@distance] {\iftikz@handle@active@nodes\expandafter\scantokens\else\expandafter\pgfutil@firstofone\fi{#3\noexpand}}
+ \pgfextra{\global\let\tikz@last@fig@name=\tikz@save@last@fig@name}
+ \egroup}}}%
+\endgroup
+
+\def\tikz@parse@label@nonactive[#1]#2:#3\pgf@nil{%
+ \def\tikz@temp{#3}%
+ \ifx\tikz@temp\pgfutil@empty
+ % no position, use default
+ \tikz@@parse@label@nonactive[#1]\tikz@label@default@pos:#2:\pgf@nil%
+ \else
+ \def\tikz@temp{#2}%
+ \ifx\tikz@temp\pgfutil@empty
+ \tikz@@parse@label@nonactive[#1]\tikz@label@default@pos:#3\pgf@nil%
+ \else
+ \tikz@@parse@label@nonactive[#1]#2:#3\pgf@nil%
+ \fi
+ \fi
+}%
+
+\def\tikz@@parse@label@nonactive[#1]#2:#3:\pgf@nil{%
+ \tikzset{%
+ append after command = {%
+ \bgroup
+ [current point is local=true]
+ \pgfextra{\let\tikz@save@last@fig@name=\tikz@last@fig@name\tikz@node@is@a@labelfalse}
+ node [tikz@label@angle = #2,
+ anchor=@auto,
+ every label,
+ #1,
+ tikz@label@post = \tikz@label@distance] {\iftikz@handle@active@nodes\expandafter\scantokens\else\expandafter\pgfutil@firstofone\fi{#3\noexpand}}
+ \pgfextra{\global\let\tikz@last@fig@name=\tikz@save@last@fig@name}
+ \egroup}}}%
+
+\expandafter\def\csname tikz@label@angle@is@right\endcsname{\def\tikz@label@angle{0}}%
+\expandafter\def\csname tikz@label@angle@is@above right\endcsname{\def\tikz@label@angle{45}}%
+\expandafter\def\csname tikz@label@angle@is@above\endcsname{\def\tikz@label@angle{90}}%
+\expandafter\def\csname tikz@label@angle@is@above left\endcsname{\def\tikz@label@angle{135}}%
+\expandafter\def\csname tikz@label@angle@is@left\endcsname{\def\tikz@label@angle{180}}%
+\expandafter\def\csname tikz@label@angle@is@below left\endcsname{\def\tikz@label@angle{225}}%
+\expandafter\def\csname tikz@label@angle@is@below\endcsname{\def\tikz@label@angle{270}}%
+\expandafter\def\csname tikz@label@angle@is@below right\endcsname{\def\tikz@label@angle{315}}%
+
+\def\tikz@compute@direction#1{%
+ \ifx\tikz@anchor\tikz@auto@text%
+ \let\tikz@do@auto@anchor=\relax
+ \pgfmathsetcount{\c@pgf@counta}{#1}%
+ \ifnum\c@pgf@counta<0\relax
+ \advance\c@pgf@counta by 360\relax%
+ \fi%
+ \ifnum\c@pgf@counta>359\relax
+ \advance\c@pgf@counta by-360\relax%
+ \fi%
+ \ifnum\c@pgf@counta<4\relax%
+ \def\tikz@anchor{west}%
+ \else\ifnum\c@pgf@counta<87\relax%
+ \def\tikz@anchor{south west}%
+ \else\ifnum\c@pgf@counta<94\relax%
+ \def\tikz@anchor{south}%
+ \else\ifnum\c@pgf@counta<177\relax%
+ \def\tikz@anchor{south east}%
+ \else\ifnum\c@pgf@counta<184\relax%
+ \def\tikz@anchor{east}%
+ \else\ifnum\c@pgf@counta<267\relax%
+ \def\tikz@anchor{north east}%
+ \else\ifnum\c@pgf@counta<274\relax%
+ \def\tikz@anchor{north}%
+ \else\ifnum\c@pgf@counta<357\relax%
+ \def\tikz@anchor{north west}%
+ \else%
+ \def\tikz@anchor{west}%
+ \fi\fi\fi\fi\fi\fi\fi\fi%
+ \fi%
+}%
+\def\tikz@auto@text{@auto}%
+
+% General node options
+\tikzset{
+ name/.code={\edef\tikz@fig@name{\tikz@pp@name{#1}}\let\tikz@id@name\tikz@fig@name},%
+ name prefix/.initial=,%
+ name suffix/.initial=,%
+ local bounding box/.style={/pgf/local bounding box/.expanded=\tikz@pp@name{#1}}
+}%
+\def\tikz@pp@name#1{\csname pgfk@/tikz/name prefix\endcsname#1\csname pgfk@/tikz/name suffix\endcsname}%
+
+
+\tikzset{
+ node contents/.code=\def\tikz@node@content{#1},
+ pic type/.code=\def\tikz@node@content{#1}, % alias
+}%
+
+\tikzset{
+ behind path/.code=\def\tikz@whichbox{\tikz@figbox@bg},
+ in front of path/.code=\def\tikz@whichbox{\tikz@figbox}
+}%
+\def\tikz@whichbox{\tikz@figbox}%
+
+\tikzoption{at}{\tikz@scan@one@point\tikz@set@at#1}%
+\def\tikz@set@at#1{\def\tikz@node@at{#1}}%
+
+\tikzoption{shape}{\edef\tikz@shape{#1}}%
+
+\tikzoption{nodes}{\tikzset{every node/.append style={#1}}}%
+
+\tikzset{alias/.code={%
+ \tikz@fig@mustbenamed
+ \begingroup
+ \toks0=\expandafter{\tikz@alias}%
+ \edef\pgf@temp{\noexpand\pgfnodealias{\tikz@pp@name{#1}}{\noexpand\tikz@fig@name}}%
+ \toks1=\expandafter{\pgf@temp}%
+ \xdef\pgf@marshal{%
+ \noexpand\def\noexpand\tikz@alias{\the\toks0 \the\toks1 }%
+ }%
+ \endgroup
+ \pgf@marshal
+}}%
+
+% deprecated:
+\def\tikzaddafternodepathoption#1{#1\tikzset{prefix after command={\pgfextra{#1}}}}%
+\tikzset{after node path/.style={append after command={#1}}}%
+
+
+% Pic options
+\tikzset{pic text/.store in=\tikzpictext}%
+\let\tikzpictext\relax
+\tikzset{pic text options/.store in=\tikzpictextoptions}%
+\let\tikzpictextoptions\pgfutil@empty
+
+
+% Anchoring
+
+\tikzoption{anchor}{\def\tikz@anchor{#1}\let\tikz@do@auto@anchor=\relax}%
+
+\tikzoption{left}[]{\def\tikz@anchor{east}\tikz@possibly@transform{x}{-}{#1}}%
+\tikzoption{right}[]{\def\tikz@anchor{west}\tikz@possibly@transform{x}{}{#1}}%
+\tikzoption{above}[]{\def\tikz@anchor{south}\tikz@possibly@transform{y}{}{#1}}%
+\tikzoption{below}[]{\def\tikz@anchor{north}\tikz@possibly@transform{y}{-}{#1}}%
+\tikzoption{above left}[]%
+ {\def\tikz@anchor{south east}%
+ \tikz@possibly@transform{x}{-}{#1}\tikz@possibly@transform{y}{}{#1}}%
+\tikzoption{above right}[]%
+ {\def\tikz@anchor{south west}%
+ \tikz@possibly@transform{x}{}{#1}\tikz@possibly@transform{y}{}{#1}}%
+\tikzoption{below left}[]%
+ {\def\tikz@anchor{north east}%
+ \tikz@possibly@transform{x}{-}{#1}\tikz@possibly@transform{y}{-}{#1}}%
+\tikzoption{below right}[]%
+ {\def\tikz@anchor{north west}%
+ \tikz@possibly@transform{x}{}{#1}\tikz@possibly@transform{y}{-}{#1}}%
+\tikzset{centered/.code=\def\tikz@anchor{center}}%
+
+\tikzoption{node distance}{\def\tikz@node@distance{#1}}%
+\def\tikz@node@distance{1cm}%
+
+% The following are deprecated:
+\tikzoption{above of}{\tikz@of{#1}{90}}%
+\tikzoption{below of}{\tikz@of{#1}{-90}}%
+\tikzoption{left of}{\tikz@of{#1}{180}}%
+\tikzoption{right of}{\tikz@of{#1}{0}}%
+\tikzoption{above left of}{\tikz@of{#1}{135}}%
+\tikzoption{below left of}{\tikz@of{#1}{-135}}%
+\tikzoption{above right of}{\tikz@of{#1}{45}}%
+\tikzoption{below right of}{\tikz@of{#1}{-45}}%
+\def\tikz@of#1#2{%
+ \def\tikz@anchor{center}%
+ \let\tikz@do@auto@anchor=\relax%
+ \tikz@addtransform{%
+ \expandafter\tikz@extract@node@dist\tikz@node@distance and\pgf@stop%
+ \pgftransformshift{\pgfpointpolar{#2}{\tikz@extracted@node@distance}}}%
+ \def\tikz@node@at{\pgfpointanchor{\tikz@pp@name{#1}}{center}}}%
+\def\tikz@extract@node@dist#1and#2\pgf@stop{%
+ \def\tikz@extracted@node@distance{#1}}%
+
+\tikzset{
+ transform shape nonlinear/.is choice,
+ transform shape nonlinear/.default=true,
+ transform shape nonlinear/true/.code=\let\tikz@nlt\relax,
+ transform shape nonlinear/false/.code=\def\tikz@nlt{\pgfapproximatenonlineartranslation},
+ transform shape nonlinear=false,
+}%
+
+
+\tikzoption{transform shape}[true]{%
+ \csname tikz@fullytransformed#1\endcsname%
+ \iftikz@fullytransformed%
+ \pgfresetnontranslationattimefalse%
+ \else%
+ \pgfresetnontranslationattimetrue%
+ \fi%
+}%
+
+\newif\iftikz@fullytransformed
+\pgfresetnontranslationattimetrue%
+
+\def\tikz@anchor{center}%
+\def\tikz@shape{rectangle}%
+
+\def\tikz@possibly@transform#1#2#3{%
+ \let\tikz@do@auto@anchor=\relax%
+ \def\tikz@test{#3}%
+ \ifx\tikz@test\pgfutil@empty%
+ \else%
+ \pgfmathsetlength{\pgf@x}{#3}%
+ \pgf@x=#2\pgf@x\relax%
+ \edef\tikz@marshal{\noexpand\tikz@addtransform{%
+ \expandafter\noexpand\csname pgftransform#1shift\endcsname{\the\pgf@x}}}%
+ \tikz@marshal%
+ \fi%
+}%
+
+
+% Inter-picture options
+\tikzoption{remember picture}[true]{\csname pgfrememberpicturepositiononpage#1\endcsname}
+\tikzset{
+ overlay/.is choice,
+ overlay/true/.code={\pgf@relevantforpicturesizefalse},
+ overlay/false/.code={\pgf@relevantforpicturesizetrue},
+ overlay/.default=true
+}
+
+
+
+% Line/curve label placement options
+\tikzoption{sloped}[true]{\csname pgfslopedattime#1\endcsname}%
+\tikzoption{allow upside down}[true]{\csname pgfallowupsidedownattime#1\endcsname}%
+
+\tikzoption{pos}{\edef\tikz@time{#1}\ifx\tikz@time\pgfutil@empty\else\pgfmathsetmacro\tikz@time{\tikz@time}\fi}%
+
+\tikzoption{auto}[]{\csname tikz@install@auto@anchor@#1\endcsname}%
+\tikzoption{swap}[]{%
+ \def\tikz@temp{left}%
+ \ifx\tikz@auto@anchor@direction\tikz@temp%
+ \def\tikz@auto@anchor@direction{right}%
+ \else%
+ \def\tikz@auto@anchor@direction{left}%
+ \fi%
+}%
+\tikzset{'/.style=swap}% shorthand
+
+
+\def\tikz@install@auto@anchor@{\let\tikz@do@auto@anchor=\tikz@auto@anchor@on}%
+\def\tikz@install@auto@anchor@false{\let\tikz@do@auto@anchor=\relax}%
+\def\tikz@install@auto@anchor@left{\let\tikz@do@auto@anchor=\tikz@auto@anchor@on\def\tikz@auto@anchor@direction{left}}%
+\def\tikz@install@auto@anchor@right{\let\tikz@do@auto@anchor=\tikz@auto@anchor@on\def\tikz@auto@anchor@direction{right}}%
+
+\let\tikz@do@auto@anchor=\relax%
+
+\def\tikz@auto@anchor@on{\csname tikz@auto@anchor@\tikz@auto@anchor@direction\endcsname}
+
+\def\tikz@auto@anchor@left{\tikz@auto@pre\tikz@auto@anchor\tikz@auto@post}%
+\def\tikz@auto@anchor@right{\tikz@auto@pre\tikz@auto@anchor@prime\tikz@auto@post}%
+
+\def\tikz@auto@anchor@direction{left}%
+
+% Text options
+\tikzoption{text}{\def\tikz@textcolor{#1}}%
+\tikzoption{font}{\def\tikz@textfont{#1}}%
+\tikzoption{node font}{\def\tikz@node@textfont{#1}}%
+\tikzoption{text opacity}{\def\tikz@textopacity{#1}}%
+\tikzoption{text width}{\def\tikz@text@width{#1}}%
+\tikzoption{text height}{\def\tikz@text@height{#1}}%
+\tikzoption{text depth}{\def\tikz@text@depth{#1}}%
+\tikzoption{text ragged}[]%
+{\def\tikz@text@action{\pgfutil@raggedright\rightskip0pt plus2em \spaceskip.3333em \xspaceskip.5em\relax}}%
+\tikzoption{text badly ragged}[]{\def\tikz@text@action{\pgfutil@raggedright\relax}}%
+\tikzoption{text ragged left}[]%
+{\def\tikz@text@action{\pgfutil@raggedleft\leftskip0pt plus2em \spaceskip.3333em \xspaceskip.5em\relax}}%
+\tikzoption{text badly ragged left}[]{\def\tikz@text@action{\pgfutil@raggedleft\relax}}%
+\tikzoption{text justified}[]{\def\tikz@text@action{\leftskip0pt\rightskip0pt\relax}}%
+\tikzoption{text centered}[]{\def\tikz@text@action{%
+ \leftskip0pt plus2em%
+ \rightskip0pt plus2em%
+ \spaceskip.3333em \xspaceskip.5em%
+ \parfillskip=0pt%
+ \iftikz@warn@for@narrow@centered\else\hbadness10000\fi%
+ \let\\=\@centercr% for latex
+ \relax}}%
+\tikzoption{text badly centered}[]%
+{\def\tikz@text@action{%
+ \let\\=\@centercr% for latex
+ \parfillskip=0pt%
+ \rightskip\pgfutil@flushglue%
+ \leftskip\pgfutil@flushglue\relax}}%
+\tikzset{badness warnings for centered text/.is if=tikz@warn@for@narrow@centered}%
+\newif\iftikz@warn@for@narrow@centered
+
+\def\tikz@text@reset{%
+ \let\tikz@text@width=\pgfutil@empty
+ \let\tikz@text@height=\pgfutil@empty
+ \let\tikz@text@depth=\pgfutil@empty
+ \let\tikz@textcolor=\pgfutil@empty
+ \let\tikz@textfont=\pgfutil@empty
+ \let\tikz@textopacity=\pgfutil@empty
+ \let\tikz@node@textfont=\pgfutil@empty
+ \def\tikz@text@action{\pgfutil@raggedright\rightskip0pt plus2em \spaceskip.3333em \xspaceskip.5em\relax}%
+}
+\tikz@text@reset
+
+
+% Alignment
+\tikzset{
+ node halign header/.initial=,
+ align/.is choice,
+ align/left/.style ={text ragged,node halign header=\tikz@align@left@header},
+ align/flush left/.style ={text badly ragged,node halign header=\tikz@align@left@header},
+ align/right/.style ={text ragged left,node halign header=\tikz@align@right@header},
+ align/flush right/.style ={text badly ragged left,node halign header=\tikz@align@right@header},
+ align/center/.style={text centered,node halign header=\tikz@align@center@header},
+ align/flush center/.style={text badly centered,node halign header=\tikz@align@center@header},
+ align/justify/.style ={text justified,node halign header=\tikz@align@left@header},
+ align/none/.style ={text justified,node halign header=},
+}%
+\def\tikz@align@left@header{##\hfil\cr}%
+\def\tikz@align@right@header{\hfil##\cr}%
+\def\tikz@align@center@header{\hfil##\hfil\cr}%
+
+
+
+% Arrow options
+\tikzoption{arrows}{\tikz@processarrows{#1}}%
+
+
+\tikzoption{>}{\pgfdeclarearrow{name=<->,means={#1}}}%
+\pgfdeclarearrow{name=|<->|, means={>[sep=0pt].|}}%
+
+\tikzoption{shorten <}{\pgfsetshortenstart{#1}}%
+\tikzoption{shorten >}{\pgfsetshortenend{#1}}%
+
+\def\tikz@processarrows#1{%
+ \def\tikz@current@arrows{#1}%
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else%
+ \pgfsetarrows{#1}%
+ \fi%
+}%
+
+\def\tikz@current@arrows{-}%
+
+% Parabola options
+\tikzoption{bend}{\tikz@scan@one@point\tikz@set@parabola@bend#1\relax}%
+\tikzoption{bend pos}{\def\tikz@parabola@bend@factor{#1}}%
+\tikzoption{parabola height}{%
+ \def\tikz@parabola@bend@factor{.5}%
+ \def\tikz@parabola@bend{\pgfpointadd{\pgfpoint{0pt}{#1}}{\tikz@last@position@saved}}}%
+
+\def\tikz@parabola@bend{\tikz@last@position@saved}%
+\def\tikz@parabola@bend@factor{0}%
+
+\def\tikz@set@parabola@bend#1{\def\tikz@parabola@bend{#1}}%
+
+% Axis options
+\tikzoption{domain}{\edef\tikz@plot@domain{#1}\expandafter\tikz@plot@samples@recalc\tikz@plot@domain\relax}%
+\tikzoption{range}{\def\tikz@plot@range{#1}}%
+\tikzoption{yrange}{\def\tikz@plot@range{#1}}%
+\let\tikz@plot@range=\pgfutil@empty
+\tikzoption{xrange}{\def\tikz@plot@xrange{#1}}%
+\let\tikz@plot@xrange=\pgfutil@empty
+
+% Plot options
+\tikzoption{smooth}[]{\let\tikz@plot@handler=\pgfplothandlercurveto}%
+\tikzoption{smooth cycle}[]{\let\tikz@plot@handler=\pgfplothandlerclosedcurve}%
+\tikzoption{sharp plot}[]{\let\tikz@plot@handler\pgfplothandlerlineto}%
+\tikzoption{sharp cycle}[]{\let\tikz@plot@handler\pgfplothandlerpolygon}%
+
+\tikzoption{tension}{\pgfsetplottension{#1}}%
+
+\tikzoption{xcomb}[]{\let\tikz@plot@handler=\pgfplothandlerxcomb}%
+\tikzoption{ycomb}[]{\let\tikz@plot@handler=\pgfplothandlerycomb}%
+\tikzoption{polar comb}[]{\let\tikz@plot@handler=\pgfplothandlerpolarcomb}%
+\tikzoption{ybar}[]{\let\tikz@plot@handler=\pgfplothandlerybar}%
+\tikzoption{ybar interval}[]{\let\tikz@plot@handler=\pgfplothandlerybarinterval}%
+\tikzoption{xbar interval}[]{\let\tikz@plot@handler=\pgfplothandlerxbarinterval}%
+\tikzoption{xbar}[]{\let\tikz@plot@handler=\pgfplothandlerxbar}%
+\tikzoption{const plot}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlineto}%
+\tikzoption{const plot mark left}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlineto}%
+\tikzoption{const plot mark right}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlinetomarkright}%
+\tikzoption{const plot mark mid}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlinetomarkmid}%
+\tikzoption{jump mark right}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkright}%
+\tikzoption{jump mark mid}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkmid}%
+\tikzoption{jump mark left}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkleft}%
+
+\tikzoption{raw gnuplot}[true]{\csname tikz@plot@raw@gnuplot#1\endcsname}%
+\tikzoption{prefix}{\def\tikz@plot@prefix{#1}}%
+\tikzoption{id}{\def\tikz@plot@id{#1}}%
+
+\tikzoption{samples}{\pgfmathsetmacro\tikz@plot@samples{max(2,#1)}\expandafter\tikz@plot@samples@recalc\tikz@plot@domain\relax}%
+\tikzoption{samples at}{\def\tikz@plot@samplesat{#1}}%
+\tikzoption{parametric}[true]{\csname tikz@plot@parametric#1\endcsname}%
+
+\tikzoption{variable}{\def\tikz@plot@var{#1}}%
+
+\tikzoption{only marks}[]{\let\tikz@plot@handler\pgfplothandlerdiscard}%
+
+\tikzoption{mark}{%
+ \def\tikz@plot@mark{#1}%
+ \def\tikz@temp{none}%
+ \ifx\tikz@temp\tikz@plot@mark
+ \let\tikz@plot@mark=\pgfutil@empty
+ \fi
+}%
+\tikzset{
+ no marks/.style={mark=none},%
+ no markers/.style={mark=none},%
+ every mark/.style={},
+ mark options/.style={%
+ every mark/.style={#1}%
+ }}%
+\tikzoption{mark size}{\pgfsetplotmarksize{#1}}%
+
+\tikzoption{mark indices}{\def\tikz@mark@list{#1}}%
+\tikzoption{mark phase}{\pgfsetplotmarkphase{#1}}%
+\tikzoption{mark repeat}{\pgfsetplotmarkrepeat{#1}}%
+
+\let\tikz@mark@list=\pgfutil@empty
+
+\let\tikz@plot@handler=\pgfplothandlerlineto
+\let\tikz@plot@mark=\pgfutil@empty
+
+\def\tikz@plot@samples{25}%
+\def\tikz@plot@domain{-5:5}%
+\def\tikz@plot@var{\x}%
+\def\tikz@plot@samplesat{-5,-4.5833333,...,5}%
+\def\tikz@plot@samples@recalc#1:#2\relax{%
+ \begingroup
+ \pgfmathparse{#1}%
+ \let\tikz@temp@start=\pgfmathresult%
+ \pgfmathparse{#2}%
+ \let\tikz@temp@end=\pgfmathresult%
+ \pgfmathsetmacro\tikz@temp@diff{(\tikz@temp@end-\tikz@temp@start)/(\tikz@plot@samples-1)}%
+ %
+ % this particular item is for backwards compatibility.
+ % Pgfplots <= 1.8 called 'samples' in a context where the 'fpu' was
+ % active... and I fear there is no simple solution to replace the
+ % new \ifdim below. Sorry.
+ \pgfkeys{/pgf/fpu/output format/fixed/.try}%
+ %
+ \pgfmathsetmacro\tikz@temp@diff@abs{abs(\tikz@temp@diff)}%
+ \ifdim\tikz@temp@diff@abs pt<0.0001pt\relax%
+ \edef\tikz@plot@samplesat{\tikz@temp@start,\tikz@temp@end}%
+ \else%
+ \pgfmathparse{\tikz@temp@start+\tikz@temp@diff}%
+ \edef\tikz@plot@samplesat{\tikz@temp@start,\pgfmathresult,...,\tikz@temp@end}%
+ \fi%
+ \pgfmath@smuggleone\tikz@plot@samplesat
+ \endgroup
+}%
+
+
+\def\tikz@plot@prefix{\jobname.}%
+\def\tikz@plot@id{pgf-plot}%
+
+\newif\iftikz@plot@parametric
+\newif\iftikz@plot@raw@gnuplot
+
+
+%
+% To and edge options
+%
+\tikzoption{to path}{\def\tikz@to@path{#1}}%
+
+\def\tikz@to@path{-- (\tikztotarget) \tikztonodes}%
+
+\tikzset{edge macro/.store in=\tikz@edge@macro}%
+\let\tikz@edge@macro\pgfutil@empty
+
+\tikzset{
+ edge node/.code={
+ \expandafter\def\expandafter\tikz@tonodes\expandafter{\tikz@tonodes #1}
+ },
+ edge label/.style={/tikz/edge node={node[auto]{#1}}},
+ edge label'/.style={/tikz/edge node={node[auto,swap]{#1}}},
+}%
+
+
+% After command options
+\tikzset{
+ append after command/.code=\expandafter\def\expandafter\tikz@after@path\expandafter{\tikz@after@path#1},
+ prefix after command/.code={%
+ \def\tikz@temp{#1}%
+ \expandafter\expandafter\expandafter\def%
+ \expandafter\expandafter\expandafter\tikz@after@path%
+ \expandafter\expandafter\expandafter{%
+ \expandafter\tikz@temp\tikz@after@path}%
+ },
+}%
+\let\tikz@after@path\pgfutil@empty
+
+
+% Tree options
+\newif\iftikz@child@missing
+\pgfkeys{/tikz/missing/.is if=tikz@child@missing}%
+
+\tikzset{edge from parent macro/.initial=\tikz@edge@from@parent@macro}%
+\def\tikz@edge@from@parent@macro#1#2{
+ [style=edge from parent, #1, /utils/exec=\tikz@node@is@a@labeltrue] \tikz@edge@to@parent@path #2}%
+
+\tikzoption{edge from parent path}{\def\tikz@edge@to@parent@path{#1}}%
+
+\tikzoption{parent anchor}{\def\tikzparentanchor{.#1}\ifx\tikzparentanchor\tikz@border@text\let\tikzparentanchor\pgfutil@empty\fi}%
+\tikzoption{child anchor}{\def\tikzchildanchor{.#1}\ifx\tikzchildanchor\tikz@border@text\let\tikzchildanchor\pgfutil@empty\fi}%
+
+\tikzoption{level distance}{\pgfmathsetlength\tikzleveldistance{#1}}%
+\tikzoption{sibling distance}{\pgfmathsetlength\tikzsiblingdistance{#1}}%
+
+\tikzoption{growth function}{\let\tikz@grow=#1}%
+
+\tikzset{grow siblings on line/.style={growth function=\tikz@grow@direction}}%
+
+\tikzoption{growth parent anchor}{\def\tikz@growth@anchor{#1}}%
+\tikzoption{grow}{\tikz@set@growth{#1}\edef\tikz@special@level{\the\tikztreelevel}}%
+\tikzoption{grow'}{\tikz@set@growth{#1}\tikz@swap@growth\edef\tikz@special@level{\the\tikztreelevel}}%
+
+\def\tikz@growth@anchor{center}%
+
+\def\tikz@special@level{-1}% never
+
+\def\tikz@swap@growth{%
+ % Swap left and right
+ \let\tikz@temp=\tikz@angle@grow@right%
+ \let\tikz@angle@grow@right=\tikz@angle@grow@left%
+ \let\tikz@angle@grow@left=\tikz@temp%
+}%
+
+\def\tikz@set@growth#1{%
+ \let\tikz@grow=\tikz@grow@direction%
+ \expandafter\ifx\csname tikz@grow@direction@#1\endcsname\relax%
+ \c@pgf@counta=#1\relax%
+ \else%
+ \c@pgf@counta=\csname tikz@grow@direction@#1\endcsname%
+ \fi%
+ \edef\tikz@angle@grow{\the\c@pgf@counta}%
+ \advance\c@pgf@counta by-90\relax%
+ \edef\tikz@angle@grow@left{\the\c@pgf@counta}%
+ \advance\c@pgf@counta by180\relax%
+ \edef\tikz@angle@grow@right{\the\c@pgf@counta}%
+}%
+
+\def\tikz@border@text{.border}%
+\let\tikzparentanchor=\pgfutil@empty
+\let\tikzchildanchor=\pgfutil@empty
+\def\tikz@edge@to@parent@path{(\tikzparentnode\tikzparentanchor) -- (\tikzchildnode\tikzchildanchor)}%
+
+\tikzleveldistance=15mm%
+\tikzsiblingdistance=15mm%
+
+\def\tikz@grow@direction@down{-90}%
+\def\tikz@grow@direction@up{90}%
+\def\tikz@grow@direction@left{180}%
+\def\tikz@grow@direction@right{0}%
+
+\def\tikz@grow@direction@south{-90}%
+\def\tikz@grow@direction@north{90}%
+\def\tikz@grow@direction@west{180}%
+\def\tikz@grow@direction@east{0}%
+
+\expandafter\def\csname tikz@grow@direction@north east\endcsname{45}%
+\expandafter\def\csname tikz@grow@direction@north west\endcsname{135}%
+\expandafter\def\csname tikz@grow@direction@south east\endcsname{-45}%
+\expandafter\def\csname tikz@grow@direction@south west\endcsname{-135}%
+
+\def\tikz@grow@direction{%
+ \pgftransformshift{\pgfpointpolar{\tikz@angle@grow}{\tikzleveldistance}}%
+ \ifnum\tikztreelevel=\tikz@special@level%
+ \else%
+ \pgf@xc=.5\tikzsiblingdistance%
+ \c@pgf@counta=\tikznumberofchildren%
+ \advance\c@pgf@counta by1\relax%
+ \pgfutil@tempdima=\c@pgf@counta\pgf@xc%
+ \pgftransformshift{\pgfpointpolar{\tikz@angle@grow@left}{\pgfutil@tempdima}}%
+ \pgftransformshift{\pgfpointpolar{\tikz@angle@grow@right}{\tikznumberofcurrentchild\tikzsiblingdistance}}%
+ \fi%
+}%
+
+\tikzset{grow=down}%
+
+
+% Snakes are in a lib:
+\tikzset{snake/.code=\tikzerror{You need to say \string\usetikzlibrary{snakes}}}%
+
+% Decorations
+\tikzset{decorate/.code=\tikzerror{You need to load a decoration library}}%
+
+% Matrix options
+\usepgfmodule{matrix}%
+
+\tikzoption{matrix}[true]{\csname tikz@is@matrix#1\endcsname}%
+
+\tikzoption{matrix anchor}{\def\tikz@matrix@anchor{#1}}%
+
+\tikzoption{column sep}{\def\pgfmatrixcolumnsep{#1}}%
+\tikzoption{row sep}{\def\pgfmatrixrowsep{#1}}%
+
+\tikzoption{cells}{\tikzset{every cell/.append style={#1}}}%
+
+\tikzoption{ampersand replacement}{\def\tikz@ampersand@replacement{#1}}%
+
+\newif\iftikz@is@matrix
+\let\tikz@matrix@anchor=\pgfutil@empty
+\let\tikz@ampersand@replacement=\pgfutil@empty
+
+
+% Automatic shorthand management
+\tikzset{%
+ handle active characters in code/.is if=tikz@handle@active@code,
+ handle active characters in nodes/.is if=tikz@handle@active@nodes,
+}%
+\newif\iftikz@handle@active@code
+\newif\iftikz@handle@active@nodes
+
+
+% Execute option
+\tikzoption{execute at begin picture}{\expandafter\def\expandafter\tikz@atbegin@picture\expandafter{\tikz@atbegin@picture#1}}%
+\tikzoption{execute at end picture}{\expandafter\def\expandafter\tikz@atend@picture\expandafter{\tikz@atend@picture#1}}%
+\tikzoption{execute at begin scope}{\expandafter\def\expandafter\tikz@atbegin@scope\expandafter{\tikz@atbegin@scope#1}}%
+\tikzoption{execute at end scope}{\expandafter\def\expandafter\tikz@atend@scope\expandafter{\tikz@atend@scope#1}}%
+\tikzoption{execute at begin to}{\expandafter\def\expandafter\tikz@atbegin@to\expandafter{\tikz@atbegin@to#1}}%
+\tikzoption{execute at end to}{\expandafter\def\expandafter\tikz@atend@to\expandafter{\tikz@atend@to#1}}%
+\tikzoption{execute at begin node}{\expandafter\def\expandafter\tikz@atbegin@node\expandafter{\tikz@atbegin@node#1}}%
+\tikzoption{execute at end node}{\expandafter\def\expandafter\tikz@atend@node\expandafter{\tikz@atend@node#1}}%
+\tikzoption{execute at begin matrix}{\expandafter\def\expandafter\tikz@atbegin@matrix\expandafter{\tikz@atbegin@matrix#1}}%
+\tikzoption{execute at end matrix}{\expandafter\def\expandafter\tikz@atend@matrix\expandafter{\tikz@atend@matrix#1}}%
+\tikzoption{execute at begin cell}{\expandafter\def\expandafter\tikz@atbegin@cell\expandafter{\tikz@atbegin@cell#1}}%
+\tikzoption{execute at end cell}{\expandafter\def\expandafter\tikz@atend@cell\expandafter{\tikz@atend@cell#1}}%
+\tikzoption{execute at empty cell}{\expandafter\def\expandafter\tikz@at@emptycell\expandafter{\tikz@at@emptycell#1}}%
+
+\let\tikz@atbegin@picture=\pgfutil@empty
+\let\tikz@atend@picture=\pgfutil@empty
+\let\tikz@atbegin@scope=\pgfutil@empty
+\let\tikz@atend@scope=\pgfutil@empty
+\let\tikz@atbegin@to=\pgfutil@empty
+\let\tikz@atend@to=\pgfutil@empty
+\let\tikz@atbegin@node=\pgfutil@empty
+\let\tikz@atend@node=\pgfutil@empty
+\let\tikz@atbegin@cell=\pgfutil@empty
+\let\tikz@atend@cell=\pgfutil@empty
+\let\tikz@at@emptycell=\pgfutil@empty
+\let\tikz@atbegin@matrix=\pgfutil@empty
+\let\tikz@atend@matrix=\pgfutil@empty
+
+
+% Pre and post actions
+\tikzset{preaction/.code=\expandafter\def\expandafter\tikz@preactions\expandafter{\tikz@preactions\tikz@extra@preaction{#1}}}%
+\tikzset{postaction/.code=\expandafter\def\expandafter\tikz@postactions\expandafter{\tikz@postactions\tikz@extra@postaction{#1}}}%
+\let\tikz@preactions=\pgfutil@empty
+\let\tikz@postactions=\pgfutil@empty
+
+% Styles
+\tikzoption{set style}{\tikzstyle#1}%
+
+% Handled in a special way.
+\def\tikzstyle{\pgfutil@ifnextchar\bgroup\tikz@style@parseA\tikz@style@parseB}%
+\def\tikz@style@parseB#1={\tikz@style@parseA{#1}=}%
+\def\tikz@style@parseA#1#2=#3[#4]{% check for an optional argument
+ \pgfutil@in@[{#2}%]
+ \ifpgfutil@in@%
+ \tikz@style@parseC{#1}#2={#4}%
+ \else%
+ \tikz@style@parseD{#1}#2={#4}%
+ \fi%
+}%
+
+\def\tikz@style@parseC#1[#2]#3=#4{%
+ \pgfkeys{/tikz/#1/.default={#2}}%
+ \pgfutil@in@+{#3}%
+ \ifpgfutil@in@%
+ \pgfkeys{/tikz/#1/.append style={#4}}%
+ \else%
+ \pgfkeys{/tikz/#1/.style={#4}}%
+ \fi}%
+\def\tikz@style@parseD#1#2=#3{%
+ \pgfutil@in@+{#2}%
+ \ifpgfutil@in@%
+ \pgfkeys{/tikz/#1/.append style={#3}}%
+ \else%
+ \pgfkeys{/tikz/#1/.style={#3}}%
+ \fi}%
+
+
+%
+%
+% Predefined styles
+%
+%
+
+\tikzset{help lines/.style= {color=gray,line width=0.2pt}}%
+
+\tikzset{every picture/.style= {}}%
+\tikzset{every path/.style= {}}%
+\tikzset{every scope/.style= {}}%
+\tikzset{every plot/.style= {}}%
+\tikzset{every node/.style= {}}%
+\tikzset{every child/.style= {}}%
+\tikzset{every child node/.style= {}}%
+\tikzset{every to/.style= {}}%
+\tikzset{every cell/.style= {}}%
+\tikzset{every matrix/.style= {}}%
+\tikzset{every edge/.style= {draw}}%
+\tikzset{every label/.style= {draw=none,fill=none}}%
+\tikzset{every pin/.style= {draw=none,fill=none}}%
+\tikzset{every pin edge/.style= {help lines}}%
+
+\tikzset{ultra thin/.style= {line width=0.1pt}}%
+\tikzset{very thin/.style= {line width=0.2pt}}%
+\tikzset{thin/.style= {line width=0.4pt}}%
+\tikzset{semithick/.style= {line width=0.6pt}}%
+\tikzset{thick/.style= {line width=0.8pt}}%
+\tikzset{very thick/.style= {line width=1.2pt}}%
+\tikzset{ultra thick/.style= {line width=1.6pt}}%
+
+\tikzset{solid/.style= {dash pattern=}}%
+\tikzset{dotted/.style= {dash pattern=on \pgflinewidth off 2pt}}%
+\tikzset{densely dotted/.style= {dash pattern=on \pgflinewidth off 1pt}}%
+\tikzset{loosely dotted/.style= {dash pattern=on \pgflinewidth off 4pt}}%
+\tikzset{dashed/.style= {dash pattern=on 3pt off 3pt}}%
+\tikzset{densely dashed/.style= {dash pattern=on 3pt off 2pt}}%
+\tikzset{loosely dashed/.style= {dash pattern=on 3pt off 6pt}}%
+\tikzset{dashdotted/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt}}%
+\tikzset{dash dot/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt}}%
+\tikzset{densely dashdotted/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt}}%
+\tikzset{densely dash dot/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt}}%
+\tikzset{loosely dashdotted/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt}}%
+\tikzset{loosely dash dot/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt}}%
+\tikzset{dashdotdotted/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt on \the\pgflinewidth off 2pt}}%
+\tikzset{densely dashdotdotted/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt on \the\pgflinewidth off 1pt}}%
+\tikzset{loosely dashdotdotted/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt on \the\pgflinewidth off 4pt}}%
+\tikzset{dash dot dot/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt on \the\pgflinewidth off 2pt}}%
+\tikzset{densely dash dot dot/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt on \the\pgflinewidth off 1pt}}%
+\tikzset{loosely dash dot dot/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt on \the\pgflinewidth off 4pt}}%
+
+
+\tikzset{transparent/.style= {opacity=0}}%
+\tikzset{ultra nearly transparent/.style={opacity=0.05}}%
+\tikzset{very nearly transparent/.style= {opacity=0.1}}%
+\tikzset{nearly transparent/.style= {opacity=0.25}}%
+\tikzset{semitransparent/.style= {opacity=0.5}}%
+\tikzset{nearly opaque/.style= {opacity=0.75}}%
+\tikzset{very nearly opaque/.style= {opacity=0.9}}%
+\tikzset{ultra nearly opaque/.style= {opacity=0.95}}%
+\tikzset{opaque/.style= {opacity=1}}%
+
+\tikzset{at start/.style= {pos=0}}%
+\tikzset{very near start/.style= {pos=0.125}}%
+\tikzset{near start/.style= {pos=0.25}}%
+\tikzset{midway/.style= {pos=0.5}}%
+\tikzset{near end/.style= {pos=0.75}}%
+\tikzset{very near end/.style= {pos=0.875}}%
+\tikzset{at end/.style= {pos=1}}%
+
+\tikzset{bend at start/.style= {bend pos=0,bend={+(0,0)}}}%
+\tikzset{bend at end/.style= {bend pos=1,bend={+(0,0)}}}%
+
+\tikzset{edge from parent/.style= {draw}}%
+
+
+
+% Animation callbacks
+\tikzset{
+ animate/.code=\tikzerror{You need to say \string\usetikzlibrary{animations} to use animations}
+}
+
+% ID callbacks
+\newif\iftikz@is@node
+\let\tikz@id@name\pgfutil@empty
+\let\tikz@id@hook\pgfutil@empty
+\def\tikz@call@id@hook{\ifx\tikz@id@hook\pgfutil@empty\else\tikz@id@hook\pgfuseid{\tikz@id@name}\fi}%
+
+
+% RDF stuff
+\let\tikz@clear@rdf@options\relax
+\let\tikz@do@rdf@post@options\relax
+\let\tikz@do@rdf@pre@options\relax
+
+
+%
+% Setting keys
+%
+
+\pgfkeys{/tikz/style/.style={#1}}%
+
+\pgfkeys{/tikz/.unknown/.code=%
+ % Is it a pgf key?
+ \let\tikz@key\pgfkeyscurrentname%
+ \pgfkeys{/pgf/\tikz@key/.try={#1}}%
+ \ifpgfkeyssuccess%
+ \else%
+ \expandafter\pgfutil@in@\expandafter!\expandafter{\tikz@key}%
+ \ifpgfutil@in@%
+ % this is a color!
+ \expandafter\tikz@addoption\expandafter{\expandafter\tikz@compat@color@set\expandafter{\tikz@key}}%
+ \edef\tikz@textcolor{\tikz@key}%
+ \else%
+ \pgfutil@doifcolorelse{\tikz@key}
+ {%
+ \expandafter\tikz@addoption\expandafter{\expandafter\tikz@compat@color@set\expandafter{\tikz@key}}%
+ \edef\tikz@textcolor{\tikz@key}%
+ }%
+ {%
+ % Ok, second chance: This might be an arrow specification:
+ \expandafter\pgfutil@in@\expandafter-\expandafter{\tikz@key}%
+ \ifpgfutil@in@%
+ % Ah, an arrow spec!
+ \expandafter\tikz@processarrows\expandafter{\tikz@key}%
+ \else%
+ % Ok, third chance: A shape!
+ \expandafter\ifx\csname pgf@sh@s@\tikz@key\endcsname\relax%
+ \pgfkeys{/errors/unknown key/.expand
+ once=\expandafter{\expandafter/\expandafter t\expandafter i\expandafter k\expandafter z\expandafter/\tikz@key}{#1}}%
+ \else%
+ \edef\tikz@shape{\tikz@key}%
+ \fi%
+ \fi%
+ }%
+ \fi%
+ \fi%
+}%
+\def\tikz@compat@color@set#1{%
+ \pgfutil@color{#1}\pgfutil@colorlet{pgffillcolor}{#1}%
+ \expandafter\let\expandafter\pgf@temp\csname\string\color@pgffillcolor\endcsname%
+ % for arrow tips:
+ \global\let\pgf@strokecolor@global=\pgf@temp
+ \global\let\pgf@fillcolor@global=\pgf@temp
+}%
+
+\def\tikz@startup@env{%
+ \ifnum\the\catcode`\;=\active\relax\expandafter\let\expandafter\tikz@origsemi\expandafter=\tikz@activesemicolon\fi%
+ \ifnum\the\catcode`\:=\active\relax\expandafter\let\expandafter\tikz@origcolon\expandafter=\tikz@activecolon\fi%
+ \ifnum\the\catcode`\|=\active\relax\expandafter\let\expandafter\tikz@origbar\expandafter=\tikz@activebar\fi%
+ \tikz@deactivatthings%
+ \iftikz@handle@active@code%
+ \tikz@switchoff@shorthands%
+ \fi%
+}%
+
+%
+% Main TikZ Environment
+%
+\newif\iftikz@inside@picture
+\tikz@inside@picturefalse
+\def\tikz@check@inside@picture{%
+ \iftikz@inside@picture%
+ \pgfwarning{Nesting tikzpictures is NOT supported}%
+ \fi%
+ \tikz@inside@picturetrue%
+}
+
+\def\tikzpicture{%
+ \begingroup%
+ \tikz@startup@env%
+ \tikz@collect@scope@anims\tikz@picture}%
+\def\tikz@picture[#1]{%
+ %\tikz@check@inside@picture%
+ \pgfpicture%
+ \let\tikz@atbegin@picture=\pgfutil@empty%
+ \let\tikz@atend@picture=\pgfutil@empty%
+ \let\tikz@transform=\relax%
+ \def\tikz@time{.5}%
+ \tikz@installcommands%
+ \scope[every picture,#1]%
+ \iftikz@handle@active@code%
+ \tikz@switchoff@shorthands%
+ \fi%
+ \expandafter\tikz@atbegin@picture%
+ \tikz@lib@scope@check%
+}%
+\def\endtikzpicture{%
+ \tikz@atend@picture%
+ \global\let\pgf@shift@baseline@smuggle=\pgf@baseline%
+ \global\let\pgf@trimleft@final@smuggle=\pgf@trimleft%
+ \global\let\pgf@trimright@final@smuggle=\pgf@trimright%
+ \global\let\pgf@remember@smuggle=\ifpgfrememberpicturepositiononpage%
+ \pgf@remember@layerlist@globally
+ \endscope%
+ \let\pgf@baseline=\pgf@shift@baseline@smuggle%
+ \let\pgf@trimleft=\pgf@trimleft@final@smuggle%
+ \let\pgf@trimright=\pgf@trimright@final@smuggle%
+ \let\ifpgfrememberpicturepositiononpage=\pgf@remember@smuggle%
+ \pgf@restore@layerlist@from@global
+ \endpgfpicture\endgroup}%
+
+
+% Inlined picture
+%
+% #1 - some code to be put in a tikzpicture environment.
+%
+% If the command is not followed by braces, everything up to the next
+% semicolon is used as argument.
+%
+% Example:
+%
+% The rectangle \tikz{\draw (0,0) rectangle (1em,1ex)} has width 1em and
+% height 1ex.
+
+
+\def\tikz{%
+ \begingroup%
+ \tikz@startup@env%
+ \tikz@collect@scope@anims\tikz@opt}%
+\def\tikz@opt[#1]{\tikzpicture[#1]\pgfutil@ifnextchar\bgroup{\tikz@}{\tikz@@single}}%
+\def\tikz@{\bgroup\tikz@auto@end@pathtrue\aftergroup\endtikzpicture\aftergroup\endgroup\let\pgf@temp=}%
+\def\tikz@@single#1{%
+ \expandafter\ifx\csname tikz@protected@command\string#1\endcsname\relax%
+ \expandafter\tikz@@%
+ \else%
+ \begingroup\def\tikz@path@do@at@end{\endgroup\endtikzpicture\endgroup}%
+ \fi%
+ #1%
+}%
+
+\expandafter\let\csname tikz@protected@command\string\draw\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\pattern\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\fill\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\filldraw\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\shade\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\shadedraw\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\clip\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\graph\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\useasboundingbox\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\node\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\coordinate\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\matrix\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\datavisualization\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\path\endcsname\pgfutil@empty%
+\expandafter\let\csname tikz@protected@command\string\pic\endcsname\pgfutil@empty%
+
+% Comment by TT: I hope I fixed the \tikz \foreach problem. The new
+% version will take a conservative approach and will only do fancy
+% stuff when the next keyword after \tikz is one of the following:
+% \draw, \fill, \filldraw, \graph, \matrix,
+\def\tikz@@{%
+ \let\tikz@next=\tikz@collectnormalsemicolon%
+ \ifnum\the\catcode`\;=\active\relax%
+ \let\tikz@next=\tikz@collectactivesemicolon%
+ \fi%
+ \tikz@next}%
+\def\tikz@collectnormalsemicolon#1;{#1;\endtikzpicture\endgroup}
+{
+ \catcode`\;=\active
+ \gdef\tikz@collectactivesemicolon#1;{#1;\endtikzpicture\endgroup}
+}%
+% End old code
+
+% Invokes '#1' if the command is invoked within a tikzpicture and
+% '#2' if not.
+\def\tikzifinpicture#1#2{%
+ \pgfutil@ifundefined{filldraw}{#2}{#1}% TT: This is a wrong
+ % test! Who uses this?...
+}%
+
+
+\def\tikz@collect@scope@anims#1{%
+ \pgfutil@ifnextchar[#1{#1[]}%]
+}%
+
+%
+% Environment for scoping graphic state settings
+%
+\def\tikz@scope@env{%
+ \pgfscope%
+ \begingroup%
+ \let\tikz@atbegin@scope=\pgfutil@empty%
+ \let\tikz@atend@scope=\pgfutil@empty%
+ \let\tikz@options=\pgfutil@empty%
+ \tikz@clear@rdf@options%
+ \let\tikz@mode=\pgfutil@empty%
+ \let\tikz@id@name=\pgfutil@empty%
+ \tikz@transparency@groupfalse%
+ \tikzset{every scope/.try}%
+ \tikz@collect@scope@anims\tikz@scope@opt%
+}%
+\def\tikz@scope@opt[#1]{%
+ \tikzset{#1}%
+ \tikz@options%
+ \tikz@do@rdf@pre@options%
+ \iftikz@transparency@group\expandafter\pgftransparencygroup\expandafter[\tikz@transparency@group@options]\tikz@blend@group\fi%
+ \tikz@is@nodefalse%
+ \tikz@call@id@hook%
+ \pgfidscope%
+ \tikz@do@rdf@post@options%
+ \begingroup%
+ \let\tikz@id@name\pgfutil@empty%
+ \expandafter\tikz@atbegin@scope%
+ \expandafter\pgfclearid%
+ \tikz@lib@scope@check%
+}%
+\def\endtikz@scope@env{%
+ \tikz@atend@scope%
+ \endgroup%
+ \endpgfidscope%
+ \iftikz@transparency@group\endpgftransparencygroup\fi%
+ \endgroup%
+ \endpgfscope%
+ \tikz@lib@scope@check%
+}%
+
+
+\def\tikz@scoped{\tikz@collect@scope@anims\tikz@scoped@opt}%
+\def\tikz@scoped@opt[#1]{\scope[#1]\pgfutil@ifnextchar\bgroup{\tikz@scoped@}{\tikz@scoped@@single}}%
+\def\tikz@scoped@{\bgroup\tikz@auto@end@pathtrue\aftergroup\endscope\let\pgf@temp=}%
+\def\tikz@scoped@@single#1{%
+ \expandafter\ifx\csname tikz@scoped@protected@command\string#1\endcsname\relax%
+ \expandafter\tikz@scoped@@%
+ \else%
+ \begingroup\def\tikz@scoped@path@do@at@end{\endgroup\endscope}%
+ \fi%
+ #1%
+}%
+\def\tikz@scoped@@{%
+ \let\tikz@scoped@next=\tikz@scoped@collectnormalsemicolon%
+ \ifnum\the\catcode`\;=\active\relax%
+ \let\tikz@scoped@next=\tikz@scoped@collectactivesemicolon%
+ \fi%
+ \tikz@scoped@next}%
+\def\tikz@scoped@collectnormalsemicolon#1;{#1;\endscope}
+{
+ \catcode`\;=\active
+ \gdef\tikz@scoped@collectactivesemicolon#1;{#1;\endscope}
+}%
+
+
+% Install a shortcut command which is only valid inside of a
+% tikzpicture.
+%
+% It works in the same way as the '\path' shortcut does: it introduces
+% a \let#1=#2 at the beginning of tikzpicture.
+%
+% #1: shortcut command inside of tikzpicture
+% #2: real command name
+\def\tikzaddtikzonlycommandshortcutlet#1#2{%
+ \expandafter\def\expandafter\tikz@installcommands\expandafter{\tikz@installcommands
+ \let#1=#2%
+ }%
+}%
+
+% Has the same effect as \tikzaddtikzonlycommandshortcutlet but uses
+% \def#1{#2} instead of \let.
+\def\tikzaddtikzonlycommandshortcutdef#1#2{%
+ \expandafter\def\expandafter\tikz@installcommands\expandafter{\tikz@installcommands
+ \def#1{#2}%
+ }%
+}%
+
+%
+% Install the abbreviated commands
+%
+\def\tikz@installcommands{%
+ \let\tikz@origscope=\scope%
+ \let\tikz@origscoped=\scoped%
+ \let\tikz@origendscope=\endscope%
+ \let\tikz@origstartscope=\startscope%
+ \let\tikz@origstopscope=\stopscope%
+ \let\tikz@origpath=\path%
+ \let\tikz@origagainpath=\againpath%
+ \let\tikz@origdraw=\draw%
+ \let\tikz@origpattern=\pattern%
+ \let\tikz@origfill=\fill%
+ \let\tikz@origfilldraw=\filldraw%
+ \let\tikz@origshade=\shade%
+ \let\tikz@origshadedraw=\shadedraw%
+ \let\tikz@origclip=\clip%
+ \let\tikz@origuseasboundingbox=\useasboundingbox%
+ \let\tikz@orignode=\node%
+ \let\tikz@origpic=\pic%
+ \let\tikz@origcoordinate=\coordinate%
+ \let\tikz@origmatrix=\matrix%
+ \let\tikz@origcalendar=\calendar%
+ \let\tikz@origdv=\datavisualization%
+ \let\tikz@origgraph=\graph%
+ %
+ \let\scope=\tikz@scope@env%
+ \let\scoped=\tikz@scoped%
+ \let\endscope=\endtikz@scope@env%
+ \let\startscope=\scope%
+ \let\stopscope=\endscope%
+ \let\path=\tikz@command@path%
+ \let\againpath=\tikz@command@againpath%
+ %
+ \def\draw{\path[draw]}%
+ \def\pattern{\path[pattern]}%
+ \def\fill{\path[fill]}%
+ \def\filldraw{\path[fill,draw]}%
+ \def\shade{\path[shade]}%
+ \def\shadedraw{\path[shade,draw]}%
+ \def\clip{\path[clip]}%
+ \def\graph{\path graph}%
+ \def\useasboundingbox{\path[use as bounding box]}%
+ \def\node{\tikz@path@overlay{node}}%
+ \def\pic{\tikz@path@overlay{pic}}%
+ \def\coordinate{\tikz@path@overlay{coordinate}}%
+ \def\matrix{\tikz@path@overlay{node[matrix]}}%
+ \def\calendar{\tikz@lib@cal@calendar}%
+ \def\datavisualization{\tikz@lib@datavisualization}%
+}%
+\ifx\tikz@lib@cal@calendar\@undefined
+\def\tikz@lib@cal@calendar{\tikzerror{You need to say \string\usetikzlibrary{calendar} to use the \string\calendar{} command}}%
+\fi
+\ifx\tikz@lib@datavisualization\@undefined
+\def\tikz@lib@datavisualization{\tikzerror{You need to say \string\usetikzlibrary{datavisualization} to use the \string\datavisualization{} command}}%
+\fi
+
+\def\tikz@path@overlay#1{%
+ \let\tikz@signal@path=\tikz@signal@path% for detection at begin of matrix cell
+ \pgfutil@ifnextchar<{\tikz@path@overlayed{#1}}{\path #1}}%
+\def\tikz@path@overlayed#1<#2>{\path<#2> #1}%
+
+\def\tikz@uninstallcommands{%
+ \let\scope=\tikz@origscope%
+ \let\scoped=\tikz@origscoped%
+ \let\endscope=\tikz@origendscope%
+ \let\startscope=\tikz@origstartscope%
+ \let\stopscope=\tikz@origstopscope%
+ \let\path=\tikz@origpath%
+ \let\againpath=\tikz@origagainpath%
+ \let\draw=\tikz@origdraw%
+ \let\pattern=\tikz@origpattern%
+ \let\fill=\tikz@origfill%
+ \let\filldraw=\tikz@origfilldraw%
+ \let\shade=\tikz@origshade%
+ \let\shadedraw=\tikz@origshadedraw%
+ \let\clip=\tikz@origclip%
+ \let\useasboundingbox=\tikz@origuseasboundingbox%
+ \let\node=\tikz@orignode%
+ \let\pic=\tikz@origpic%
+ \let\coordinate=\tikz@origcoordinate%
+ \let\matrix=\tikz@origmatrix%
+ \let\calendar=\tikz@origcalendar%
+ \let\datavisualization=\tikz@origdv%
+ \let\graph=\tikz@origgraph%
+}%
+
+
+{%
+ \catcode`\;=12
+ \gdef\tikz@nonactivesemicolon{;}%
+ \catcode`\:=12
+ \gdef\tikz@nonactivecolon{:}%
+ \catcode`\|=12
+ \gdef\tikz@nonactivebar{|}%
+ \catcode`\!=12
+ \gdef\tikz@nonactiveexlmark{!}%
+ \catcode`\;=\active
+ \catcode`\:=\active
+ \catcode`\|=\active
+ \catcode`\"=\active
+ \catcode`\!=\active
+ \gdef\tikz@activesemicolon{;}%
+ \gdef\tikz@activecolon{:}%
+ \gdef\tikz@activebar{|}%
+ \gdef\tikz@activequotes{"}%
+ \global\let\tikz@active@quotes@token="%
+ \gdef\tikz@activeexlmark{!}%
+ \gdef\tikz@deactivatthings{%
+ \def;{\tikz@nonactivesemicolon}%
+ \def:{\tikz@nonactivecolon}%
+ \def|{\tikz@nonactivebar}%
+ \def!{\tikz@nonactiveexlmark}%
+ }%
+}%
+
+\let\tikz@orig@shorthands\pgfutil@empty
+\def\tikz@switchoff@shorthands{%
+ \ifx\tikz@orig@shorthands\pgfutil@empty%
+ \edef\tikz@orig@shorthands{%
+ \catcode\noexpand`\noexpand\;\the\catcode`\;\relax%
+ \catcode\noexpand`\noexpand\:\the\catcode`\:\relax%
+ \catcode\noexpand`\noexpand\|\the\catcode`\|\relax%
+ \catcode\noexpand`\noexpand\!\the\catcode`\!\relax%
+ \catcode\noexpand`\noexpand\,\the\catcode`\,\relax%
+ \catcode\noexpand`\noexpand\<\the\catcode`\<\relax%
+ \catcode\noexpand`\noexpand\>\the\catcode`\>\relax%
+ \catcode\noexpand`\noexpand\"\the\catcode`\"\relax%
+ \catcode\noexpand`\noexpand\'\the\catcode`\'\relax%
+ \catcode\noexpand`\noexpand\-\the\catcode`\-\relax%
+ \catcode\noexpand`\noexpand\=\the\catcode`\=\relax%
+ \catcode\noexpand`\noexpand\.\the\catcode`\.\relax%
+ \catcode\noexpand`\noexpand\$\the\catcode`\$\relax%
+ }%
+ \catcode`\;12\relax%
+ \catcode`\:12\relax%
+ \catcode`\|12\relax%
+ \catcode`\!12\relax%
+ \catcode`\,12\relax%
+ \catcode`\<12\relax%
+ \catcode`\>12\relax%
+ \catcode`\"12\relax%
+ \catcode`\'12\relax%
+ \catcode`\-12\relax%
+ \catcode`\=12\relax%
+ \catcode`\.12\relax%
+ \catcode`\$3\relax%
+ \fi%
+}%
+
+
+
+% Constructs a path and draws/fills them according to the current
+% settings.
+
+\def\tikz@command@path{%
+ \let\tikz@signal@path=\tikz@signal@path% for detection at begin of matrix cell
+ \pgfutil@ifnextchar[{\tikz@check@earg}%]
+ {\pgfutil@ifnextchar<{\tikz@doopt}{\tikz@@command@path}}}%
+\pgfutil@protected\def\tikz@signal@path{\tikz@signal@path}%
+\def\tikz@check@earg[#1]{%
+ \pgfutil@ifnextchar<{\tikz@swap@args[#1]}{\tikz@@command@path[#1]}}
+\def\tikz@swap@args[#1]<#2>{\tikz@command@path<#2>[#1]}%
+
+\def\tikz@doopt{%
+ \let\tikz@next=\tikz@eargnormalsemicolon%
+ \ifnum\the\catcode`\;=\active\relax%
+ \let\tikz@next=\tikz@eargactivesemicolon%
+ \fi%
+ \tikz@next}%
+\long\def\tikz@eargnormalsemicolon<#1>#2;{\alt<#1>{\tikz@@command@path#2;}{\tikz@path@do@at@end}}%
+{
+ \catcode`\;=\active
+ \long\global\def\tikz@eargactivesemicolon<#1>#2;{\alt<#1>{\tikz@@command@path#2;}{\tikz@path@do@at@end}}%
+}
+
+\def\tikz@@command@path{%
+ \edef\tikzscope@linewidth{\the\pgflinewidth}%
+ \begingroup%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \let\tikz@path@do@at@end=\tikz@lib@scope@check%
+ \let\tikz@options=\pgfutil@empty%
+ \tikz@clear@rdf@options%
+ \let\tikz@mode=\pgfutil@empty%
+ \let\tikz@moveto@waiting=\relax%
+ \let\tikz@timer=\relax%
+ \let\tikz@tangent=\relax%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \let\tikz@preactions=\pgfutil@empty%
+ \let\tikz@postactions=\pgfutil@empty%
+ \tikz@snakedfalse%
+ \tikz@decoratepathfalse%
+ \tikz@node@is@a@labelfalse%
+ \tikz@resetexpandcount
+ \pgf@path@lastx=0pt%
+ \pgf@path@lasty=0pt%
+ \tikz@lastx=0pt%
+ \tikz@lasty=0pt%
+ \tikz@lastxsaved=0pt%
+ \tikz@lastysaved=0pt%
+ \tikzset{every path/.try}%
+ \tikz@scan@next@command%
+}%
+\def\tikz@scan@next@command{%
+ \ifx\tikz@collected@onpath\pgfutil@empty%
+ \else%
+ \tikz@invoke@collected@onpath%
+ \fi%
+ \afterassignment\tikz@handle\let\pgf@let@token=%
+}%
+\newcount\tikz@expandcount
+\def\tikz@resetexpandcount{\tikz@expandcount=100\relax}
+\let\tikz@collected@onpath=\pgfutil@empty%
+
+\edef\tikz@frozen@relax@token{\ifnum0=0\fi}
+
+% Central dispatcher for commands
+\def\tikz@handle{%
+ \pgfutil@switch\pgfutil@ifx\pgf@let@token{%
+ {(}{\let\pgfutil@next\tikz@movetoabs}%)
+ {+}{\let\pgfutil@next\tikz@movetorel}%
+ {-}{\let\pgfutil@next\tikz@lineto}%
+ {.}{\let\pgfutil@next\tikz@dot}%
+ {r}{\let\pgfutil@next\tikz@rect}%
+ {n}{\let\pgfutil@next\tikz@fig}%
+ {[}{\let\pgfutil@next\tikz@parse@options}%]
+ {c}{\let\pgfutil@next\tikz@cchar}%
+ {\bgroup}{\let\pgfutil@next\tikz@beginscope}%
+ {\egroup}{\let\pgfutil@next\tikz@endscope}%
+ {;}{\let\pgfutil@next\tikz@finish}%
+ {a}{\let\pgfutil@next\tikz@a@char}%
+ {e}{\let\pgfutil@next\tikz@e@char}%
+ {g}{\let\pgfutil@next\tikz@g@char}%
+ {s}{\let\pgfutil@next\tikz@schar}%
+ {|}{\let\pgfutil@next\tikz@vh@lineto}%
+ {p}{\pgfsetmovetofirstplotpoint\let\pgfutil@next\tikz@pchar}%
+ {t}{\let\pgfutil@next\tikz@to}%
+ {\pgfextra}{\let\pgfutil@next\tikz@extra}%
+ {\foreach}{\let\pgfutil@next\tikz@foreach}%
+ {f}{\let\pgfutil@next\tikz@fchar}%
+ {\pgf@stop}{\let\pgfutil@next\relax}%
+ {\par}{\let\pgfutil@next\tikz@scan@next@command}%
+ {d}{\let\pgfutil@next\tikz@decoration}%
+ {l}{\let\pgfutil@next\tikz@l@char}%
+ {:}{\let\pgfutil@next\tikz@colon@char}%
+ {\relax}{\relax\let\pgfutil@next\tikz@scan@next@command}%
+ }{\tikz@resetexpandcount\pgfutil@next}{\tikz@expand}%
+}%
+
+\def\tikz@l@char{%
+ \pgfutil@ifnextchar e{\tikz@let@command}{%
+ \pgfutil@ifnextchar i{\tikz@lsystem}{%
+ \pgfutil@ifnextchar-{\tikz@@lsystem}{\tikz@expand}%
+ }%
+ }%
+}%
+
+\def\tikz@lsystem{%
+ \tikzerror{You need to say \string\usetikzlibrary{lindenmayersystems} to draw Lindenmayer systems}
+}%
+
+\def\tikz@@lsystem{%
+ \tikzerror{You need to say \string\usetikzlibrary{lindenmayersystems} to draw L-systems}
+}%
+
+\def\tikz@pchar{\pgfutil@ifnextchar l{\tikz@plot}{\pgfutil@ifnextchar i{\tikz@subpicture}{\tikz@parabola}}}%
+\def\tikz@cchar{%
+ \pgfutil@ifnextchar i{\tikz@circle}%
+ {\pgfutil@ifnextchar h{\tikz@children}{\tikz@cochar}}}%
+\def\tikz@cochar o{%
+ \pgfutil@ifnextchar o{\tikz@coordinate}{\tikz@cosine}}%
+\def\tikz@e@char{%
+ \pgfutil@ifnextchar l{\tikz@ellipse}{\tikz@@e@char}}%
+\def\tikz@a@char{%
+ \pgfutil@ifnextchar r{\tikz@arcA}{\tikzerror{Arc expected}}}%
+\def\tikz@@e@char dge{%
+ \pgfutil@ifnextchar f{\tikz@edgetoparent}{\tikz@edge@plain}}%
+
+\def\tikz@schar{\pgfutil@ifnextchar i{\tikz@sine}{\tikz@svg@path}}%
+
+\def\tikz@g@char r{\pgfutil@ifnextchar i{\tikz@grid}{\tikz@graph}}%
+
+% svg syntax
+% svg[options] {...}
+
+\def\tikz@svg@path{%
+ \tikzerror{You need to say \string\usetikzlibrary{svg.path} to use the svg path command}
+}%
+
+
+\def\tikz@finish{%
+ % Rendering pipeline
+ %
+ % Step 1: The path background box
+ %
+ \box\tikz@figbox@bg%
+ %
+ % Step 2: Decorate path
+ %
+ \iftikz@decoratepath%
+ \tikz@lib@dec@decorate@path%
+ \fi%
+ %
+ % Step 3: Preactions
+ %
+ \pgfsyssoftpath@getcurrentpath\tikz@actions@path%
+ \edef\tikz@restorepathsize{%
+ \global\pgf@pathmaxx=\the\pgf@pathmaxx%
+ \global\pgf@pathmaxy=\the\pgf@pathmaxy%
+ \global\pgf@pathminx=\the\pgf@pathminx%
+ \global\pgf@pathminy=\the\pgf@pathminy%
+ }%
+ \tikz@preactions%
+ %
+ % Step 4: Reset modes
+ %
+ \let\tikz@path@picture=\pgfutil@empty%
+ \tikz@mode@fillfalse%
+ \tikz@mode@drawfalse%
+ \tikz@mode@doublefalse%
+ \tikz@mode@clipfalse%
+ \tikz@mode@boundaryfalse%
+ \tikz@mode@fade@pathfalse%
+ \tikz@mode@fade@scopefalse%
+ \edef\tikz@pathextend{%
+ {\noexpand\pgfqpoint{\the\pgf@pathminx}{\the\pgf@pathminy}}%
+ {\noexpand\pgfqpoint{\the\pgf@pathmaxx}{\the\pgf@pathmaxy}}%
+ }%
+ \tikz@mode% installs the mode settings
+ % Path fading counts as an option:
+ \iftikz@mode@fade@path%
+ \tikz@addoption{%
+ \iftikz@fade@adjust%
+ \iftikz@mode@draw%
+ \pgfsetfadingforcurrentpathstroked{\tikz@path@fading}{\tikz@do@fade@transform}%
+ \else%
+ \pgfsetfadingforcurrentpath{\tikz@path@fading}{\tikz@do@fade@transform}%
+ \fi%
+ \else%
+ \pgfsetfading{\tikz@path@fading}{\tikz@do@fade@transform}%
+ \fi%
+ \tikz@mode@fade@pathfalse% no more fading...
+ }%
+ \fi%
+ %
+ % Step 5: Install scope fading
+ %
+ \iftikz@mode@fade@scope%
+ \iftikz@fade@adjust%
+ \iftikz@mode@draw%
+ \pgfsetfadingforcurrentpathstroked{\tikz@scope@fading}{\tikz@do@fade@transform}%
+ \else%
+ \pgfsetfadingforcurrentpath{\tikz@scope@fading}{\tikz@do@fade@transform}%
+ \fi%
+ \else%
+ \pgfsetfading{\tikz@scope@fading}{\tikz@do@fade@transform}%
+ \fi%
+ \tikz@mode@fade@scopefalse%
+ \fi%
+ %
+ % Step 5': Setup options
+ %
+ \ifx\tikz@options\pgfutil@empty%
+ \else%
+ \pgfsys@beginscope%
+ \let\pgfscope@stroke@color=\pgf@strokecolor@global%
+ \let\pgfscope@fill@color=\pgf@fillcolor@global%
+ \begingroup%
+ \tikz@options%
+ \fi%
+ \tikz@do@rdf@pre@options%
+ %
+ % Step 5'': Setup animations
+ %
+ \tikz@is@nodefalse%
+ \tikz@call@id@hook%
+ \iftikz@mode@clip\else%
+ \pgfidscope%
+ \tikz@do@rdf@post@options%
+ \begingroup%
+ \fi% open an animation scope here, unless clipping is done
+ %
+ % Step 6: Do a fill if shade or a path picture follows.
+ %
+ \iftikz@mode@fill%
+ \iftikz@mode@shade%
+ \pgfsyssoftpath@getcurrentpath\tikz@temppath
+ \pgfprocessround{\tikz@temppath}{\tikz@temppath}% change the path
+ \pgfsyssoftpath@setcurrentpath\tikz@temppath%
+ \pgfsyssoftpath@invokecurrentpath%
+ \pgfpushtype%
+ \pgfusetype{.path fill}%
+ \pgfsys@fill%
+ \pgfpoptype%
+ \tikz@mode@fillfalse% no more filling...
+ \else%
+ \ifx\tikz@path@picture\pgfutil@empty%
+ \else%
+ \pgfsyssoftpath@getcurrentpath\tikz@temppath
+ \pgfprocessround{\tikz@temppath}{\tikz@temppath}% change the path
+ \pgfsyssoftpath@setcurrentpath\tikz@temppath%
+ \pgfsyssoftpath@invokecurrentpath%
+ \pgfpushtype%
+ \pgfusetype{.path fill}%
+ \pgfsys@fill%
+ \pgfpoptype%
+ \tikz@mode@fillfalse% no more filling...
+ \fi%
+ \fi%
+ \fi%
+ %
+ % Step 7: Do a shade if necessary.
+ %
+ \iftikz@mode@shade%
+ \pgfsyssoftpath@getcurrentpath\tikz@temppath
+ \pgfprocessround{\tikz@temppath}{\tikz@temppath}% change the path
+ \pgfsyssoftpath@setcurrentpath\tikz@temppath%
+ \pgfpushtype%
+ \pgfusetype{.path shade}%
+ \pgfshadepath{\tikz@shading}{\tikz@shade@angle}%
+ \pgfpoptype%
+ \tikz@mode@shadefalse% no more shading...
+ \fi%
+ %
+ % Step 8: Do a path picture if necessary.
+ %
+ \ifx\tikz@path@picture\pgfutil@empty%
+ \else%
+ \begingroup%
+ \pgfusetype{.path picture}%
+ \pgfidscope%
+ \pgfsys@beginscope%
+ \let\tikz@id@name\pgfutil@empty%
+ \pgfclearid%
+ \pgfsyssoftpath@getcurrentpath\tikz@temppath
+ \pgfprocessround{\tikz@temppath}{\tikz@temppath}% change the path
+ \pgfsyssoftpath@setcurrentpath\tikz@temppath%
+ \pgfsyssoftpath@invokecurrentpath%
+ \pgfsys@clipnext%
+ \pgfsys@discardpath%
+ \pgf@relevantforpicturesizefalse%
+ \expandafter\def\csname pgf@sh@ns@path picture bounding box\endcsname{rectangle}
+ \expandafter\edef\csname pgf@sh@np@path picture bounding box\endcsname{%
+ \def\noexpand\southwest{\noexpand\pgfqpoint{\the\pgf@pathminx}{\the\pgf@pathminy}}%
+ \def\noexpand\northeast{\noexpand\pgfqpoint{\the\pgf@pathmaxx}{\the\pgf@pathmaxy}}%
+ }
+ \expandafter\def\csname pgf@sh@nt@path picture bounding box\endcsname{{1}{0}{0}{1}{0pt}{0pt}}
+ \expandafter\def\csname pgf@sh@pi@path picture bounding box\endcsname{\pgfpictureid}
+ \pgfinterruptpath%
+ \tikz@path@picture%
+ \endpgfinterruptpath%
+ \pgfsys@endscope%
+ \endpgfidscope%
+ \endgroup%
+ \let\tikz@path@picture=\pgfutil@empty%
+ \fi%
+ %
+ % Step 9: Double stroke, if necessary
+ %
+ \iftikz@mode@draw%
+ \iftikz@mode@double%
+ % Change line width
+ \begingroup%
+ \pgfsys@beginscope%
+ \tikz@double@setup%
+ \fi%
+ \fi%
+ %
+ % Step 10: Do stroke/fill/clip as needed
+ %
+ \pgfpushtype%
+ \edef\tikz@temp{\noexpand\pgfusepath{%
+ \iftikz@mode@fill fill,\fi%
+ \iftikz@mode@draw draw,\fi%
+ \iftikz@mode@clip clip\fi%
+ }}%
+ \pgfusetype{.path}%
+ \tikz@temp%
+ \pgfpoptype%
+ \tikz@mode@fillfalse% no more filling
+ %
+ % Step 11: Double stroke, if necessary
+ %
+ \iftikz@mode@draw%
+ \iftikz@mode@double%
+ \pgfsys@endscope%
+ \endgroup%
+ \fi%
+ \fi%
+ \tikz@mode@drawfalse% no more stroking
+ %
+ % Step 12: Postactions
+ %
+ \tikz@postactions%
+ %
+ % Step 13: Add labels and nodes
+ %
+ \box\tikz@figbox%
+ %
+ % Step 14: Close animations
+ %
+ \iftikz@mode@clip\else\endgroup\endpgfidscope\fi%
+ %
+ % Step 14: Close option brace
+ %
+ \ifx\tikz@options\pgfutil@empty%
+ \else%
+ \endgroup%
+ \global\let\pgf@strokecolor@global=\pgfscope@stroke@color%
+ \global\let\pgf@fillcolor@global=\pgfscope@fill@color%
+ \pgfsys@endscope%
+ \iftikz@mode@clip%
+ \tikzerror{Extra options not allowed for clipping path command.}%
+ \fi%
+ \fi%
+ \iftikz@mode@clip%
+ \aftergroup\pgf@relevantforpicturesizefalse%
+ \fi%
+ \iftikz@mode@boundary%
+ \aftergroup\pgf@relevantforpicturesizefalse%
+ \fi%
+ \endgroup%
+ \global\pgflinewidth=\tikzscope@linewidth%
+ \tikz@path@do@at@end%
+}%
+\let\tikz@lib@scope@check\pgfutil@empty% this is a hook for the scopes library
+\def\tikz@path@do@at@end{\tikz@lib@scope@check}%
+\def\tikz@@pathtext{@path}%
+
+\def\pgf@outer@auto@adjust@hook{%
+ {%
+ \tikz@mode@drawfalse%
+ \tikz@mode%
+ \expandafter%
+ }%
+ \iftikz@mode@draw\else%
+ \pgfkeyslet{/pgf/outer xsep}\pgf@zero@text
+ \pgfkeyslet{/pgf/outer ysep}\pgf@zero@text
+ \fi%
+}%
+
+% Extra actions
+
+\def\tikz@extra@preaction#1{%
+ {%
+ \pgfsys@beginscope%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \path[#1];% do extra path
+ \pgfsyssoftpath@setcurrentpath\tikz@actions@path% restore
+ \tikz@restorepathsize%
+ \pgfsys@endscope%
+ }%
+}%
+
+\def\tikz@extra@postaction#1{%
+ {%
+ \pgfsys@beginscope%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \tikz@restorepathsize%
+ \path[#1]\pgfextra{\pgfsyssoftpath@setcurrentpath\tikz@actions@path};% do extra path
+ \pgf@resetpathsizes%
+ \pgfsys@endscope%
+ }%
+}%
+
+
+
+\def\tikz@skip#1{\tikz@scan@next@command#1}%
+\def\tikz@expand{%
+ \advance\tikz@expandcount by -1
+ \ifnum\tikz@expandcount<0\relax%
+ \expandafter\pgfutil@firstoftwo
+ \else
+ \expandafter\pgfutil@secondoftwo
+ \fi
+ {%
+ \tikzerror{Giving up on this path. Did you forget a semicolon?}%
+ % since the last token caused an error we should reinsert it and therefore save it
+ \global\let\tikz@expand@last@token=\pgf@let@token
+ \tikz@finish%
+ %
+ % To be combatible with `scopes` lib, which uses a redefined
+ % \tikz@lib@scope@check to check the next token, the reinsertion is done
+ % here, not at the end of (every) \tikz@finish.
+ %
+ \expandafter\let\expandafter\tikz@expand@last@token@\csname tikz@expand@last@token\endcsname
+ \global\let\tikz@expand@last@token=\relax
+ \tikz@expand@last@token@
+ }{%
+ \tikz@@expand
+ }%
+}
+
+\def\tikz@@expand{%
+ \expandafter\tikz@scan@next@command\pgf@let@token}%
+
+
+
+% Syntax for scopes:
+% {scoped path commands}
+
+\newif\iftikz@auto@end@path
+
+\def\tikz@beginscope{\begingroup\tikz@auto@end@pathfalse\tikz@scan@next@command}%
+\def\tikz@endscope{%
+ \iftikz@auto@end@path\expandafter\tikz@finish\expandafter\egroup\else\expandafter\tikz@@endscope\fi%
+}%
+\def\tikz@@endscope{%
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \global\let\tikz@tangent@temp\tikz@tangent%
+ \edef\tikz@marshal{%
+ \tikz@lastx=\the\tikz@lastx%
+ \tikz@lasty=\the\tikz@lasty%
+ \iftikz@current@point@local%
+ \else%
+ \tikz@lastxsaved=\the\tikz@lastxsaved%
+ \tikz@lastysaved=\the\tikz@lastysaved%
+ \ifx\tikz@moveto@waiting\relax%
+ \let\tikz@moveto@waiting\relax%
+ \else%
+ \def\noexpand\tikz@moveto@waiting{\tikz@moveto@waiting}%
+ \fi%
+ \iftikz@shapeborder%
+ \noexpand\tikz@shapebordertrue%
+ \def\noexpand\tikz@shapeborder@name{\tikz@shapeborder@name}%
+ \else%
+ \noexpand\tikz@shapeborderfalse%
+ \fi%
+ \fi%
+ }%
+ \expandafter%
+ \endgroup\tikz@marshal%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \let\tikz@tangent\tikz@tangent@temp%
+ \tikz@scan@next@command}%
+
+
+% Syntax for pgfextra:
+% \pgfextra {normal tex text}
+% \pgfextra normal tex text \endpgfextra
+
+\def\tikz@extra{\pgfutil@ifnextchar\bgroup\tikz@@extra\relax}%
+\long\def\tikz@@extra#1{#1\tikz@scan@next@command}%
+\let\endpgfextra=\tikz@scan@next@command
+
+\def\pgfextra{pgfextra}%
+
+
+% Syntax for foreach:
+%
+% foreach \var in {list} {path text}
+%
+% or
+%
+% \foreach \var in {list} {path text}
+%
+% Example:
+%
+% \draw (0,0) \foreach \x in {1,2,3} {-- (\x,0) circle (1cm)} -- (5,5);
+
+\def\tikz@fchar oreach{\tikz@foreach}%
+
+\def\tikz@foreach{%
+ \def\pgffor@beginhook{%
+ \tikz@lastx=\tikz@foreach@save@lastx%
+ \tikz@lasty=\tikz@foreach@save@lasty%
+ \tikz@lastxsaved=\tikz@foreach@save@lastxsaved%
+ \tikz@lastysaved=\tikz@foreach@save@lastysaved%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \expandafter\tikz@scan@next@command\pgfutil@firstofone}%
+ \def\pgffor@endhook{\pgfextra{%
+ \xdef\tikz@foreach@save@lastx{\the\tikz@lastx}%
+ \xdef\tikz@foreach@save@lasty{\the\tikz@lasty}%
+ \xdef\tikz@foreach@save@lastxsaved{\the\tikz@lastxsaved}%
+ \xdef\tikz@foreach@save@lastysaved{\the\tikz@lastysaved}%
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \pgfutil@gobble}}%
+ \def\pgffor@afterhook{%
+ \tikz@lastx=\tikz@foreach@save@lastx%
+ \tikz@lasty=\tikz@foreach@save@lasty%
+ \tikz@lastxsaved=\tikz@foreach@save@lastxsaved%
+ \tikz@lastysaved=\tikz@foreach@save@lastysaved%
+ \let\pgffor@beginhook\relax%
+ \let\pgffor@endhook\relax%
+ \let\pgffor@afterhook\relax%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \tikz@scan@next@command}%
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \xdef\tikz@foreach@save@lastx{\the\tikz@lastx}%
+ \xdef\tikz@foreach@save@lasty{\the\tikz@lasty}%
+ \xdef\tikz@foreach@save@lastxsaved{\the\tikz@lastxsaved}%
+ \xdef\tikz@foreach@save@lastysaved{\the\tikz@lastysaved}%
+ \foreach}%
+
+
+% Syntax for againpath:
+% \againpath \somepathname
+
+\def\tikz@command@againpath#1{%
+ \pgfextra{%
+ \pgfsyssoftpath@getcurrentpath\tikz@temp%
+ \expandafter\pgfutil@g@addto@macro\expandafter\tikz@temp\expandafter{#1}%
+ \pgfsyssoftpath@setcurrentpath\tikz@temp%
+ }%
+}%
+
+
+% animation syntax
+% :attribute = {...}
+
+\def\tikz@colon@char#1=#2{%
+ \tikz@scan@next@command{[animate={myself:{#1}={#2}}]}%
+}%
+
+
+
+%
+% When this if is set, a just-scanned point is a shape and its border
+% position still needs to be determined, depending on subsequent
+% commands.
+%
+
+\newif\iftikz@shapeborder
+
+
+% Syntax for moveto:
+% <point>
+\def\tikz@movetoabs{\tikz@moveto(}%
+\def\tikz@movetorel{\tikz@moveto+}%
+\def\tikz@moveto{%
+ \tikz@scan@one@point{\tikz@@moveto}}%
+\def\tikz@@moveto#1{%
+ \tikz@make@last@position{#1}%
+ \iftikz@shapeborder%
+ % ok, the moveto will have to wait. flag that we have a moveto in
+ % waiting:
+ \edef\tikz@moveto@waiting{\tikz@shapeborder@name}%
+ \else%
+ \tikz@@movetosave{\tikz@last@position}%
+ \let\tikz@moveto@waiting=\relax%
+ \fi%
+ \tikz@scan@next@command%
+}%
+
+ % Wrapper around \pgfpathmoveto that adds a save
+\def\tikz@@movetosave#1{%
+ {\pgftransformreset
+ \pgf@process{#1}%
+ \xdef\tikz@marshal{%
+ \tikz@lastmovetox=\the\pgf@x\relax%
+ \tikz@lastmovetoy=\the\pgf@y\relax%
+ }%
+ }%
+ \tikz@marshal
+ \pgfpathmoveto{#1}%
+}%
+
+
+\let\tikz@moveto@waiting=\relax % normally, nothing is waiting...
+
+\def\tikz@flush@moveto{%
+ \ifx\tikz@moveto@waiting\relax%
+ \else%
+ \tikz@@movetosave{\tikz@last@position}%
+ \fi%
+ \let\tikz@moveto@waiting=\relax%
+}%
+
+
+\def\tikz@flush@moveto@toward#1#2#3{%
+ % #1 = a point towards which the last moveto should be corrected
+ % #2 = a dimension to which the corrected x-coordinate should be stored
+ % #3 = a dimension for the corrected y-coordinate
+ \ifx\tikz@moveto@waiting\relax%
+ % do nothing
+ \else%
+ \pgf@process{\pgfpointshapeborder{\tikz@moveto@waiting}{#1}}%
+ #2=\pgf@x%
+ #3=\pgf@y%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+ \tikz@@movetosave{\pgfqpoint{\pgf@x}{\pgf@y}}%
+ \fi%
+ \let\tikz@moveto@waiting=\relax%
+}%
+
+
+%
+% Collecting labels on the path
+%
+
+\def\tikz@collect@coordinate@onpath#1c{%
+ \pgfutil@ifnextchar y{\tikz@cycle@expander@add#1}{\tikz@collect@coordinate@onpath@{#1}}}%
+\def\tikz@collect@coordinate@onpath@#1oordinate{%
+ \pgfutil@ifnextchar[{\tikz@@collect@coordinate@opt#1}{\tikz@@collect@coordinate@opt#1[]}}%}%
+\def\tikz@@collect@coordinate@opt#1[#2]{%
+ \pgfutil@ifnextchar({\tikz@@collect@coordinate#1[#2]}{%
+ \tikz@collect@label@onpath#1node[shape=coordinate,#2]{}}}%}%
+\def\tikz@@collect@coordinate#1[#2](#3){%
+ \tikz@collect@label@onpath#1node[shape=coordinate,#2](#3){}}%
+
+\newif\iftikz@collect@pic
+
+\def\tikz@collect@label@onpath#1node{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath node}%
+ \let\tikz@collect@cont#1%
+ \tikz@collect@picfalse%
+ \tikz@collect@label@scan}%
+
+\def\tikz@collect@pic@onpath#1pic{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath pic}%
+ \let\tikz@collect@cont#1
+ \tikz@collect@pictrue%
+ \tikz@collect@label@scan}%
+
+\def\tikz@collect@label@scan{%
+ \pgfutil@ifnextchar f{\tikz@collect@nodes}{%
+ \pgfutil@ifnextchar({\tikz@collect@paran}%
+ {\pgfutil@ifnextchar[{\tikz@collect@options}%
+ {\pgfutil@ifnextchar:{\tikz@collect@animation}%
+ {\pgfutil@ifnextchar\bgroup{\tikz@collect@arg}%
+ {\tikz@collect@cont}}}}}%
+}%}}%
+
+\def\tikz@collect@nodes foreach#1in{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath foreach#1in}%
+ \pgfutil@ifnextchar\bgroup\tikz@collect@nodes@group\tikz@collect@nodes@one%
+}%
+\def\tikz@collect@nodes@one#1{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath #1}%
+ \tikz@collect@label@scan%
+}%
+\def\tikz@collect@nodes@group#1{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{#1}}%
+ \tikz@collect@label@scan%
+}%
+
+\def\tikz@collect@animation#1=#2{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath#1={#2}}%
+ \tikz@collect@label@scan%
+}%
+\def\tikz@collect@paran#1){%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath#1)}%
+ \tikz@collect@label@scan%
+}%
+\def\tikz@collect@options#1]{%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath#1]}%
+ \tikz@collect@label@scan%
+}%
+\def\tikz@collect@arg#1{%
+ \iftikz@handle@active@nodes%
+ \iftikz@collect@pic%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{#1}}%
+ \else%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{\scantokens{#1}}}%
+ \fi%
+ \else%
+ \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{#1}}%
+ \fi%
+ \tikz@collect@cont%
+}%
+
+\def\tikz@invoke@collected@onpath{%
+ \tikz@node@is@a@labeltrue%
+ \let\tikz@temp=\tikz@collected@onpath%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \expandafter\tikz@scan@next@command\tikz@temp\pgf@stop%
+ \tikz@node@is@a@labelfalse%
+}%
+
+
+%
+% Macros for the cycle command
+%
+
+\def\tikz@cycle@expander#1{\pgfutil@ifnextchar c{\tikz@cycle@expander@{#1}}{#1}}%
+\def\tikz@cycle@expander@#1c{\pgfutil@ifnextchar y{\tikz@cycle@expander@add{#1}}{#1c}}%
+\def\tikz@cycle@expander@add#1ycle{#1(current subpath start)--cycle}%
+
+
+
+
+% Syntax for lineto:
+% -- <point>
+
+\def\tikz@lineto{%
+ \pgfutil@ifnextchar |%
+ {\expandafter\tikz@hv@lineto\pgfutil@gobble}%
+ {\expandafter\pgfutil@ifnextchar\tikz@activebar{\expandafter\tikz@hv@lineto\pgfutil@gobble}%
+ {\expandafter\tikz@lineto@mid\pgfutil@gobble}}}%
+\def\tikz@lineto@mid{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@lineto@mid}%
+ {%
+ \pgfutil@ifnextchar c{\tikz@close}{%
+ \pgfutil@ifnextchar p{\tikz@lineto@plot@or@pic}{\tikz@scan@one@point{\tikz@@lineto}}}}}%
+\def\tikz@lineto@plot@or@pic p{%
+ \pgfutil@ifnextchar i{\tikz@collect@pic@onpath\tikz@lineto@mid p}{%
+ \pgfsetlinetofirstplotpoint\tikz@plot}%
+}%
+\def\tikz@@lineto#1{%
+ % Record the starting point for later labels on the path:
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}
+ \iftikz@shapeborder%
+ % ok, target is a shape. recalculate end
+ \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\tikz@last@position}}%
+ \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}%
+ \tikz@flush@moveto@toward{\tikz@last@position}\pgf@x\pgf@y%
+ \tikz@path@lineto{\tikz@last@position}%
+ \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \tikz@make@last@position{#1}%
+ \edef\tikz@moveto@waiting{\tikz@shapeborder@name}%
+ \else%
+ % target is a reasonable point...
+ % Record the starting point for later labels on the path:
+ \tikz@make@last@position{#1}%
+ \tikz@flush@moveto@toward{\tikz@last@position}\pgf@x\pgf@y%
+ \tikz@path@lineto{\tikz@last@position}%
+ \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \fi%
+ \let\tikz@timer=\tikz@timer@line%
+ \let\tikz@tangent\tikz@timer@start%
+ \tikz@scan@next@command%
+}%
+
+% snake or lineto?
+\def\tikz@path@lineto#1{%
+ \iftikz@snaked%
+ {
+ \pgfsyssoftpathmovetorelevantfalse%
+ \pgfpathsnakesto{\tikz@presnake,{\tikz@snake}{\tikz@mainsnakelength}{\noexpand\tikz@snake@install@trans}{},\tikz@postsnake}{#1}%
+ }
+ \else%
+ \pgfpathlineto{#1}%
+ \fi%
+}%
+
+% snake or lineto?
+\def\tikz@path@close#1{%
+ \iftikz@snaked%
+ {%
+ \pgftransformreset%
+ \pgfpathsnakesto{\tikz@presnake,{\tikz@snake}{\tikz@mainsnakelength}{\noexpand\tikz@snake@install@trans}{},\tikz@postsnake}{#1}%
+ }%
+ \fi%
+ \pgfpathclose%
+}%
+
+
+% Syntax for lineto horizontal/vertical:
+% -| <point>
+
+\def\tikz@hv@lineto{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@hv@lineto}{%
+ \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@hv@lineto}%
+ {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@hv@lineto}%
+ {\tikz@scan@one@point{\tikz@@hv@lineto}}}}}%
+\def\tikz@@hv@lineto#1{%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \pgf@yc=\tikz@lasty%
+ \tikz@make@last@position{#1}%
+ \edef\tikz@tangent{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\pgf@yc}}%
+ \tikz@flush@moveto@toward{\pgfqpoint{\tikz@lastx}{\pgf@yc}}\pgf@x\pgf@yc%
+ \iftikz@shapeborder%
+ % ok, target is a shape. have to work now:
+ {%
+ \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\pgfqpoint{\tikz@lastx}{\pgf@yc}}}%
+ \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}%
+ \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\pgf@yc}}%
+ \tikz@path@lineto{\tikz@last@position}%
+ \xdef\tikz@timer@end@temp{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% move out of group
+ }%
+ \let\tikz@timer@end=\tikz@timer@end@temp%
+ \edef\tikz@moveto@waiting{\tikz@shapeborder@name}%
+ \else%
+ \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\pgf@yc}}%
+ \tikz@path@lineto{\tikz@last@position}%
+ \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% move out of group
+ \fi%
+ \let\tikz@timer=\tikz@timer@hvline%
+ \tikz@scan@next@command%
+}%
+
+% Syntax for lineto vertical/horizontal:
+% |- <point>
+
+\def\tikz@vh@lineto-{\tikz@vh@lineto@next}%
+\def\tikz@vh@lineto@next{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@vh@lineto@next}{%
+ \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@vh@lineto@next}%
+ {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@vh@lineto@next}%
+ {\tikz@scan@one@point\tikz@@vh@lineto}}}}%
+\def\tikz@@vh@lineto#1{%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \pgf@xc=\tikz@lastx%
+ \tikz@make@last@position{#1}%
+ \edef\tikz@tangent{\noexpand\pgfqpoint{\the\pgf@xc}{\the\tikz@lasty}}%
+ \tikz@flush@moveto@toward{\pgfqpoint{\pgf@xc}{\tikz@lasty}}\pgf@xc\pgf@y%
+ \iftikz@shapeborder%
+ % ok, target is a shape. have to work now:
+ {%
+ \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\pgfqpoint{\pgf@xc}{\tikz@lasty}}}%
+ \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}%
+ \tikz@path@lineto{\pgfqpoint{\pgf@xc}{\tikz@lasty}}%
+ \tikz@path@lineto{\tikz@last@position}%
+ \xdef\tikz@timer@end@temp{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% move out of group
+ }%
+ \let\tikz@timer@end=\tikz@timer@end@temp%
+ \edef\tikz@moveto@waiting{\tikz@shapeborder@name}%
+ \else%
+ \tikz@path@lineto{\pgfqpoint{\pgf@xc}{\tikz@lasty}}%
+ \tikz@path@lineto{\tikz@last@position}%
+ \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \fi%
+ \let\tikz@timer=\tikz@timer@vhline%
+ \tikz@scan@next@command%
+}%
+
+% Syntax for cycle:
+% -- cycle
+\def\tikz@close c{%
+ \pgfutil@ifnextchar o{\tikz@collect@coordinate@onpath\tikz@lineto@mid c}% oops, a coordinate
+ {\tikz@@close c}}%
+\def\tikz@@close cycle{%
+ \tikz@flush@moveto%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}
+ \tikz@make@last@position{\expandafter\pgfpoint\pgfsyssoftpath@lastmoveto}%
+ \tikz@path@close{\expandafter\pgfpoint\pgfsyssoftpath@lastmoveto}%
+ \def\pgfstrokehook{}%
+ \edef\tikz@timer@end{%\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \noexpand\pgfqpoint{\the\tikz@lastmovetox}{\the\tikz@lastmovetoy}}%
+ \let\tikz@timer=\tikz@timer@line%
+ \let\tikz@tangent\tikz@timer@start%
+ \tikz@scan@next@command%
+}%
+
+
+% Syntax for options:
+% [options]
+\def\tikz@parse@options#1]{%
+ \tikzset{#1}%
+ \tikz@scan@next@command%
+}%
+
+% Syntax for edges:
+% edge [options] (coordinate)
+% edge [options] node {node text} (coordinate)
+% edge :attribute={...} [options] node {node text} (coordinate)
+\def\tikz@edge@plain{%
+ \begingroup%
+ \ifx\tikz@to@use@whom\pgfutil@undefined\else\tikz@to@use@whom\fi
+ \let\tikz@to@or@edge@function=\tikz@do@edge%
+ \let\tikz@@to@local@options\pgfutil@empty%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \tikz@to@or@edge}%
+
+% Syntax for to paths:
+% to [options] (coordinate)
+% to [options] node {node text} (coordinate)
+% to :attribute={...} [options] node {node text} (coordinate)
+\def\tikz@to o{%
+ \tikz@to@use@last@coordinate%
+ \let\tikz@to@or@edge@function=\tikz@do@to%
+ \let\tikz@@to@local@options\pgfutil@empty%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \tikz@to@or@edge}%
+
+\def\tikz@to@or@edge{%
+ \pgfutil@ifnextchar[{\tikz@to@or@edge@option}{%
+ \pgfutil@ifnextchar:{\tikz@to@or@edge@animation}{%
+ \tikz@@to@collect}}%]
+}%
+\def\tikz@to@or@edge@option[#1]{%
+ \expandafter\def\expandafter\tikz@@to@local@options\expandafter{\tikz@@to@local@options,#1}%
+ \tikz@to@or@edge%
+}%
+\def\tikz@to@or@edge@animation:#1=#2{%
+ \expandafter\def\expandafter\tikz@@to@local@options\expandafter{\tikz@@to@local@options,%
+ animate={myself:{#1}={#2}}}%
+ \tikz@to@or@edge%
+}%
+\def\tikz@@to@collect{%
+ \pgfutil@ifnextchar(\tikz@@to@or@edge@coordinate%)
+ {\pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@@to@collect}%
+ {\pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@@to@collect}%
+ {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@@to@collect}%
+ {\pgfutil@ifnextchar +{\tikz@scan@one@point\tikz@@to@or@edge@math}%
+ {\tikzerror{(, +, coordinate, pic, or node expected}%)
+ \tikz@@to@or@edge@coordinate()}}}}}%
+}%
+
+\def\tikz@@to@or@edge@coordinate({%
+ \pgfutil@ifnextchar${%$
+ % Ok, parse directly
+ \tikz@scan@one@point\tikz@@to@or@edge@math(%
+ }{%
+ \pgfutil@ifnextchar[{%]
+ \tikz@scan@one@point\tikz@@to@or@edge@math(%
+ }{%
+ \tikz@@to@or@edge@@coordinate(%
+ }%
+ }%
+}%
+\def\tikz@@to@or@edge@math#1{%
+ \pgf@process{#1}%
+ \iftikz@updatecurrent\else
+ \tikz@updatenextfalse
+ \fi
+ \edef\tikztotarget{\the\pgf@x,\the\pgf@y}%
+ \tikz@to@or@edge@function%
+}%
+
+\def\tikz@@to@or@edge@@coordinate(#1){%
+ \def\tikztotarget{#1}%
+ \tikz@to@or@edge@function%
+}%
+
+\def\tikz@do@edge{%
+ \ifx\tikz@edge@macro\pgfutil@empty%
+ \setbox\tikz@whichbox=\hbox\bgroup%
+ \unhbox\tikz@whichbox%
+ \hbox\bgroup
+ \bgroup%
+ \pgfinterruptpath%
+ \pgfscope%
+ \let\tikz@transform=\pgfutil@empty%
+ \let\tikz@options=\pgfutil@empty%
+ \tikz@clear@rdf@options%
+ \let\tikz@tonodes=\tikz@collected@onpath%
+ \def\tikztonodes{{\pgfextra{\tikz@node@is@a@labeltrue}\tikz@tonodes}}%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \tikz@options%
+ \tikz@do@rdf@pre@options%
+ \pgfidscope%
+ \tikz@do@rdf@post@options%
+ \tikz@transform%
+ \let\tikz@transform=\relax%
+ % Typeset node:
+ \let\tikz@after@path\pgfutil@empty%
+ \tikz@atbegin@to%
+ \tikz@enable@edge@quotes%
+ \path[style=every edge]\expandafter[\tikz@@to@local@options](\tikztostart)\tikz@to@path
+ \pgfextra{\global\let\tikz@after@path@smuggle=\tikz@after@path};%
+ \tikz@atend@to%
+ \endpgfidscope%
+ \endpgfscope%
+ \endpgfinterruptpath%
+ \egroup
+ \egroup%
+ \egroup%
+ \global\setbox\tikz@tempbox=\box\tikz@whichbox%
+ \expandafter\endgroup%
+ \expandafter\setbox\tikz@whichbox=\box\tikz@tempbox%
+ \else%
+ \expandafter\expandafter\expandafter\tikz@edge@macro%
+ \expandafter\expandafter\expandafter{\expandafter\tikz@@to@local@options\expandafter}\expandafter{\tikz@collected@onpath}%
+ \endgroup%
+ \let\tikz@after@path@smuggle=\pgfutil@empty%
+ \fi%
+ \expandafter\tikz@scan@next@command\tikz@after@path@smuggle%
+}%
+
+\def\tikz@do@to{%
+ \let\tikz@tonodes=\tikz@collected@onpath%
+ \def\tikztonodes{{\pgfextra{\tikz@node@is@a@labeltrue}\tikz@tonodes}}%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \tikz@scan@next@command%
+ {%
+ \pgfextra{\let\tikz@after@path\pgfutil@empty}%
+ \pgfextra{\tikz@atbegin@to}%
+ \pgfextra{\tikz@enable@edge@quotes}%
+ [style=every to]\expandafter[\tikz@@to@local@options]\tikz@to@path%
+ \pgfextra{\tikz@atend@to}%
+ \pgf@stop%
+ \expandafter\tikz@scan@next@command\expandafter%
+ }\tikz@after@path%
+ \pgfextra{\tikz@updatenexttrue\tikz@updatecurrenttrue}%
+}%
+
+
+\def\tikz@to@use@last@coordinate{%
+ \iftikz@shapeborder%
+ \edef\tikztostart{\tikz@shapeborder@name}%
+ \else%
+ \edef\tikztostart{\the\tikz@lastx,\the\tikz@lasty}%
+ \fi%
+}%
+\def\tikz@to@use@last@fig@name{%
+ \edef\tikztostart{\tikz@to@last@fig@name}%
+}%
+
+
+
+% Syntax for graph path command:
+% graph [options] {...}
+% See the graph library for details
+
+\def\tikz@graph aph{\tikz@lib@graph@parser}%
+
+\def\tikz@lib@graph@parser{\pgfutil@ifnextchar[\tikz@graph@error{\tikz@graph@error[]}}%]%
+\def\tikz@graph@error[#1]#2{%
+ \tikzerror{You need to say \string\usetikzlibrary{graphs} in order to use the graph syntax}%
+ \tikz@lib@graph@parser@done%
+}%
+
+\def\tikz@lib@graph@parser@done{%
+ \tikz@scan@next@command%
+}%
+
+
+
+
+% Syntax for edge from parent:
+% edge from parent [options]
+\def\tikz@edgetoparent from parent{\pgfutil@ifnextchar[\tikz@@edgetoparent{\tikz@@edgetoparent[]}}%}%
+\def\tikz@@edgetoparent[#1]{%
+ \let\tikz@edge@to@parent@needed=\pgfutil@empty%
+ \def\tikz@edgetoparent@options{#1}%
+ \begingroup%
+ \let\tikz@collected@onpath=\pgfutil@empty%
+ \tikz@edgetoparentcollect%
+}%
+\def\tikz@edgetoparentcollect{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@edgetoparentcollect}%
+ {%
+ \expandafter%
+ \endgroup%
+ \expandafter\tikz@edgetoparent@rollout\expandafter{\tikz@collected@onpath}%
+ }%
+}%
+
+\def\tikz@edgetoparent@rollout#1{%
+ \pgfkeysgetvalue{/tikz/edge from parent macro}\tikz@etop@temp
+ \expandafter\tikz@scan@next@command\expandafter\tikz@etop@temp\expandafter{\tikz@edgetoparent@options}{#1}%
+}%
+
+
+% Syntax for bezier curves
+% .. controls(point) and (point) .. (target)
+% .. controls(point) .. (target)
+% .. (target) % currently not supported
+
+\def\tikz@dot.{\tikz@@dot}%
+\def\tikz@@dot{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@@dot}{%
+ \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@@dot}%
+ {\pgfutil@ifnextchar c{\tikz@curveto@double}{\tikz@curveto@auto}}}%
+}%
+
+\def\tikz@curveto@double co{%
+ \pgfutil@ifnextchar o{\tikz@collect@coordinate@onpath\tikz@@dot co}
+ {\tikz@cureveto@@double}}%
+\def\tikz@cureveto@@double ntrols#1{%
+ \tikz@scan@one@point\tikz@curveA#1%
+}%
+\def\tikz@curveA#1{%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ {%
+ \tikz@lastxsaved=\tikz@lastx%
+ \tikz@lastysaved=\tikz@lasty%
+ \tikz@make@last@position{#1}%
+ \xdef\tikz@curve@first{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ }%
+ \pgfutil@ifnextchar a
+ {\tikz@curveBand}%
+ {\let\tikz@curve@second\tikz@curve@first\tikz@curveCdots}%
+}%
+\def\tikz@curveBand and{%
+ \tikz@scan@one@point\tikz@curveB%
+}%
+\def\tikz@curveB#1{%
+ \def\tikz@curve@second{#1}%
+ \tikz@curveCdots}
+\def\tikz@curveCdots{%
+ \afterassignment\tikz@curveCdot\let\pgfutil@next=}%
+\def\tikz@curveCdot.{%
+ \ifx\pgfutil@next.%
+ \else%
+ \tikzerror{Dot expected}%
+ \fi%
+ \iftikz@updatenext
+ \tikz@updatecurrenttrue%
+ \fi
+ \tikz@curveCcheck%
+}%
+\def\tikz@curveCcheck{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@curveCcheck}{%
+ \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@curveCcheck}%
+ {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@curveCcheck}
+ {\tikz@scan@one@point\tikz@curveC}}}%
+}%
+\def\tikz@curveC#1{%
+ \tikz@make@last@position{#1}%
+ \edef\tikz@curve@third{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ {%
+ \tikz@lastxsaved=\tikz@lastx%
+ \tikz@lastysaved=\tikz@lasty%
+ \tikz@make@last@position{\tikz@curve@second}%
+ \xdef\tikz@curve@second{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ }%
+ %
+ % Start recalculating things in case start and end are shapes.
+ %
+ % First, the start:
+ \ifx\tikz@moveto@waiting\relax%
+ \else%
+ \pgf@process{\pgfpointshapeborder{\tikz@moveto@waiting}{\tikz@curve@first}}%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+ \tikz@@movetosave{\pgfqpoint{\pgf@x}{\pgf@y}}%
+ \fi%
+ \let\tikz@timer@cont@one=\tikz@curve@first%
+ \let\tikz@timer@cont@two=\tikz@curve@second%
+ % Second, the end:
+ \iftikz@shapeborder%
+ % ok, target is a shape. recalculate third
+ {%
+ \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\tikz@curve@second}}%
+ \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}%
+ \edef\tikz@curve@third{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \pgfpathcurveto{\tikz@curve@first}{\tikz@curve@second}{\tikz@curve@third}%
+ \global\let\tikz@timer@end@temp=\tikz@curve@third% move out of group
+ }%
+ \let\tikz@timer@end=\tikz@timer@end@temp%
+ \edef\tikz@moveto@waiting{\tikz@shapeborder@name}%
+ \else%
+ \pgfpathcurveto{\tikz@curve@first}{\tikz@curve@second}{\tikz@curve@third}%
+ \let\tikz@timer@end=\tikz@curve@third
+ \let\tikz@moveto@waiting=\relax%
+ \fi%
+ \let\tikz@timer=\tikz@timer@curve%
+ \let\tikz@tangent=\tikz@curve@second%
+ \tikz@scan@next@command%
+}%
+
+
+% Syntax for rectangles:
+% rectangle <corner point>
+\def\tikz@rect ectangle{%
+ \tikz@flush@moveto%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \tikz@@rect}%
+\def\tikz@@rect{%
+ \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@@rect}{%
+ \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@@rect}%
+ {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@@rect}%
+ {
+ \pgf@xa=\tikz@lastx\relax%
+ \pgf@ya=\tikz@lasty\relax%
+ \tikz@scan@one@point\tikz@rectB}}}}%
+\def\tikz@rectB#1{%
+ \tikz@make@last@position{#1}%
+ \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \let\tikz@timer=\tikz@timer@line%
+ \tikz@@movetosave{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+ \tikz@path@lineto{\pgfqpoint{\pgf@xa}{\tikz@lasty}}%
+ \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}%
+ \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\pgf@ya}}%
+ \iftikz@snaked%
+ \tikz@path@lineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+ \fi%
+ \pgfpathclose%
+ \tikz@@movetosave{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}%
+ \def\pgfstrokehook{}%
+ \let\tikz@tangent\relax%
+ \tikz@scan@next@command%
+}%
+
+
+
+% Syntax for grids:
+% grid <corner point>
+\def\tikz@grid id{%
+ \tikz@flush@moveto%
+ \pgf@xa=\tikz@lastx\relax%
+ \pgf@ya=\tikz@lasty\relax%
+ \pgfutil@ifnextchar[{\tikz@gridA}{\tikz@gridA[]}}%}%
+\def\tikz@gridA[#1]{%
+ \def\tikz@grid@options{#1}%
+ \tikz@cycle@expander{\tikz@scan@one@point\tikz@gridB}}%
+\def\tikz@gridB#1{%
+ \tikz@make@last@position{#1}%
+ \let\tikz@tangent\relax%
+ {%
+ \let\tikz@after@path\pgfutil@empty%
+ \expandafter\tikzset\expandafter{\tikz@grid@options}
+ \tikz@checkunit{\tikz@grid@x}%
+ \iftikz@isdimension%
+ \pgf@process{\pgfpoint{\tikz@grid@x}{0pt}}%
+ \else%
+ \pgf@process{\pgfpointxy{\tikz@grid@x}{0}}%
+ \fi%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \tikz@checkunit{\tikz@grid@y}%
+ \iftikz@isdimension%
+ \pgf@process{\pgfpoint{0pt}{\tikz@grid@y}}%
+ \else%
+ \pgf@process{\pgfpointxy{0}{\tikz@grid@y}}%
+ \fi%
+ \advance\pgf@xb by\pgf@x%
+ \advance\pgf@yb by\pgf@y%
+ \pgfpathgrid[stepx=\pgf@xb,stepy=\pgf@yb]%
+ {\pgfqpoint{\pgf@xa}{\pgf@ya}}{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}%
+ \expandafter}%
+ \expandafter\tikz@scan@next@command\tikz@after@path%
+}%
+
+
+
+% Syntax for plot:
+% plot [local options] ... % starts with a moveto
+% -- plot [local options] ... % starts with a lineto
+\def\tikz@plot lot{%
+ \tikz@flush@moveto%
+ \pgfutil@ifnextchar[{\tikz@@plot}{\tikz@@plot[]}}%}%
+\def\tikz@@plot[#1]{%
+ \let\tikz@tangent\tikz@tangent@lookup%
+ \begingroup%
+ \let\tikz@after@path\pgfutil@empty%
+ \let\tikz@options=\pgfutil@empty%
+ \tikzset{every plot/.try}%
+ \tikzset{#1}%
+ \pgfutil@ifnextchar f{\tikz@plot@f}%
+ {\pgfutil@ifnextchar c{\tikz@plot@scan@points}%
+ {\pgfutil@ifnextchar ({\tikz@plot@expression}{%
+ \tikzerror{Cannot parse this plotting data}%
+ \endgroup}}}}%
+\def\tikz@plot@f f{\pgfutil@ifnextchar i{\tikz@plot@file}{\tikz@plot@function}}%
+
+\def\tikz@plot@file ile#1{\def\tikz@plot@data{\pgfplotxyfile{#1}}\tikz@@@plot}%
+\def\tikz@plot@scan@points coordinates#1{%
+ \pgfplothandlerrecord\tikz@plot@data%
+ \pgfplotstreamstart%
+ \pgfutil@ifnextchar\pgf@stop{\pgfplotstreamend\expandafter\tikz@@@plot\pgfutil@gobble}
+ {\tikz@scan@one@point\tikz@plot@next@point}%
+ #1\pgf@stop%
+}%
+\def\tikz@plot@next@point#1{%
+ \pgfplotstreampoint{#1}%
+ \pgfutil@ifnextchar\pgf@stop{\pgfplotstreamend\expandafter\tikz@@@plot\pgfutil@gobble}%
+ {\tikz@scan@one@point\tikz@plot@next@point}%
+}%
+\def\tikz@plot@function unction#1{%
+ \def\tikz@plot@filename{\tikz@plot@prefix\tikz@plot@id}%
+ \iftikz@plot@raw@gnuplot%
+ \def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{#1}}%
+ \else%
+ \iftikz@plot@parametric%
+ \def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{%
+ set samples \tikz@plot@samples;
+ set parametric;
+ plot [t=\tikz@plot@domain]
+ [\tikz@plot@xrange]
+ [\tikz@plot@range]
+ #1}}%
+ \else%
+ \def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{%
+ set samples \tikz@plot@samples;
+ plot [x=\tikz@plot@domain]
+ \ifx\tikz@plot@range\pgfutil@empty\else[\tikz@plot@range]\fi
+ #1}}%
+ \fi%
+ \fi%
+ \tikz@@@plot%
+}%
+
+\def\tikz@plot@no@resample{%
+ \pgfutil@IfFileExists{\tikz@plot@filename.table}%
+ {\def\tikz@plot@data{\pgfplotxyfile{\tikz@plot@filename.table}}}%
+ {}%
+}%
+
+\def\tikz@plot@expression(#1){%
+ \edef\tikz@plot@data{\noexpand\pgfplotfunction{\expandafter\noexpand\tikz@plot@var}{\tikz@plot@samplesat}}%
+ \expandafter\def\expandafter\tikz@plot@data\expandafter{\tikz@plot@data{\tikz@scan@one@point\pgfutil@firstofone(#1)}}%
+ \tikz@@@plot%
+}%
+
+\def\tikz@@@plot{%
+ \def\pgfplotlastpoint{\pgfpointorigin}%
+ \tikz@plot@handler%
+ \tikz@plot@data%
+ \global\let\tikz@@@temp=\pgfplotlastpoint%
+ \ifx\tikz@plot@mark\pgfutil@empty%
+ \else%
+ % Marks are drawn after the path.
+ \setbox\tikz@whichbox=\hbox{%
+ \unhbox\tikz@whichbox%
+ \hbox{{%
+ \pgfinterruptpath%
+ \pgfscope%
+ \let\tikz@options=\pgfutil@empty%
+ \let\tikz@transform=\pgfutil@empty%
+ \tikzset{every mark}%
+ \tikz@options%
+ \ifx\tikz@mark@list\pgfutil@empty%
+ \pgfplothandlermark{\tikz@transform\pgfuseplotmark{\tikz@plot@mark}}%
+ \else
+ \pgfplothandlermarklisted{\tikz@transform\pgfuseplotmark{\tikz@plot@mark}}{\tikz@mark@list}%
+ \fi
+ \tikz@plot@data%
+ \endpgfscope
+ \endpgfinterruptpath%
+ }}%
+ }%
+ \fi%
+ \global\setbox\tikz@tempbox=\box\tikz@whichbox%
+ \global\let\tikz@after@path@smuggle=\tikz@after@path
+ \expandafter\endgroup%
+ \expandafter\setbox\tikz@whichbox=\box\tikz@tempbox%
+ \tikz@make@last@position{\tikz@@@temp}%
+ \expandafter\tikz@scan@next@command\tikz@after@path@smuggle%
+}%
+
+
+\pgfdeclareplotmark{ball}
+{%
+ \def\tikz@shading{ball}%
+ \shade (0pt,0pt) circle (\pgfplotmarksize);%
+}%
+
+
+
+
+% Syntax for cosine curves:
+% cos <end of quarter-period>
+\def\tikz@cosine s{\tikz@cycle@expander{\tikz@scan@one@point\tikz@@cosine}}
+\def\tikz@@cosine#1{%
+ \let\tikz@tangent\tikz@tangent@lookup%
+ \tikz@flush@moveto%
+ \pgf@process{#1}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \advance\pgf@xc by-\tikz@lastx%
+ \advance\pgf@yc by-\tikz@lasty%
+ \advance\tikz@lastx by\pgf@xc%
+ \advance\tikz@lasty by\pgf@yc%
+ \tikz@lastxsaved=\tikz@lastx%
+ \tikz@lastysaved=\tikz@lasty%
+ \tikz@updatecurrenttrue%
+ \pgfpathcosine{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ \tikz@scan@next@command%
+}%
+
+% Syntax for sine curves:
+% sin <end of quarter-period>
+\def\tikz@sine in{\tikz@cycle@expander{\tikz@scan@one@point\tikz@@sine}}
+\def\tikz@@sine#1{%
+ \let\tikz@tangent\tikz@tangent@lookup%
+ \tikz@flush@moveto%
+ \pgf@process{#1}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \advance\pgf@xc by-\tikz@lastx%
+ \advance\pgf@yc by-\tikz@lasty%
+ \advance\tikz@lastx by\pgf@xc%
+ \advance\tikz@lasty by\pgf@yc%
+ \tikz@lastxsaved=\tikz@lastx%
+ \tikz@lastysaved=\tikz@lasty%
+ \tikz@updatecurrenttrue%
+ \pgfpathsine{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ \tikz@scan@next@command%
+}%
+
+% Syntax for parabolas:
+% parabola[options] bend <coordinate> <coordinate>
+\def\tikz@parabola arabola{%
+ \let\tikz@tangent\tikz@tangent@lookup%
+ \pgfutil@ifnextchar[{\tikz@parabola@options}{\tikz@parabola@options[]}}%}%
+
+\def\tikz@parabola@options[#1]{%
+ \def\tikz@parabola@option{#1}%
+ \pgfutil@ifnextchar b{\tikz@parabola@scan@bend}{\tikz@cycle@expander{\tikz@scan@one@point\tikz@parabola@semifinal}}}%
+\def\tikz@parabola@scan@bend bend{\tikz@scan@one@point\tikz@parabola@scan@bendB}%
+\def\tikz@parabola@scan@bendB#1{%
+ \def\tikz@parabola@bend{#1}%
+ \tikz@cycle@expander{\tikz@scan@one@point\tikz@parabola@semifinal}%
+}%
+\def\tikz@parabola@semifinal#1{%
+ \tikz@flush@moveto%
+ % Save original start:
+ \pgf@xb=\tikz@lastx%
+ \pgf@yb=\tikz@lasty%
+ \tikz@make@last@position{#1}%
+ \pgf@xc=\tikz@lastx%
+ \pgf@yc=\tikz@lasty%
+ \begingroup% now calculate bend:
+ \let\tikz@after@path\pgfutil@empty%
+ \expandafter\tikzset\expandafter{\tikz@parabola@option}%
+ \tikz@lastxsaved=\tikz@parabola@bend@factor\tikz@lastx%
+ \tikz@lastysaved=\tikz@parabola@bend@factor\tikz@lasty%
+ \advance\tikz@lastxsaved by\pgf@xb%
+ \advance\tikz@lastysaved by\pgf@yb%
+ \advance\tikz@lastxsaved by-\tikz@parabola@bend@factor\pgf@xb%
+ \advance\tikz@lastysaved by-\tikz@parabola@bend@factor\pgf@yb%
+ \expandafter\tikz@make@last@position\expandafter{\tikz@parabola@bend}%
+ % Calculate delta from bend
+ \advance\pgf@xc by-\tikz@lastx%
+ \advance\pgf@yc by-\tikz@lasty%
+ % Ok, now calculate delta to bend
+ \advance\tikz@lastx by-\pgf@xb%
+ \advance\tikz@lasty by-\pgf@yb%
+ \xdef\tikz@parabola@b{{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}}%
+ \expandafter\endgroup%
+ \expandafter\expandafter\expandafter\pgfpathparabola\expandafter\tikz@parabola@b%
+ \expandafter\tikz@scan@next@command\tikz@after@path%
+}%
+
+
+% Syntax for circles:
+% circle [options] % where options should set, at least, radius
+% circle (radius) % deprecated
+%
+% Syntax for ellipses:
+% ellipse [options] % identical to circle.
+% ellipse (x-radius and y-radius) % deprecated
+%
+% radii can be dimensionless, then they are in the xy-system
+\def\tikz@circle ircle{\tikz@flush@moveto\tikz@@circle}%
+\def\tikz@ellipse llipse{\tikz@flush@moveto\tikz@@circle}%
+\def\tikz@@circle{%
+ \let\tikz@tangent\relax%
+ \pgfutil@ifnextchar(\tikz@@@circle
+ {\pgfutil@ifnextchar[\tikz@circle@opt{%])
+ \advance\tikz@expandcount by -10\relax% go down quickly
+ \ifnum\tikz@expandcount<0\relax%
+ \let\pgfutil@next=\tikz@@circle@normal%
+ \else%
+ \let\pgfutil@next=\tikz@@circle@scanexpand%
+ \fi%
+ \pgfutil@next%
+ }}%
+}%
+\def\tikz@@circle@scanexpand{\expandafter\tikz@@circle}%
+\def\tikz@@circle@normal{\tikz@circle@opt[]}%
+
+\def\tikz@circle@opt[#1]{%
+ {%
+ \def\tikz@node@at{\tikz@last@position}%
+ \let\tikz@transform=\pgfutil@empty%
+ \tikzset{every circle/.try,#1}%
+ \pgftransformshift{\tikz@node@at}%
+ \tikz@transform%
+ \tikz@do@ellipse{\pgfkeysvalueof{/tikz/x radius}}{\pgfkeysvalueof{/tikz/y radius}}
+ }%
+ \tikz@scan@next@command%
+}%
+
+\def\tikz@@@circle(#1){%
+ {%
+ \pgftransformshift{\tikz@last@position}%
+ \pgfutil@in@{ and }{#1}%
+ \ifpgfutil@in@%
+ \tikz@@ellipseB(#1)%
+ \else%
+ \tikz@do@circle{#1}%
+ \fi%
+ }%
+ \tikz@scan@next@command%
+}%
+\def\tikz@@ellipseB(#1 and #2){%
+ \tikz@do@ellipse{#1}{#2}%
+}%
+\def\tikz@do@circle#1{%
+ \pgfmathparse{#1}%
+ \let\tikz@ellipse@x=\pgfmathresult
+ \ifpgfmathunitsdeclared
+ \pgfpathellipse{\pgfpointorigin}%
+ {\pgfqpoint{\tikz@ellipse@x pt}{0pt}}%
+ {\pgfpoint{0pt}{\tikz@ellipse@x pt}}%
+ \else
+ \pgfpathellipse{\pgfpointorigin}%
+ {\pgfpointxy{\tikz@ellipse@x}{0}}%
+ {\pgfpointxy{0}{\tikz@ellipse@x}}%
+ \fi
+}
+\def\tikz@do@ellipse#1#2{
+ \pgfmathparse{#1}%
+ \let\tikz@ellipse@x=\pgfmathresult%
+ \ifpgfmathunitsdeclared%
+ \pgfmathparse{#2}%
+ \let\tikz@ellipse@y=\pgfmathresult%
+ \ifpgfmathunitsdeclared%
+ \pgfpathellipse{\pgfpointorigin}{%
+ \pgfqpoint{\tikz@ellipse@x pt}{0pt}}{\pgfpoint{0pt}{\tikz@ellipse@y pt}}%
+ \else%
+ \tikzerror{You cannot mix dimensions and dimensionless values in an ellipse}%
+ \fi%
+ \else%
+ \pgfmathparse{#2}%
+ \let\tikz@ellipse@y=\pgfmathresult%
+ \ifpgfmathunitsdeclared%
+ \tikzerror{You cannot mix dimensions and dimensionless values in an ellipse}%
+ \else%
+ \pgfpathellipse{\pgfpointorigin}{%
+ \pgfpointxy{\tikz@ellipse@x}{0}}{\pgfpointxy{0}{\tikz@ellipse@y}}%
+ \fi%
+ \fi%
+}%
+
+% Syntax for arcs:
+% arc [options]
+%
+% (The syntax with parentheses is deprecated.)
+\def\tikz@arcA rc{\tikz@flush@moveto\tikz@arc@cont}%
+\def\tikz@arc@cont{%
+ \pgfutil@ifnextchar(%)
+ {\tikz@@arcto}{%
+ \pgfutil@ifnextchar[%]
+ {\tikz@arc@opt}%
+ {%
+ \advance\tikz@expandcount by -10\relax% go down quickly
+ \ifnum\tikz@expandcount<0\relax%
+ \let\pgfutil@next=\tikz@@arc@normal%
+ \else%
+ \let\pgfutil@next=\tikz@@arc@scanexpand%
+ \fi%
+ \pgfutil@next%
+ }%
+ }%
+}%
+\def\tikz@@arc@scanexpand{\expandafter\tikz@arc@cont}%
+\def\tikz@@arc@normal{\tikz@arc@opt[]}%
+
+
+\def\tikz@arc@opt[#1]{%
+ {%
+ \tikzset{every arc/.try,#1}%
+ \pgfkeysgetvalue{/tikz/start angle}\tikz@s
+ \pgfkeysgetvalue{/tikz/end angle}\tikz@e
+ \pgfkeysgetvalue{/tikz/delta angle}\tikz@d
+ \ifx\tikz@s\pgfutil@empty%
+ \pgfmathsetmacro\tikz@s{\tikz@e-\tikz@d}
+ \else
+ \ifx\tikz@e\pgfutil@empty%
+ \pgfmathsetmacro\tikz@e{\tikz@s+\tikz@d}
+ \fi%
+ \fi%
+ \xdef\pgf@marshal{\noexpand%
+ \tikz@do@arc{\tikz@s}{\tikz@e}
+ {\pgfkeysvalueof{/tikz/x radius}}
+ {\pgfkeysvalueof{/tikz/y radius}}}%
+ }%
+ \pgf@marshal%
+ \tikz@arcfinal%
+}%
+
+\def\tikz@@arcto(#1){%
+ \edef\tikz@temp{(#1)}%
+ \expandafter\tikz@@@arcto@check@slashand\tikz@temp%
+}%
+
+\def\tikz@@@arcto@check@slashand(#1:#2:#3){%
+ \pgfutil@in@{ and }{#3}%
+ \ifpgfutil@in@%
+ \tikz@parse@arc@and(#1:#2:#3)%
+ \else%
+ \tikz@parse@arc@and(#1:#2:{#3} and {#3})%
+ \fi%
+ \tikz@arcfinal%
+}%
+
+\def\tikz@parse@arc@and(#1:#2:#3 and #4){%
+ \tikz@do@arc{#1}{#2}{#3}{#4}%
+}%
+\def\tikz@do@arc#1#2#3#4{%
+ \let\tikz@tangent\tikz@tangent@lookup%
+ \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \pgfmathsetmacro\tikz@timer@start@angle{#1}%
+ \pgfmathsetmacro\tikz@timer@end@angle{#2}%
+ \pgfmathparse{#3}%
+ \let\tikz@arc@x=\pgfmathresult%
+ \ifpgfmathunitsdeclared%
+ \pgfmathparse{#4}%
+ \let\tikz@arc@y=\pgfmathresult%
+ \ifpgfmathunitsdeclared%
+ \tikz@@@arcfinal{\pgfpatharc{\tikz@timer@start@angle}{\tikz@timer@end@angle}{\tikz@arc@x pt and \tikz@arc@y pt}}
+ {\pgfpointpolar{\tikz@timer@start@angle}{\tikz@arc@x pt and \tikz@arc@y pt}}
+ {\pgfpointpolar{\tikz@timer@end@angle}{\tikz@arc@x pt and \tikz@arc@y pt}}%
+ \edef\tikz@timer@zero@axis{\noexpand\pgfqpoint{\tikz@arc@x pt}{0pt}}
+ \edef\tikz@timer@ninety@axis{\noexpand\pgfqpoint{0pt}{\tikz@arc@y pt}}
+ \else%
+ \tikzerror{You cannot mix dimensions and dimensionless values in an arc}%
+ \fi%
+ \else%
+ \pgfmathparse{#4}%
+ \let\tikz@arc@y=\pgfmathresult%
+ \ifpgfmathunitsdeclared%
+ \tikzerror{You cannot mix dimensions and dimensionless values in an arc}%
+ \else%
+ \tikz@@@arcfinal{\pgfpatharcaxes{\tikz@timer@start@angle}{\tikz@timer@end@angle}{\pgfpointxy{\tikz@arc@x}{0}}{\pgfpointxy{0}{\tikz@arc@y}}}
+ {\pgfpointpolarxy{\tikz@timer@start@angle}{\tikz@arc@x and \tikz@arc@y}}{\pgfpointpolarxy{\tikz@timer@end@angle}{\tikz@arc@x and \tikz@arc@y}}%
+ \pgf@process{\pgfpointxy{\tikz@arc@x}{0}}
+ \edef\tikz@timer@zero@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+ \pgf@process{\pgfpointxy{0}{\tikz@arc@y}}
+ \edef\tikz@timer@ninety@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+ \fi%
+ \fi%
+}%
+
+\def\tikz@@@arcfinal#1#2#3{%
+ #1%
+ \pgf@process{#2}
+ \xdef\tikz@arc@save@first{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@process{#3}
+ \xdef\tikz@arc@save@second{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+}%
+
+\def\tikz@arcfinal{%
+ \pgf@process{\tikz@arc@save@first}%
+ \advance\tikz@lastx by-\pgf@x%
+ \advance\tikz@lasty by-\pgf@y%
+ \pgf@process{\tikz@arc@save@second}%
+ \advance\tikz@lastx by\pgf@x%
+ \advance\tikz@lasty by\pgf@y%
+ \tikz@lastxsaved=\tikz@lastx%
+ \tikz@lastysaved=\tikz@lasty%
+ \let\tikz@timer=\tikz@timer@arc%
+ \tikz@scan@next@command%
+}%
+
+
+% Syntax for coordinates:
+% coordinate[options] (coordinate name) at (point)
+% where ``at (point)'' is optional
+\def\tikz@coordinate ordinate{%
+ \pgfutil@ifnextchar[{\tikz@@coordinate@opt}{\tikz@@coordinate@opt[]}}%
+\def\tikz@@coordinate@opt[#1]{%
+ \pgfutil@ifnextchar({\tikz@@coordinate[#1]}
+ {\tikz@fig ode[shape=coordinate,#1]{}}}%}%
+\def\tikz@@coordinate[#1](#2){%
+ \pgfutil@ifnextchar a{\tikz@@coordinate@at[#1](#2)}
+ {\tikz@fig ode[shape=coordinate,#1](#2){}}}%
+\def\tikz@@coordinate@at[#1](#2)a{%
+ \pgfutil@ifnextchar t{\tikz@@coordinate@@at[#1](#2)a}%
+ {\tikz@fig ode[shape=coordinate,#1](#2){}a}%
+}%
+\def\tikz@@coordinate@@at[#1](#2)at#3({%
+ \def\tikz@coordinate@caller{\tikz@fig ode[shape=coordinate,#1](#2)at}%
+ \tikz@scan@one@point\tikz@@coordinate@at@math(%
+}%
+\def\tikz@@coordinate@at@math#1{%
+ \pgf@process{#1}%
+ \edef\tikz@temp{(\the\pgf@x,\the\pgf@y)}%
+ \expandafter\tikz@coordinate@caller\tikz@temp{}%
+}%
+
+
+
+% Syntax for nodes:
+% node foreach \var in {list} ... :attribute={...} [options] (node name) at (pos) {label text}
+%
+% all of :attribute, [options], (node name), at(pos), and foreach are
+% optional. There can be multiple options and the ordering is not
+% important as in node[draw] (a) [rotate=10] {text}, *except* that all
+% foreach statements must come first.
+%
+% A label text always ``ends'' the node.
+%
+\def\tikz@fig ode{%
+ \pgfutil@ifnextchar a\tikz@test@also{%
+ \pgfutil@ifnextchar f{\tikz@nodes@start}\tikz@normal@fig}}%
+\def\tikz@test@also a{\pgfutil@ifnextchar l\tikz@node@also{\tikz@normal@fig a}}%
+\def\tikz@normal@fig{%
+ \edef\tikz@save@line@width{\the\pgflinewidth}%
+ \begingroup%
+ \let\tikz@fig@name=\pgfutil@empty%
+ \begingroup%
+ \tikz@is@matrixfalse%
+ \let\nodepart=\tikz@nodepart%
+ \let\tikz@atbegin@scope=\pgfutil@empty%
+ \let\tikz@atend@scope=\pgfutil@empty%
+ \let\tikz@do@after@node=\tikz@scan@next@command%
+ \let\tikz@options=\pgfutil@empty%
+ \tikz@clear@rdf@options%
+ \let\tikz@id@name=\pgfutil@empty%
+ \let\tikz@after@path=\pgfutil@empty%
+ \let\tikz@transform=\pgfutil@empty%
+ \let\tikz@mode=\pgfutil@empty%
+ \tikz@decoratepathfalse%
+ \let\tikz@preactions=\pgfutil@empty%
+ \let\tikz@postactions=\pgfutil@empty%
+ \let\tikz@alias=\pgfutil@empty%
+ \def\tikz@node@at{\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+ \let\tikz@time@for@matrix\tikz@time%
+ \let\tikz@node@content\relax%
+ \pgfgetpath\tikzpathuptonow%
+ \iftikz@node@is@a@label%
+ \else%
+ \let\tikz@time\pgfutil@empty%
+ \fi%
+ \tikz@node@reset@hook%
+ \tikzset{every node/.try}%
+ \tikz@@scan@fig}%
+\def\tikz@@scan@fig{%
+ \pgfutil@ifnextchar a{\tikz@fig@scan@at}
+ {\pgfutil@ifnextchar({\tikz@fig@scan@name}
+ {\pgfutil@ifnextchar[{\tikz@fig@scan@options}%
+ {\pgfutil@ifnextchar:{\tikz@fig@scan@animation}%
+ {\pgfutil@ifnextchar\bgroup{\tikz@fig@main}%
+ {\tikzerror{A node must have a (possibly empty) label text}%
+ \tikz@fig@main{}}}}}}}%}}%
+\def\tikz@fig@scan@at at{%
+ \tikz@scan@one@point\tikz@@fig@scan@at}%
+\def\tikz@@fig@scan@at#1{%
+ \def\tikz@node@at{#1}\tikz@@scan@fig}%
+\def\tikz@fig@scan@name(#1){%
+ \pgfkeysvalueof{/tikz/name/.@cmd}#1\pgfeov% CF : this is now ALWAYS consistent with 'name=' option; allows overrides.
+ \tikz@@scan@fig}%
+% make it \long to allow \par in "pin" options etc:
+\long\def\tikz@fig@scan@options[#1]{\iftikz@node@is@pic\tikz@enable@pic@quotes\else\tikz@enable@node@quotes\fi\tikzset{#1}\ifx\tikz@node@content\relax\expandafter\tikz@@scan@fig\else\tikz@expand@node@contents\fi}%
+\def\tikz@fig@scan@animation:#1=#2{\tikzset{animate={myself:{#1}={#2}}}\tikz@@scan@fig}%
+\def\tikz@expand@node@contents{%
+ \expandafter\tikz@@scan@fig\expandafter{\tikz@node@content}%
+}%
+\let\tikz@node@reset@hook=\pgfutil@empty%
+\let\tikz@node@begin@hook=\pgfutil@empty%
+\def\tikz@fig@main{%
+ \iftikz@node@is@pic%
+ \tikz@node@is@picfalse%
+ \expandafter\tikz@subpicture@handle%
+ \else%
+ \afterassignment\tikz@@fig@main\expandafter\let\expandafter\next\expandafter=%
+ \fi}%
+\def\tikz@@fig@main{%
+ \pgfutil@ifundefined{pgf@sh@s@\tikz@shape}%
+ {\tikzerror{Unknown shape ``\tikz@shape.'' Using ``rectangle'' instead}%
+ \def\tikz@shape{rectangle}}%
+ {}%
+ \expandafter\xdef\csname tikz@dcl@coord@\tikz@fig@name\endcsname{%
+ \csname tikz@scan@point@coordinate\endcsname}%
+ \tikzset{every \tikz@shape\space node/.try}%
+ \tikz@node@textfont%
+ \tikz@node@begin@hook%
+ \iftikz@is@matrix%
+ \let\tikz@next=\tikz@do@matrix%
+ \else%
+ \let\tikz@next=\tikz@do@fig%
+ \fi%
+ \tikz@next%
+}%
+\let\tikz@nodepart@list\pgfutil@empty
+\def\tikz@do@fig{%
+ % Ok, reset all node part boxes
+ \pgfutil@for\tikz@temp:=\tikz@nodepart@list\do{%
+ \expandafter\setbox\csname pgfnodepart\tikz@temp box\endcsname=\box\pgfutil@voidb@x%
+ }%
+ \setbox\pgfnodeparttextbox=\hbox%
+ \bgroup%
+ \pgfinterruptpicture%
+ \pgfsys@begin@text%
+ \pgfsys@text@to@black@hook%
+ \tikzset{every text node part/.try}%
+ \ifx\tikz@textopacity\pgfutil@empty%
+ \else%
+ \pgfsetfillopacity{\tikz@textopacity}%
+ \pgfsetstrokeopacity{\tikz@textopacity}%
+ \fi%
+ \ifx\tikz@text@width\pgfutil@empty%
+ \tikz@textfont%
+ \else%
+ \begingroup%
+ \pgfmathsetlength{\pgf@x}{\tikz@text@width}%
+ \pgfutil@minipage[t]{\pgf@x}\leavevmode\hbox{}%
+ \tikz@textfont%
+ \tikz@text@action%
+ \fi%
+ \tikz@atbegin@node%
+ \bgroup%
+ \aftergroup\unskip%
+ % Some color stuff has been moved from here to outside; this is
+ % necessary for support of dvisvgm and of animation
+ % snapshots.
+ \ifx\tikz@textcolor\pgfutil@empty%
+ \else%
+ \pgfutil@colorlet{.}{\tikz@textcolor}%
+ \pgfutil@color{\tikz@textcolor}%
+ \fi%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \tikz@uninstallcommands%
+ \iftikz@handle@active@code%
+ \tikz@orig@shorthands%
+ \let\tikz@orig@shorthands\pgfutil@empty%
+ \fi%
+ \ifnum\the\catcode`\;=\active\relax\expandafter\let\tikz@activesemicolon=\tikz@origsemi\fi%
+ \ifnum\the\catcode`\:=\active\relax\expandafter\let\tikz@activecolon=\tikz@origcolon\fi%
+ \ifnum\the\catcode`\|=\active\relax\expandafter\let\tikz@activebar=\tikz@origbar\fi%
+ \aftergroup\tikz@fig@collectresetcolor%
+ \tikz@signal@halign@check%
+ \tikz@text@reset%
+ \tikz@halign@check%
+ \ignorespaces%
+}%
+\def\tikz@fig@collectresetcolor{%
+ % Hacks for special packages that mess with \aftergroup
+ \pgfutil@ifnextchar\reset@color% hack for color package
+ {\reset@color\afterassignment\tikz@fig@collectresetcolor\let\tikz@temp=}\tikz@fig@boxdone%
+}%
+\def\tikz@fig@boxdone{%
+ \tikz@atend@node%
+ \ifx\tikz@text@width\pgfutil@empty%
+ \else%
+ \pgfutil@endminipage%
+ \endgroup%
+ \fi%
+ \pgfsys@end@text%
+ \endpgfinterruptpicture%
+ \egroup%
+ \pgfutil@ifnextchar c{\tikz@fig@mustbenamed\tikz@fig@continue}%
+ {\pgfutil@ifnextchar[{\tikz@fig@mustbenamed\tikz@fig@continue}%
+ {\pgfutil@ifnextchar t{\tikz@fig@mustbenamed\tikz@fig@continue}
+ {\pgfutil@ifnextchar e{\tikz@fig@mustbenamed\tikz@fig@continue}
+ {\ifx\tikz@after@path\pgfutil@empty\expandafter\tikz@fig@continue\else\expandafter\tikz@fig@mustbenamed\expandafter\tikz@fig@continue\fi}}}}}%}%
+
+\tikzset{
+ matrix/inner style/every cell/.code={%
+ \tikzset{every cell/.try={\the\pgfmatrixcurrentrow}{\the\pgfmatrixcurrentcolumn}}%
+ },
+ matrix/inner style/column/.code={%
+ \tikzset{column \the\pgfmatrixcurrentcolumn/.try}%
+ },
+ matrix/inner style/even odd column/.code={
+ \ifodd\pgfmatrixcurrentcolumn%
+ \tikzset{every odd column/.try}%
+ \else%
+ \tikzset{every even column/.try}%
+ \fi
+ },
+ matrix/inner style/row/.code={%
+ \tikzset{row \the\pgfmatrixcurrentrow/.try}%
+ },
+ matrix/inner style/even odd row/.code={%
+ \ifodd\pgfmatrixcurrentrow%
+ \tikzset{every odd row/.try}%
+ \else%
+ \tikzset{every even row/.try}%
+ \fi
+ },
+ matrix/inner style/cell/.code={%
+ \tikzset{row \the\pgfmatrixcurrentrow\space column \the\pgfmatrixcurrentcolumn/.try}%
+ },
+ matrix/inner style order/.store in=\tikz@common@matrix@code@styleorder,
+ matrix/inner style order={
+ every cell,
+ column,
+ even odd column,
+ row,
+ even odd row,
+ cell
+ },
+}%
+
+\def\tikz@do@matrix{%
+ \tikzset{every matrix/.try}%
+ \tikz@node@transformations%
+ \tikz@fig@mustbenamed%
+ \setbox\tikz@whichbox=\hbox\bgroup%
+ \unhbox\tikz@whichbox%
+ \hbox\bgroup\bgroup%
+ \pgfinterruptpath%
+ \pgfscope%
+ \ifx\tikz@time\pgfutil@empty\let\tikz@time\tikz@time@for@matrix\fi%
+ \tikz@options%
+ \tikz@do@rdf@pre@options%
+ \tikz@is@nodefalse%
+ \tikz@call@id@hook%
+ \pgfidscope%
+ \tikz@do@rdf@post@options%
+ \begingroup%
+ \let\tikz@id@name\pgfutil@empty%
+ \pgfclearid%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \let\tikzmatrixname=\tikz@fig@name%
+ \edef\tikz@m@anchor{\ifx\tikz@matrix@anchor\pgfutil@empty\tikz@anchor\else\tikz@matrix@anchor\fi}%
+ \expandafter\pgfutil@in@\expandafter{\expandafter.\expandafter}\expandafter{\tikz@m@anchor}%
+ \ifpgfutil@in@%
+ \expandafter\tikz@matrix@split\tikz@m@anchor\relax%
+ \else%
+ \def\tikz@matrix@shift{\pgfpointorigin}%
+ \fi%
+ \let\tikz@transform=\relax%
+ \pgfmatrixbeforeassemblenode{\tikzset{every outer matrix/.try}}%
+ \pgfmatrix%
+ {\tikz@shape}%
+ {\tikz@m@anchor}%
+ {\tikz@fig@name}%
+ {%
+ \pgfutil@tempdima=\pgflinewidth%
+ {\begingroup\tikz@finish}%
+ \global\pgflinewidth=\pgfutil@tempdima%
+ }%
+ {\tikz@matrix@shift}%
+ {%
+ \tikz@matrix@make@active@ampersand%
+ \def\pgfmatrixbegincode{%
+ \pgfsys@beginscope%
+ \tikz@common@matrix@code%
+ \tikz@atbegin@cell%
+ }%
+ \def\tikz@common@matrix@code{%
+ \let\tikz@options=\pgfutil@empty%
+ \let\tikz@mode=\pgfutil@empty%
+ \pgfutil@for\pgf@temp:=\tikz@common@matrix@code@styleorder\do{%
+ \toks0=\expandafter{\romannumeral-`0\expandafter\pgfutil@trimspaces\expandafter{\pgf@temp}}%
+ \def\pgf@marshal{}%
+ \pgfutil@ifxempty\pgf@temp{}{%
+ \edef\pgf@marshal{\noexpand\tikzset{matrix/inner style/.cd,\the\toks0}}%
+ }%
+ \pgf@marshal
+ }%
+ \tikz@options%
+ }%
+ \def\pgfmatrixendcode{%
+ \tikz@atend@cell%
+ \pgfsys@endscope%
+ }%
+ \def\pgfmatrixemptycode{%
+ \pgfsys@beginscope%
+ \tikz@common@matrix@code%
+ \tikz@at@emptycell%
+ \pgfsys@endscope%
+ }%
+ \tikz@atbegin@matrix%
+ \aftergroup\tikz@do@matrix@cont}%
+ \bgroup%
+}%
+\def\tikz@do@matrix@cont{%
+ \tikz@atend@matrix%
+ \endgroup%
+ \endpgfidscope%
+ \endpgfscope
+ \endpgfinterruptpath%
+ \egroup\egroup%
+ \egroup%
+ %
+ \tikz@node@finish%
+}%
+{%
+ \catcode`\&=13
+ \gdef\tikz@matrix@make@active@ampersand{%
+ \ifx\tikz@ampersand@replacement\pgfutil@empty%
+ \catcode`\&=13%
+ \let&=\pgfmatrixnextcell%
+ \else%
+ \expandafter\let\tikz@ampersand@replacement=\pgfmatrixnextcell%
+ \fi%
+ }%
+}%
+
+
+\def\tikz@matrix@split#1.#2\relax{%
+ \def\tikz@m@anchor{text}%
+ \def\tikz@matrix@shift{\pgfpointanchor{#1}{#2}}%
+}%
+
+\def\tikz@fig@continue{%
+ \ifx\tikz@text@width\pgfutil@empty%
+ \else%
+ \pgfmathsetlength{\pgf@x}{\tikz@text@width}%
+ \wd\pgfnodeparttextbox=\pgf@x%
+ \fi%
+ \ifx\tikz@text@height\pgfutil@empty%
+ \else%
+ \pgfmathsetlength{\pgf@x}{\tikz@text@height}%
+ \ht\pgfnodeparttextbox=\pgf@x%
+ \fi%
+ \ifx\tikz@text@depth\pgfutil@empty%
+ \else%
+ \pgfmathsetlength{\pgf@x}{\tikz@text@depth}%
+ \dp\pgfnodeparttextbox=\pgf@x%
+ \fi%
+ %
+ % Node transformation
+ %
+ \tikz@node@transformations%
+ \tikz@nlt%
+ %
+ \setbox\tikz@whichbox=\hbox{%
+ \unhbox\tikz@whichbox%
+ \hbox{{%
+ \pgfinterruptpath%
+ \pgfscope%
+ \tikz@options%
+ \tikz@do@rdf@pre@options%
+ \tikz@is@nodetrue%
+ \tikz@call@id@hook%
+ \pgfidscope%
+ \tikz@do@rdf@post@options%
+ \let\tikz@id@name\pgfutil@empty%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ % Add color modifications to text box
+ \setbox\pgfnodeparttextbox=\hbox{{%
+ \pgfsys@begin@text% Colors moved here...
+ \ifx\tikz@textcolor\pgfutil@empty%
+ \else%
+ \pgfutil@colorlet{.}{\tikz@textcolor}%
+ \fi%
+ \pgfsetcolor{.}%
+ \pgfusetype{.text}%
+ \pgfidscope%
+ \box\pgfnodeparttextbox%
+ \endpgfidscope%
+ \pgfsys@end@text%
+ }}%
+ \pgfmultipartnode{\tikz@shape}{\tikz@anchor}{\tikz@fig@name}{%
+ \pgfutil@tempdima=\pgflinewidth%
+ {\begingroup\tikz@finish}%
+ \global\pgflinewidth=\pgfutil@tempdima%
+ }%
+ \endpgfidscope%
+ \endpgfscope%
+ \endpgfinterruptpath%
+ }}%
+ }%
+ %
+ \tikz@alias%
+ \tikz@node@finish%
+}%
+
+
+\def\tikz@fig@mustbenamed{%
+ \ifx\tikz@fig@name\pgfutil@empty%
+ % Assign a dummy name
+ \global\advance\tikz@fig@count by1\relax
+ \edef\tikz@fig@name{tikz@f@\the\tikz@fig@count}%
+ \let\tikz@id@name\tikz@fig@name%
+ \fi%
+}%
+
+\def\tikz@node@transformations{%
+ %
+ % Possibly, we are ``online''
+ %
+ \ifx\tikz@time\pgfutil@empty%
+ \pgftransformshift{\tikz@node@at}%
+ \iftikz@fullytransformed%
+ \else%
+ \pgftransformresetnontranslations%
+ \fi%
+ \else%
+ \tikz@do@auto@anchor%
+ \tikz@timer%
+ \fi%
+ % Invoke local transformations
+ \tikz@transform%
+}%
+
+\def\tikz@node@finish{%
+ \global\let\tikz@last@fig@name=\tikz@fig@name%
+ \global\let\tikz@after@path@smuggle=\tikz@after@path%
+ % shift box outside group
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \endgroup\endgroup%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \global\pgflinewidth=\tikz@save@line@width%
+ \tikz@do@after@path@smuggle%
+ \tikz@node@is@picfalse
+ \tikz@do@after@node%
+}%
+\let\tikz@fig@continue@orig=\tikz@fig@continue
+
+\def\tikz@do@after@node{\tikz@scan@next@command}%
+
+\def\tikz@do@after@path@smuggle{%
+ \let\tikz@to@last@fig@name=\tikz@last@fig@name%
+ \let\tikz@to@use@whom=\tikz@to@use@last@fig@name%
+ \let\tikzlastnode=\tikz@last@fig@name%
+ \ifx\tikz@after@path@smuggle\pgfutil@empty%
+ \else%
+ \ifpgflatenodepositioning%
+ \expandafter\expandafter\expandafter\tikz@call@late%
+ \expandafter\expandafter\expandafter{\expandafter\tikz@last@fig@name\expandafter}\expandafter{\tikz@after@path@smuggle}%
+ \else%
+ \tikz@scan@next@command{\tikz@after@path@smuggle}\pgf@stop%
+ \fi%
+ \fi%
+}%
+
+\def\tikz@call@late#1#2{\pgfnodepostsetupcode{#1}{\path[late options={name={#1},append after command={#2}}];}}%
+
+\newif\iftikz@do@align
+
+% Alignment handling
+\def\tikz@signal@halign@check{%
+ \tikz@do@alignfalse
+ \ifx\tikz@text@width\pgfutil@empty%
+ \pgfkeysgetvalue{/tikz/node halign header}\tikz@align@header%
+ \ifx\tikz@align@header\pgfutil@empty%
+ \else%
+ \tikz@do@aligntrue%
+ \fi%
+ \fi%
+}
+\def\tikz@halign@check{%
+ \iftikz@do@align%
+ % Bingo
+ \setbox\tikz@align@aligned@box=\box\pgfutil@voidb@x% void
+ \let\\=\tikz@align@newline%
+ \expandafter\tikz@start@align%
+ \fi%
+}%
+\def\tikz@align@newline{\pgfutil@protect\tikz@align@newline@}%
+\def\tikz@align@newline@{\unskip\pgfutil@ifnextchar[\tikz@@align@newline{\tikz@@align@newline[0pt]}}%}%
+\def\tikz@@align@newline[#1]{\egroup\tikz@align@continue\pgfmathparse{#1}\let\tikz@align@temp=\pgfmathresult\tikz@start@align}%
+% Two safe boxes for alignment:
+\let\tikz@align@aligned@box=\pgfnodeparttextbox
+\let\tikz@align@line@box=\tikz@figbox
+
+\def\tikz@start@align{%
+ % Start collecting text:
+ \setbox\tikz@align@line@box=\hbox\bgroup\bgroup%
+ \aftergroup\tikz@align@collectresetcolor\ignorespaces%
+}%
+\def\tikz@align@collectresetcolor{%
+ \pgfutil@ifnextchar\reset@color%
+ {\reset@color\afterassignment\tikz@align@collectresetcolor\let\tikz@temp=}%
+ {\tikz@align@end@check}%
+}%
+\def\tikz@align@end@check{%
+ \egroup%
+ \ifvoid\tikz@align@aligned@box%
+ \setbox\tikz@align@aligned@box=\box\tikz@align@line@box%
+ \else%
+ \setbox\tikz@align@aligned@box=\vbox{%
+ \expandafter\expandafter\expandafter\halign\expandafter\expandafter\expandafter{\tikz@align@header%
+ \box\tikz@align@aligned@box\cr%
+ \noalign{\vskip\tikz@align@temp pt}%
+ \unhbox\tikz@align@line@box\unskip\cr}}%
+ \fi%
+ \pgfutil@ifnextchar\tikz@align@continue{}
+ {%
+ % Main continue
+ \box\tikz@align@aligned@box%
+ \egroup%
+ }%
+}%
+\def\tikz@align@continue{\tikz@@align@continue}%
+\let\tikz@@align@continue=\pgfutil@empty
+
+
+\def\tikz@node@also lso{\pgfutil@ifnextchar[\tikz@node@also@opt{\tikz@node@also@opt[]}}%
+\def\tikz@node@also@opt[#1]{
+ \pgfutil@ifnextchar(%)
+ {\tikz@node@also@opt@cont[#1]}%
+ {\tikzerror{Syntax error in node also: ``('' expected.}%
+ \tikz@scan@next@command}%
+}%
+\def\tikz@node@also@opt@cont[#1](#2){\tikzset{late options={name=#2,#1}}\tikz@scan@next@command}%
+
+
+
+% Syntax for parts of nodes:
+% node ... {... \nodepart[options]{name} ... \nodepart{name} ...}
+
+\def\tikz@nodepart{\pgfutil@ifnextchar[\tikz@@nodepart{\tikz@@nodepart[]}}%}%
+\def\tikz@@nodepart[#1]#2{%
+ \tikz@atend@node%
+ \unskip%
+ \gdef\tikz@nodepart@options{#1}%
+ \gdef\tikz@nodepart@name{#2}%
+ \global\let\tikz@fig@continue=\tikz@nodepart@continue%
+ \pgfutil@ifnextchar x{\egroup\relax}{\egroup\relax}% gobble spaces
+}%
+\def\tikz@nodepart@continue{%
+ \global\let\tikz@fig@continue=\tikz@fig@continue@orig%
+ \ifx\tikz@nodepart@list\pgfutil@empty%
+ \let\tikz@nodepart@list\tikz@nodepart@name%
+ \else%
+ \edef\tikz@nodepart@list{\tikz@nodepart@list,\tikz@nodepart@name}%
+ \fi%
+ % Now start new box:
+ \expandafter\setbox\csname pgfnodepart\tikz@nodepart@name box\endcsname=\hbox%
+ \bgroup%
+ \pgfinterruptpicture%
+ \pgfsys@begin@text%
+ \pgfsys@text@to@black@hook%
+ \tikzset{every \tikz@nodepart@name\space node part/.try}%
+ \expandafter\tikzset\expandafter{\tikz@nodepart@options}%
+ \ifx\tikz@textopacity\pgfutil@empty%
+ \else%
+ \pgfsetfillopacity{\tikz@textopacity}%
+ \pgfsetstrokeopacity{\tikz@textopacity}%
+ \fi%
+ % Colors moved here...
+ \ifx\tikz@textcolor\pgfutil@empty%
+ \else%
+ \pgfutil@colorlet{.}{\tikz@textcolor}%
+ \fi%
+ \pgfsetcolor{.}%
+ \ifx\tikz@text@width\pgfutil@empty%
+ \tikz@textfont%
+ \else%
+ \begingroup%
+ \pgfmathsetlength{\pgf@x}{\tikz@text@width}%
+ \pgfutil@minipage[t]{\pgf@x}\leavevmode\hbox{}%
+ \tikz@textfont%
+ \tikz@text@action%
+ \fi%
+ \bgroup%
+ \aftergroup\unskip%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \tikz@uninstallcommands%
+ \iftikz@handle@active@code%
+ \tikz@orig@shorthands%
+ \let\tikz@orig@shorthands\pgfutil@empty%
+ \fi%
+ \ifnum\the\catcode`\;=\active\relax\expandafter\let\tikz@activesemicolon=\tikz@origsemi\fi%
+ \ifnum\the\catcode`\:=\active\relax\expandafter\let\tikz@activecolon=\tikz@origcolon\fi%
+ \ifnum\the\catcode`\|=\active\relax\expandafter\let\tikz@activebar=\tikz@origbar\fi%
+ \tikz@atbegin@node%
+ \aftergroup\tikz@fig@collectresetcolor%
+ \tikz@signal@halign@check%
+ \tikz@text@reset%
+ \tikz@halign@check%
+ \ignorespaces%
+}%
+
+
+%
+% Node foreach
+%
+
+\def\tikz@nodes@start{%
+ \let\tikz@nodes@list\pgfutil@empty%
+ \iftikz@node@is@pic%
+ \def\tikz@nodes@collect{pic }%
+ \else%
+ \def\tikz@nodes@collect{node }%
+ \fi%
+ \tikz@nodes%
+}%
+\def\tikz@nodes foreach{\pgfutil@ifnextchar x\tikz@nodes@\tikz@nodes@}% get rid of spaces
+\def\tikz@nodes@#1in{%
+ \expandafter\def\expandafter\tikz@nodes@list\expandafter{\tikz@nodes@list\foreach#1in}%
+ \pgfutil@ifnextchar\bgroup\tikz@nodes@group\tikz@nodes@one%
+}%
+\def\tikz@nodes@one#1{%
+ \expandafter\def\expandafter\tikz@nodes@list\expandafter{\tikz@nodes@list#1}%
+ \pgfutil@ifnextchar f\tikz@nodes\tikz@nodes@scan%
+}%
+\def\tikz@nodes@group#1{%
+ \expandafter\def\expandafter\tikz@nodes@list\expandafter{\tikz@nodes@list{#1}}%
+ \pgfutil@ifnextchar f\tikz@nodes\tikz@nodes@scan%
+}%
+\def\tikz@nodes@scan{%
+ \pgfutil@ifnextchar a{\tikz@nodes@at}%
+ {\pgfutil@ifnextchar({\tikz@nodes@name}%
+ {\pgfutil@ifnextchar[{\tikz@nodes@opt}%
+ {\pgfutil@ifnextchar\bgroup{\tikz@nodes@main}%
+ {\tikzerror{Nodes must have a (possibly empty) label text}%
+ \tikz@fig@main{}}}}}}%}}%
+
+% Look ahead whether the next character is a (. If that is the case, we scan
+% until ), otherwise we grab a single token and append.
+\def\tikz@nodes@at at{\pgfutil@ifnextchar({\tikz@nodes@at@}{\tikz@nodes@at@@}}%
+\def\tikz@nodes@at@#1){%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect at#1)}%
+ \tikz@nodes@scan}%
+\def\tikz@nodes@at@@#1{%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect at#1}%
+ \tikz@nodes@scan}%
+
+\def\tikz@nodes@name#1){%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect#1)}%
+ \tikz@nodes@scan}%
+\def\tikz@nodes@opt#1]{%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect#1]}%
+ \tikz@nodes@scan}%
+\def\tikz@nodes@main#1{%
+ \iftikz@handle@active@nodes%
+ \iftikz@node@is@pic%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect{#1}}%
+ \else%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect{\scantokens{#1}}}%
+ \fi%
+ \else%
+ \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect{#1}}%
+ \fi%
+ % Ok, got everything.
+ % Now, start building parse text.
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \tikz@nodes@list{%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \expandafter\tikz@scan@next@command\tikz@nodes@collect\pgfextra\relax%
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ }%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \tikz@scan@next@command%
+}%
+
+
+
+%
+% "late" options can be used to "redo" a node
+%
+\tikzset{late options/.code=\tikz@late@options{#1}}%
+\def\tikz@late@options#1{%
+ % Do a "virtual" node:
+ \begingroup%
+ \iftikz@shapeborder%
+ \let\tikz@fig@name=\tikz@shapeborder@name%
+ \else%
+ \let\tikz@fig@name=\pgfutil@empty%
+ \fi%
+ \tikz@is@matrixfalse%
+ \let\tikz@options=\pgfutil@empty%
+ \tikz@clear@rdf@options%
+ \let\tikz@after@path=\pgfutil@empty%
+ \let\tikz@afternodepathoptions=\pgfutil@empty%
+ \let\tikz@alias=\pgfutil@empty%
+ \let\tikz@transform=\pgfutil@empty%
+ \tikz@decoratepathfalse%
+ \tikz@node@reset@hook%
+ \tikz@enable@node@quotes%
+ \tikzset{every node/.try,#1}%
+ \ifx\tikz@fig@name\pgfutil@empty%
+ \tikzerror{Late options must reference some existing node}%
+ \fi%
+ \tikz@node@begin@hook%
+ \tikz@alias%
+ \tikzgdlatenodeoptionacallback{\tikz@fig@name}%
+ \global\let\tikz@last@fig@name=\tikz@fig@name%
+ \global\let\tikz@after@path@smuggle=\tikz@after@path%
+ \endgroup%
+ \tikz@do@after@path@smuggle%
+}%
+
+
+% Auto placement
+
+\def\tikz@auto@pre{%
+ \begingroup
+ \pgfresetnontranslationattimefalse
+ \ifpgfslopedattime
+ \pgfslopedattimefalse%
+ \else
+ \pgfslopedattimetrue%
+ \fi
+ \pgfallowupsidedownattimetrue%
+ \tikz@timer%
+ \pgf@x=\pgf@pt@aa pt%
+ \pgf@y=\pgf@pt@ab pt%
+ \pgfpointnormalised{}%
+}%
+
+\def\tikz@auto@post{%
+ \global\let\tikz@anchor@smuggle=\tikz@anchor%
+ \endgroup%
+ \let\tikz@anchor=\tikz@anchor@smuggle%
+}%
+
+\def\tikz@auto@anchor{%
+ \ifdim\pgf@x>0.05pt%
+ \ifdim\pgf@y>0.05pt%
+ \def\tikz@anchor{south east}%
+ \else\ifdim\pgf@y<-0.05pt%
+ \def\tikz@anchor{south west}%
+ \else
+ \def\tikz@anchor{south}%
+ \fi\fi%
+ \else\ifdim\pgf@x<-0.05pt%
+ \ifdim\pgf@y>0.05pt%
+ \def\tikz@anchor{north east}%
+ \else\ifdim\pgf@y<-0.05pt%
+ \def\tikz@anchor{north west}%
+ \else
+ \def\tikz@anchor{north}%
+ \fi\fi%
+ \else%
+ \ifdim\pgf@y>0pt%
+ \def\tikz@anchor{east}%
+ \else%
+ \def\tikz@anchor{west}%
+ \fi%
+ \fi\fi%
+}%
+
+\def\tikz@auto@anchor@prime{%
+ \ifdim\pgf@x>0.05pt%
+ \ifdim\pgf@y>0.05pt%
+ \def\tikz@anchor{north west}%
+ \else\ifdim\pgf@y<-0.05pt%
+ \def\tikz@anchor{north east}%
+ \else
+ \def\tikz@anchor{north}%
+ \fi\fi%
+ \else\ifdim\pgf@x<-0.05pt%
+ \ifdim\pgf@y>0.05pt%
+ \def\tikz@anchor{south west}%
+ \else\ifdim\pgf@y<-0.05pt%
+ \def\tikz@anchor{south east}%
+ \else
+ \def\tikz@anchor{south}%
+ \fi\fi%
+ \else%
+ \ifdim\pgf@y>0pt%
+ \def\tikz@anchor{west}%
+ \else%
+ \def\tikz@anchor{east}%
+ \fi%
+ \fi\fi%
+}%
+
+
+%
+% Callbacks: Please see the documentation of the graph drawing
+% lib for info on these callbacks
+%
+\def\tikzgdeventcallback#1#2{}%
+\def\tikzgdeventgroupcallback#1{}%
+\def\tikzgdlatenodeoptionacallback#1{}%
+
+% Syntax for trees:
+% node {...} child [options] {...} child [options] {...} ...
+% node {...} child [options] foreach \var in {list} [options] {...} ...
+
+\def\tikz@children{%
+ % Start collecting the children:
+ \let\tikz@children@list=\pgfutil@empty%
+ \tikznumberofchildren=0\relax%
+ \tikz@collect@children c}%
+
+\def\tikz@collect@children{\pgfutil@ifnextchar c{\tikz@collect@children@cchar}{\tikz@children@collected}}%
+\def\tikz@collect@children@cchar c{\pgfutil@ifnextchar h{\tikz@collect@child}{\tikz@children@collected c}}%
+\def\tikz@collect@child hild{\pgfutil@ifnextchar[{\tikz@collect@childA}{\tikz@collect@childA[]}}%}%
+\def\tikz@collect@childA[#1]{\pgfutil@ifnextchar f{\tikz@collect@children@foreach[#1]}{\tikz@collect@childB[#1]}}%
+\def\tikz@collect@childB[#1]{%
+ \advance\tikznumberofchildren by1\relax
+ \expandafter\def\expandafter\tikz@children@list\expandafter{\tikz@children@list \tikz@childnode[#1]}%
+ \pgfutil@ifnextchar\bgroup{\tikz@collect@child@code}{\tikz@collect@child@code{}}}%
+\def\tikz@collect@child@code#1{%
+ \expandafter\def\expandafter\tikz@children@list\expandafter{\tikz@children@list{#1}}%
+ \tikz@collect@children%
+}%
+\def\tikz@collect@children@foreach[#1]foreach#2in#3{%
+ \pgfutil@ifnextchar\bgroup{\tikz@collect@children@foreachA{#1}{#2}{#3}}{\tikz@collect@children@foreachA{#1}{#2}{#3}{}}}%
+\def\tikz@collect@children@foreachA#1#2#3#4{%
+ \expandafter\def\expandafter\tikz@children@list\expandafter
+ {\tikz@children@list\tikz@childrennodes[#1]{#2}{#3}{#4}}%
+ \c@pgf@counta=\tikznumberofchildren%
+ \foreach#2in{#3}%
+ {%
+ \global\advance\c@pgf@counta by1\relax%
+ }%
+ \tikznumberofchildren=\c@pgf@counta%
+ \tikz@collect@children%
+}%
+\long\def\tikz@children@collected{%
+ \begingroup%
+ \advance\tikztreelevel by 1\relax%
+ \tikzgdeventgroupcallback{descendants}%
+ \let\tikz@options=\pgfutil@empty%
+ \tikz@clear@rdf@options%
+ \let\tikz@transform=\pgfutil@empty%
+ \tikzset{level/.try=\the\tikztreelevel,level \the\tikztreelevel/.try}%
+ \tikz@transform%
+ \let\tikz@transform=\relax%
+ \let\tikzparentnode=\tikz@last@fig@name%
+ \ifx\tikz@grow\relax\else%
+ % Transform to center of node
+ \pgftransformshift{\pgfpointanchor{\tikzparentnode}{\tikz@growth@anchor}}%
+ \fi%
+ \tikznumberofcurrentchild=0\relax%
+ \tikz@children@list%
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \endgroup%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \tikz@scan@next@command%
+}%
+
+% Syntax for children:
+%
+% child [all children options] foreach \var in {values} [child options] {...}
+\def\tikz@childrennodes[#1]#2#3#4{%
+ \c@pgf@counta=\tikznumberofcurrentchild\relax%
+ \setbox\tikz@tempbox=\box\tikz@figbox%
+ \setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ \foreach#2in{#3}{%
+ \tikznumberofcurrentchild=\c@pgf@counta\relax%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+ \tikz@childnode[#1]{#4}%
+ % we must now make the current child number and the figbox survive
+ % the group
+ \global\c@pgf@counta=\tikznumberofcurrentchild\relax%
+ \global\setbox\tikz@tempbox=\box\tikz@figbox%
+ \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg%
+ }%
+ \tikznumberofcurrentchild=\c@pgf@counta\relax%
+ \setbox\tikz@figbox=\box\tikz@tempbox%
+ \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg%
+}%
+
+
+% Syntax for child:
+%
+% child
+%
+% child[options]
+%
+% child[options] {node (name) {child node text} ...
+% edge from parent[options] node {label text} node {label text}}
+
+\def\tikz@childnode[#1]#2{%
+ \advance\tikznumberofcurrentchild by1\relax%
+ {\tikzset{every child/.try,#1}\expandafter}%
+ \iftikz@child@missing%
+ \tikzgdeventcallback{node}{}%
+ \else%
+ \setbox\tikz@whichbox=\hbox\bgroup%
+ \unhbox\tikz@whichbox%
+ \hbox\bgroup\bgroup%
+ \pgfinterruptpath%
+ \pgfscope%
+ \let\tikz@transform=\pgfutil@empty%
+ \tikzset{every child/.try,#1}%
+ \tikz@options%
+ \tikz@transform%
+ \let\tikz@transform=\relax%
+ \tikz@grow%
+ % Typeset node:
+ \edef\tikz@parent@node@name{[name=\tikzparentnode-\the\tikznumberofcurrentchild,style=every child node]}%
+ \def\tikz@child@node@text{[shape=coordinate]{}}
+ \tikz@parse@child@node#2\pgf@stop%
+ \expandafter\expandafter\expandafter\node
+ \expandafter\tikz@parent@node@name
+ \tikz@child@node@text
+ \pgfextra{\global\let\tikz@childnode@name=\tikz@last@fig@name};%
+ \let\tikzchildnode=\tikz@childnode@name%
+ {%
+ \def\tikz@edge@to@parent@needed{edge from parent}
+ \ifx\tikz@child@node@rest\pgfutil@empty%
+ \path edge from parent;%
+ \else%
+ \path \tikz@child@node@rest \tikz@edge@to@parent@needed;%
+ \fi%
+ }%
+ \endpgfscope%
+ \endpgfinterruptpath%
+ \egroup\egroup%
+ \egroup%
+ \fi%
+}%
+
+\def\tikz@parse@child@node{%
+ \pgfutil@ifnextchar n{\tikz@parse@child@node@n}%
+ {\pgfutil@ifnextchar c{\tikz@parse@child@node@c}%
+ {\pgfutil@ifnextchar\pgf@stop\tikz@parse@child@node@rest\tikz@parse@child@node@expand}}}%
+\def\tikz@parse@child@node@expand{%
+ \advance\tikz@expandcount by-1\relax%
+ \ifnum\tikz@expandcount<0\relax%
+ \expandafter\tikz@parse@child@node@rest%
+ \else%
+ \expandafter\expandafter\expandafter\tikz@parse@child@node%
+ \fi%
+}%
+\def\tikz@parse@child@node@rest#1\pgf@stop{\tikz@resetexpandcount\def\tikz@child@node@rest{#1}}%
+\def\tikz@parse@child@node@c c{\tikz@resetexpandcount\pgfutil@ifnextchar o{\tikz@parse@child@node@co}{\tikz@parse@child@node@rest c}}%
+\def\tikz@parse@child@node@co o{\pgfutil@ifnextchar o{\tikz@parse@child@node@coordinate}{\tikz@parse@child@node@rest co}}%
+\def\tikz@parse@child@node@coordinate ordinate{%
+ \pgfutil@ifnextchar ({\tikz@@parse@child@node@coordinate}{%
+ \def\tikz@child@node@text{[shape=coordinate]{}}%
+ \tikz@parse@child@node@rest}}%}%
+\def\tikz@@parse@child@node@coordinate(#1){%
+ \pgfutil@ifnextchar a{\tikz@p@c@n@c@at(#1)}{%
+ \def\tikz@child@node@text{[shape=coordinate,name=#1]{}}%
+ \tikz@parse@child@node@rest}}%
+\def\tikz@p@c@n@c@at(#1)at#2({%
+ \def\tikz@child@node@text@pre{[shape=coordinate,name=#1]at}%
+ \tikz@scan@one@point\tikz@p@c@n@c@at@math(%
+}%
+\def\tikz@p@c@n@c@at@math#1{%
+ \pgf@process{#1}%
+ \edef\tikz@marshal{(\the\pgf@x,\the\pgf@y){}}%
+ \expandafter\expandafter\expandafter\def%
+ \expandafter\expandafter\expandafter\tikz@child@node@text%
+ \expandafter\expandafter\expandafter{\expandafter\tikz@child@node@text@pre\tikz@marshal}%
+ \tikz@parse@child@node@rest%
+}%
+\def\tikz@parse@child@node@n node{\tikz@resetexpandcount%
+ \let\tikz@child@node@text=\pgfutil@empty%
+ \tikz@p@c@s}%
+\def\tikz@p@c@s{%
+ \pgfutil@ifnextchar a{\tikz@p@c@s@at}
+ {\pgfutil@ifnextchar ({\tikz@p@c@s@paran}
+ {\pgfutil@ifnextchar [{\tikz@p@c@s@bra}
+ {\pgfutil@ifnextchar \bgroup{\tikz@p@c@s@group}
+ {\tikzerror{Cannot parse this node}}}}}}%}}%
+\def\tikz@p@c@s@at at#1({%
+ \tikz@scan@one@point\tikz@p@c@s@at@math(%
+}%
+\def\tikz@p@c@s@at@math#1{%
+ \pgf@process{#1}%
+ \edef\tikz@marshal{ at(\the\pgf@x,\the\pgf@y)}%
+ \expandafter\expandafter\expandafter\def%
+ \expandafter\expandafter\expandafter\tikz@child@node@text%
+ \expandafter\expandafter\expandafter{\expandafter\tikz@child@node@text\tikz@marshal}
+ \tikz@p@c@s}%
+\def\tikz@p@c@s@paran(#1){%
+ \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text(#1)}
+ \tikz@p@c@s}%
+\def\tikz@p@c@s@bra[#1]{%
+ \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text[#1]}
+ \tikz@p@c@s}%
+\def\tikz@p@c@s@group#1{%
+ \iftikz@handle@active@nodes%
+ \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text{\scantokens{#1}}}%
+ \else%
+ \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text{#1}}
+ \fi%
+ \tikz@parse@child@node@rest%
+}%
+
+
+
+%
+% Syntax for decorated subpaths:
+%
+% decorate [option] { subpath }
+%
+\def\tikz@decoration ecorate{%
+ \pgfutil@ifnextchar[{\tikz@lib@decoration}{\tikz@lib@decoration[]}%]
+}%
+
+\def\tikz@lib@decoration[#1]#2{\tikzerror{You need to load a decoration library}}%
+
+% The decorate path command:
+\def\tikz@lib@dec@decorate@path{\tikzerror{You need to load a decoration library}}%
+
+
+
+%
+% Syntax for let :
+%
+% let \p1 = (coordinate), \p2 = (coordinate),... in
+%
+\def\tikz@let@command et#1in{%
+ \tikzerror{You need to say \string\usetikzlibrary{calc} to use the let command}%
+ \tikz@scan@next@command%
+}%
+
+
+%
+% Syntax for pictures:
+%
+% as for nodes, but with "pic" instead of "node"
+%
+\newif\iftikz@node@is@pic
+\def\tikz@subpicture ic{\tikz@node@is@pictrue\tikz@scan@next@command node}%
+\def\tikz@subpicture@handle#1{%
+ \pgfkeys@spdef\tikz@temp{#1}%
+ \expandafter\tikz@subpicture@handle@\expandafter{\tikz@temp}%
+}%
+\def\tikz@subpicture@handle@#1{
+ \pgfkeys{/tikz/pics/.cd,#1}%
+ \tikz@node@transformations%
+ \let\tikz@transform=\relax%
+ \let\tikz@picmode\tikz@mode%
+ \tikzset{name prefix ../.style/.expanded={/tikz/name prefix=\pgfkeysvalueof{/tikz/name prefix}}}%
+ \ifx\tikz@fig@name\pgfutil@empty\else%
+ \tikzset{name prefix/.expanded=\tikz@fig@name}%
+ \fi%
+ \pgfkeysvalueof{/tikz/pics/setup code}%
+ \pgfkeysgetvalue{/tikz/pics/code}{\tikz@pic@code}
+ \ifx\tikz@pic@code\pgfutil@empty\else%
+ \setbox\tikz@whichbox=\hbox\bgroup%
+ \unhbox\tikz@whichbox%
+ \hbox\bgroup
+ \bgroup%
+ \pgfinterruptpath%
+ \pgfscope%
+ \tikz@options%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \tikz@atbegin@scope%
+ \scope[every pic/.try]%
+ \tikz@pic@code%
+ \endscope%
+ \tikz@atend@scope%
+ \endpgfscope%
+ \endpgfinterruptpath%
+ \egroup
+ \egroup%
+ \egroup%
+ \fi%
+ \pgfkeysgetvalue{/tikz/pics/foreground code}{\tikz@pic@code}
+ \ifx\tikz@pic@code\pgfutil@empty\else%
+ \setbox\tikz@figbox=\hbox\bgroup%
+ \unhbox\tikz@figbox%
+ \hbox\bgroup
+ \bgroup%
+ \pgfinterruptpath%
+ \pgfscope%
+ \tikz@options%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \tikz@atbegin@scope%
+ \scope[every front pic/.try]%
+ \tikz@pic@code%
+ \endscope%
+ \tikz@atend@scope%
+ \endpgfscope%
+ \endpgfinterruptpath%
+ \egroup
+ \egroup%
+ \egroup%
+ \fi%
+ \pgfkeysgetvalue{/tikz/pics/background code}{\tikz@pic@code}
+ \ifx\tikz@pic@code\pgfutil@empty\else%
+ \setbox\tikz@figbox@bg=\hbox\bgroup%
+ \unhbox\tikz@figbox@bg%
+ \hbox\bgroup
+ \bgroup%
+ \pgfinterruptpath%
+ \pgfscope%
+ \tikz@options%
+ \setbox\tikz@figbox=\box\pgfutil@voidb@x%
+ \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x%
+ \tikz@atbegin@scope%
+ \scope[every behind pic/.try]%
+ \tikz@pic@code%
+ \endscope%
+ \tikz@atend@scope%
+ \endpgfscope%
+ \endpgfinterruptpath%
+ \egroup
+ \egroup%
+ \egroup%
+ \fi%
+ \tikz@node@finish%
+}%
+\tikzset{
+ pic actions/.code=\tikz@addmode{\tikz@picmode}
+}%
+
+% Setting up the picture codes:
+\tikzset{
+ pics/setup code/.initial=,
+ pics/code/.initial=,
+ pics/background code/.initial=,
+ pics/foreground code/.initial=
+}%
+
+% Defining pictures:
+
+\def\tikzdeclarepic#1#2{\pgfkeys{/tikz/#1/.cd,#2}}%
+
+\pgfkeysdef{/handlers/.pic}{%
+ \edef\pgf@temp{\pgfkeyscurrentpath}%
+ \edef\pgf@temp{\expandafter\tikz@smuggle@pics@in\pgf@temp\pgf@stop}%
+ \expandafter\pgfkeys\expandafter{\pgf@temp/.style={code={#1}}}%
+}%
+\def\tikz@smuggle@pics@in/tikz/#1\pgf@stop{/tikz/pics/#1}%
+
+%
+% Timers
+%
+
+\def\tikz@timer@line{%
+ \pgftransformlineattime{\tikz@time}{\tikz@timer@start}{\tikz@timer@end}%
+}%
+
+\def\tikz@timer@vhline{%
+ \ifdim\tikz@time pt<0.5pt% first half
+ \pgf@process{\tikz@timer@start}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{\tikz@timer@end}%
+ \pgf@xb=\tikz@time pt%
+ \pgf@xb=2\pgf@xb%
+ \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}{\noexpand\tikz@timer@start}{%
+ \noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@y}}}%
+ \tikz@marshal%
+ \else% second half
+ \pgf@process{\tikz@timer@start}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{\tikz@timer@end}%
+ \pgf@xb=\tikz@time pt%
+ \pgf@xb=2\pgf@xb%
+ \advance\pgf@xb by-1pt%
+ \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}%
+ {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@y}}{\noexpand\tikz@timer@end}}%
+ \tikz@marshal%
+ \fi%
+}%
+
+\def\tikz@timer@hvline{%
+ \ifdim\tikz@time pt<0.5pt% first half
+ \pgf@process{\tikz@timer@start}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{\tikz@timer@end}%
+ \pgf@xb=\tikz@time pt%
+ \pgf@xb=2\pgf@xb%
+ \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}{\noexpand\tikz@timer@start}{%
+ \noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@ya}}}%
+ \tikz@marshal%
+ \else% second half
+ \pgf@process{\tikz@timer@start}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{\tikz@timer@end}%
+ \pgf@xb=\tikz@time pt%
+ \pgf@xb=2\pgf@xb%
+ \advance\pgf@xb by-1pt%
+ \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}%
+ {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@ya}}{\noexpand\tikz@timer@end}}%
+ \tikz@marshal%
+ \fi%
+}%
+
+\def\tikz@timer@curve{%
+ \pgftransformcurveattime{\tikz@time}{\tikz@timer@start}{\tikz@timer@cont@one}{\tikz@timer@cont@two}{\tikz@timer@end}%
+}%
+
+
+\def\tikz@timer@arc{%
+ \pgfmathcos@{\tikz@timer@start@angle}%
+ \let\tikz@angle@cos\pgfmathresult%
+ \pgfmathsin@{\tikz@timer@start@angle}%
+ \let\tikz@angle@sin\pgfmathresult%
+ \pgftransformarcaxesattime{\tikz@time}{%
+ \pgfpointdiff{%
+ \pgfpointadd{%
+ \pgfpointscale{\tikz@angle@cos}{\tikz@timer@zero@axis}%
+ }{%
+ \pgfpointscale{\tikz@angle@sin}{\tikz@timer@ninety@axis}%
+ }%
+ }%
+ {\tikz@timer@start}%
+ }%
+ {\tikz@timer@zero@axis}%
+ {\tikz@timer@ninety@axis}%
+ {\tikz@timer@start@angle}{\tikz@timer@end@angle}%
+}%
+
+
+
+%
+% Coordinate systems
+%
+
+\def\tikzdeclarecoordinatesystem#1#2{%
+ \expandafter\def\csname tikz@parse@cs@#1\endcsname(##1){%
+ \pgf@process{%
+ #2%
+ \global\let\tikz@smubble@b=\tikz@shapeborder@name%
+ }%
+ \let\tikz@shapeborder@name=\tikz@smubble@b%
+ \edef\tikz@return@coordinate{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
+}%
+\def\tikzaliascoordinatesystem#1#2{%
+ \edef\pgf@marshal{\noexpand\let\expandafter\noexpand\csname
+ tikz@parse@cs@#1\endcsname=\expandafter\noexpand\csname
+ tikz@parse@cs@#2\endcsname}%
+ \pgf@marshal%
+}%
+
+
+% Default coordinate systems:
+
+\tikzdeclarecoordinatesystem{canvas}
+{%
+ \tikzset{cs/.cd,x=0pt,y=0pt,#1}%
+ \pgfpoint{\tikz@cs@x}{\tikz@cs@y}%
+}%
+
+\tikzdeclarecoordinatesystem{canvas polar}
+{%
+ \tikzset{cs/.cd,angle=0,radius=0cm,#1}%
+ \pgfpointpolar{\tikz@cs@angle}{\tikz@cs@xradius and \tikz@cs@yradius}%
+}%
+
+\tikzdeclarecoordinatesystem{xyz}
+{%
+ \tikzset{cs/.cd,x=0,y=0,z=0,#1}%
+ \pgfpointxyz{\tikz@cs@x}{\tikz@cs@y}{\tikz@cs@z}%
+}%
+
+\tikzdeclarecoordinatesystem{xyz polar}
+{%
+ \tikzset{cs/.cd,angle=0,radius=0,#1}%
+ \pgfpointpolarxy{\tikz@cs@angle}{\tikz@cs@xradius and \tikz@cs@yradius}%
+}%
+\tikzaliascoordinatesystem{xy polar}{xyz polar}%
+
+
+\tikzdeclarecoordinatesystem{node}
+{%
+ \tikzset{cs/.cd,name=,anchor=none,angle=none,#1}%
+ \ifx\tikz@cs@anchor\tikz@nonetext%
+ \ifx\tikz@cs@angle\tikz@nonetext%
+ \expandafter\ifx\csname pgf@sh@ns@\tikz@cs@node\endcsname\tikz@coordinate@text%
+ \else
+ \aftergroup\tikz@shapebordertrue%
+ \edef\tikz@shapeborder@name{\tikz@pp@name{\tikz@cs@node}}%
+ \fi%
+ \pgfpointanchor{\tikz@pp@name{\tikz@cs@node}}{center}%
+ \else%
+ \pgfpointanchor{\tikz@pp@name{\tikz@cs@node}}{\tikz@cs@angle}%
+ \fi%
+ \else%
+ \pgfpointanchor{\tikz@pp@name{\tikz@cs@node}}{\tikz@cs@anchor}%
+ \fi%
+}%
+
+% Intersection coordinates
+\tikzset{cs/first line/.code=\def\tikz@cs@line@a{#1}\def\tikz@cs@type@a{line}}%
+\tikzset{cs/second line/.code=\def\tikz@cs@line@b{#1}\def\tikz@cs@type@b{line}}%
+
+\tikzset{cs/first node/.code=\tikz@cs@unpack{\tikz@cs@node@a}{\tikz@cs@type@a}{#1}}%
+\tikzset{cs/second node/.code=\tikz@cs@unpack{\tikz@cs@node@b}{\tikz@cs@type@b}{#1}}%
+
+\def\tikz@cs@unpack#1#2#3{%
+ \expandafter\ifx\csname pgf@sh@ns@#3\endcsname\relax%
+ \tikzerror{Undefined node ``#3''}%
+ \else%
+ \def#1{#3}%
+ \edef#2{\csname pgf@sh@ns@#3\endcsname}%
+ \fi%
+}%
+
+\tikzset{cs/solution/.initial=1}%
+
+\tikzset{cs/horizontal line through/.store in=\tikz@cs@hori@line}%
+\tikzset{cs/vertical line through/.store in=\tikz@cs@vert@line}%
+
+\tikzdeclarecoordinatesystem{intersection}
+{%
+ \tikzset{cs/.cd,#1}%
+ \expandafter\ifx\csname tikz@intersect@\tikz@cs@type@a @and@\tikz@cs@type@b\endcsname\relax%
+ \tikzerror{I do not know how to compute the intersection
+ of a \tikz@cs@type@a and a \tikz@cs@type@b. Try saying
+ \string\usetikzlibrary{calc}}%
+ \pgfpointorigin%
+ \else%
+ \csname tikz@intersect@\tikz@cs@type@a @and@\tikz@cs@type@b\endcsname%
+ \fi%
+}%
+
+\def\tikz@intersect@line@and@line{%
+ \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@a%
+ \pgf@xa=\pgf@xc%
+ \pgf@ya=\pgf@yc%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@b%
+ \edef\pgf@marshal{%
+ {\noexpand\pgfpointintersectionoflines%
+ {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+ {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}%
+ {\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+ {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}}%
+ \pgf@marshal%
+}%
+
+\def\tikz@parse@line#1--{%
+ \pgf@process{#1}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \tikz@scan@one@point\pgf@process%
+}%
+
+
+\tikzdeclarecoordinatesystem{perpendicular}
+{%
+ \tikzset{cs/.cd,#1}%
+ \expandafter\tikz@scan@one@point\expandafter\tikz@parse@intersection@a\tikz@cs@hori@line%
+ \expandafter\tikz@scan@one@point\expandafter\tikz@parse@intersection@b\tikz@cs@vert@line%
+ \pgfqpoint{\the\pgf@xb}{\the\pgf@ya}
+}%
+
+\tikzdeclarecoordinatesystem{barycentric}
+{%
+ {%
+ \pgf@xa=0pt% point
+ \pgf@ya=0pt%
+ \pgf@xb=0pt% sum
+ \tikz@bary@dolist#1,=,%
+ \pgfmathparse{1/\the\pgf@xb}%
+ \global\pgf@x=\pgfmathresult\pgf@xa%
+ \global\pgf@y=\pgfmathresult\pgf@ya%
+ }%
+}%
+
+\def\tikz@bary@dolist#1=#2,{%
+ \def\tikz@temp{#1}%
+ \ifx\tikz@temp\pgfutil@empty%
+ \else
+ \pgf@process{\pgfpointanchor{#1}{center}}%
+ \pgfmathparse{#2}%
+ \advance\pgf@xa by\pgfmathresult\pgf@x%
+ \advance\pgf@ya by\pgfmathresult\pgf@y%
+ \advance\pgf@xb by\pgfmathresult pt%
+ \expandafter\tikz@bary@dolist%
+ \fi%
+}%
+
+\tikzset{cs/x/.store in=\tikz@cs@x}%
+\tikzset{cs/y/.store in=\tikz@cs@y}%
+\tikzset{cs/z/.store in=\tikz@cs@z}%
+\tikzset{cs/angle/.store in=\tikz@cs@angle}%
+\tikzset{cs/x radius/.store in=\tikz@cs@xradius}%
+\tikzset{cs/y radius/.store in=\tikz@cs@yradius}%
+\tikzset{cs/radius/.style={/tikz/cs/x radius={#1},/tikz/cs/y radius={#1}}}%
+\tikzset{cs/name/.store in=\tikz@cs@node}%
+\tikzset{cs/anchor/.store in=\tikz@cs@anchor}%
+
+
+
+%
+% Coordinate management
+%
+
+
+% Last position visited
+\def\tikz@last@position{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}%
+\def\tikz@last@position@saved{\pgfqpoint{\tikz@lastxsaved}{\tikz@lastysaved}}%
+
+% Make given point the last position visited
+\def\tikz@make@last@position#1{%
+ \pgf@process{#1}%
+ \tikz@lastx=\pgf@x\relax%
+ \tikz@lasty=\pgf@y\relax%
+ \iftikz@updatecurrent%
+ \tikz@lastxsaved=\pgf@x\relax%
+ \tikz@lastysaved=\pgf@y\relax%
+ \fi%
+ \iftikz@updatenext
+ \tikz@updatecurrenttrue%
+ \fi
+}%
+
+\newif\iftikz@updatecurrent
+\tikz@updatecurrenttrue
+\newif\iftikz@updatenext
+\tikz@updatenexttrue
+
+
+
+% Scanner: Scans a point or a relative point.
+% It then calls the first parameter with the argument set to an
+% appropriate pgf command representing that point.
+
+\def\tikz@scan@one@point#1{%
+ \let\tikz@to@use@whom=\tikz@to@use@last@coordinate%
+ \tikz@shapeborderfalse%
+ \pgfutil@ifnextchar+{\tikz@scan@relative#1}{\tikz@scan@absolute#1}}%
+\def\tikz@scan@absolute#1{%
+ \pgfutil@ifnextchar({\tikz@scan@@absolute#1}%)
+ {%
+ \advance\tikz@expandcount by -1
+ \ifnum\tikz@expandcount<0\relax%
+ \let\pgfutil@next=\tikz@@scangiveup%
+ \else%
+ \let\pgfutil@next=\tikz@@scanexpand%
+ \fi%
+ \pgfutil@next{#1}%
+ }%
+}%
+\def\tikz@@scanexpand#1{\expandafter\tikz@scan@one@point\expandafter#1}%
+\def\tikz@@scangiveup#1{\tikzerror{Cannot parse this coordinate}#1{\pgfpointorigin}}%
+\def\tikz@scan@@absolute#1({%
+ \pgfutil@ifnextchar[% uhoh... options!
+ {\def\tikz@scan@point@recall{#1}\tikz@scan@options}%
+ {\tikz@@@scan@@absolute#1(}%
+}%
+
+\def\tikz@scan@options[#1]#2{%
+ \def\tikz@scan@point@options{#1}%
+ \tikz@@@scan@@absolute\tikz@scan@handle@options(#2%
+}%
+
+\def\tikz@scan@handle@options#1{%
+ {%
+ % Ok, compute point with options set and zero transformation
+ % matrix:
+ \pgftransformreset%
+ \let\tikz@transform=\pgfutil@empty%
+ \expandafter\tikzset\expandafter{\tikz@scan@point@options}%
+ \tikz@transform%
+ \pgf@process{\pgfpointtransformed{#1}}%
+ \xdef\tikz@marshal{\expandafter\noexpand\tikz@scan@point@recall{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
+ }%
+ \tikz@marshal%
+}%
+
+\def\tikz@@@scan@@absolute#1({%
+ \pgfutil@ifnextchar{$}%$
+ {\tikz@parse@calculator#1(}
+ {\tikz@scan@no@calculator#1(}%
+}%
+\def\tikz@scan@no@calculator#1(#2){%
+ \edef\tikz@scan@point@coordinate{(#2)}%
+ \expandafter\tikz@@scan@@no@calculator\expandafter#1\tikz@scan@point@coordinate%
+}%
+\def\tikz@@scan@@no@calculator#1(#2){%
+ \pgfutil@in@{cs:}{#2}%
+ \ifpgfutil@in@%
+ \let\pgfutil@next\tikz@parse@coordinatesystem%
+ \else%
+ \pgfutil@in@{intersection }{#2}%
+ \ifpgfutil@in@%
+ \let\pgfutil@next\tikz@parse@intersection%
+ \else%
+ \pgfutil@in@|{#2}%
+ \ifpgfutil@in@
+ \pgfutil@in@{-|}{#2}%
+ \ifpgfutil@in@
+ \let\pgfutil@next\tikz@parse@hv%
+ \else%
+ \let\pgfutil@next\tikz@parse@vh%
+ \fi%
+ \else%
+ \pgfutil@in@:{#2}%
+ \ifpgfutil@in@
+ \let\pgfutil@next\tikz@parse@polar%
+ \else%
+ \pgfutil@in@,{#2}%
+ \ifpgfutil@in@%
+ \let\pgfutil@next\tikz@parse@regular%
+ \else%
+ \let\pgfutil@next\tikz@parse@node%
+ \fi%
+ \fi%
+ \fi%
+ \fi%
+ \fi%
+ \pgfutil@next#1(#2)%
+}%
+
+\def\tikz@parse@calculator#1($#2$){%
+ \tikzerror{You need to say \string\usetikzlibrary{calc} for coordinate calculation}%
+ #1{\pgfpointorigin}%
+}%
+
+\def\tikz@parse@coordinatesystem#1(#2 cs:#3){%
+ \let\tikz@return@coordinate=\pgfpointorigin%
+ \pgfutil@ifundefined{tikz@parse@cs@#2}
+ {\tikzerror{Unknown coordinate system '#2'}}
+ {\csname tikz@parse@cs@#2\endcsname(#3)}%
+ \expandafter#1\expandafter{\tikz@return@coordinate}%
+}%
+
+
+\newif\iftikz@isdimension
+\def\tikz@checkunit#1{%
+ \pgfmathparse{#1}%
+ \let\iftikz@isdimension=\ifpgfmathunitsdeclared%
+}%
+
+\def\tikz@parse@polar#1(#2:#3){%
+ \pgfutil@ifundefined{tikz@polar@dir@#2}
+ {\tikz@@parse@polar#1({#2}:{#3})}
+ {\tikz@@parse@polar#1(\csname tikz@polar@dir@#2\endcsname:{#3})}%
+}%
+\def\tikz@@parse@polar#1(#2:#3){%
+ \pgfutil@in@{ and }{#3}%
+ \ifpgfutil@in@%
+ \edef\tikz@args{({#2}:#3)}%
+ \else%
+ \edef\tikz@args{({#2}:{#3} and {#3})}%
+ \fi%
+ \expandafter\tikz@@@parse@polar\expandafter#1\tikz@args%
+}%
+\def\tikz@@@parse@polar#1(#2:#3 and #4){%
+ \tikz@checkunit{#3}%
+ \iftikz@isdimension%
+ \tikz@checkunit{#4}%
+ \iftikz@isdimension%
+ \def\tikz@next{#1{\pgfpointpolar{#2}{#3 and #4}}}%
+ \else%
+ \tikzerror{You cannot mix dimension and dimensionless values for polar coordinates}
+ \def\tikz@next{#1{\pgfpointorigin}}%
+ \fi%
+ \else%
+ \tikz@checkunit{#4}%
+ \iftikz@isdimension%
+ \tikzerror{You cannot mix dimension and dimensionless values for polar coordinates}
+ \def\tikz@next{#1{\pgfpointorigin}}%
+ \else%
+ \def\tikz@next{#1{\pgfpointpolarxy{#2}{#3 and #4}}}%
+ \fi%
+ \fi%
+ \tikz@next%
+}%
+\def\tikz@polar@dir@up{90}%
+\def\tikz@polar@dir@down{-90}%
+\def\tikz@polar@dir@left{180}%
+\def\tikz@polar@dir@right{0}%
+\def\tikz@polar@dir@north{90}%
+\def\tikz@polar@dir@south{-90}%
+\def\tikz@polar@dir@east{0}%
+\def\tikz@polar@dir@west{180}%
+\expandafter\def\csname tikz@polar@dir@north east\endcsname{45}%
+\expandafter\def\csname tikz@polar@dir@north west\endcsname{135}%
+\expandafter\def\csname tikz@polar@dir@south east\endcsname{-45}%
+\expandafter\def\csname tikz@polar@dir@south west\endcsname{-135}%
+
+
+% MW:
+% Check to see if the y-coordinate is inside {}. If it is, scan it and
+% reinsert it into the stream inside an extra group.
+%
+\def\tikz@parse@regular#1(#2,{%
+ \pgfutil@ifnextchar\bgroup{\tikz@@parse@regular#1{#2}}{\tikz@@@parse@regular#1{#2}}%
+}%
+\def\tikz@@parse@regular#1#2#3{%
+ \pgfutil@ifnextchar[{% Uh oh! An array index.
+ \tikz@@@parse@regular#1{#2}{#3}}%
+ {\tikz@@@parse@regular#1{#2}{{#3}}}}%
+
+% Originally \def\tikz@parse@regular#1(#2,#3){%
+%
+\def\tikz@@@parse@regular#1#2#3){%
+ \pgfutil@in@,{#3}%
+ \ifpgfutil@in@%
+ \tikz@parse@splitxyz{#1}{#2}#3,%
+ \else%
+ \tikz@checkunit{#2}%
+ \iftikz@isdimension%
+ \tikz@checkunit{#3}%
+ \iftikz@isdimension%
+ \def\pgfutil@next{#1{\pgfpoint{#2}{#3}}}%
+ \else%
+ \def\pgfutil@next{#1{\pgfpointadd{\pgfpoint{#2}{0pt}}{\pgfpointxy{0}{#3}}}}%
+ \fi%
+ \else%
+ \tikz@checkunit{#3}%
+ \iftikz@isdimension%
+ \def\pgfutil@next{#1{\pgfpointadd{\pgfpoint{0pt}{#3}}{\pgfpointxy{#2}{0}}}}%
+ \else%
+ \def\pgfutil@next{#1{\pgfpointxy{#2}{#3}}}%
+ \fi%
+ \fi%
+ \fi%
+ \pgfutil@next%
+}%
+
+\def\tikz@parse@splitxyz#1#2#3,#4,{%
+ \def\pgfutil@next{#1{\pgfpointxyz{#2}{#3}{#4}}}%
+}%
+
+\def\tikz@coordinate@text{coordinate}%
+
+\def\tikz@parse@node#1(#2){%
+ \pgfutil@in@.{#2}% Ok, flag this
+ \ifpgfutil@in@
+ \tikz@calc@anchor#2\tikz@stop%
+ \else%
+ \tikz@calc@anchor#2.center\tikz@stop% to be on the save side, in
+ % case iftikz@shapeborder is ignored...
+ \ifcsname pgf@sh@ns@\tikz@pp@name{#2}\endcsname
+ \expandafter\ifx\csname pgf@sh@ns@\tikz@pp@name{#2}\endcsname\tikz@coordinate@text%
+ \else
+ \tikz@shapebordertrue%
+ \def\tikz@shapeborder@name{\tikz@pp@name{#2}}%
+ \fi%
+ \else\ifcsname pgf@sh@ns@#2\endcsname
+ \expandafter\ifx\csname pgf@sh@ns@#2\endcsname\tikz@coordinate@text%
+ \else
+ \tikz@shapebordertrue%
+ \def\tikz@shapeborder@name{#2}%
+ \fi%
+ \fi\fi
+ \fi%
+ \edef\tikz@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
+ \tikz@marshal%
+}%
+
+\def\tikz@calc@anchor#1.#2\tikz@stop{%
+ % Check if a shape with name prefix exists, otherwise try the global name
+ % without prefix.
+ \ifcsname pgf@sh@ns@\tikz@pp@name{#1}\endcsname%
+ \pgfpointanchor{\tikz@pp@name{#1}}{#2}%
+ \else
+ \pgfpointanchor{#1}{#2}%
+ \fi
+}%
+
+
+\def\tikz@parse@hv#1(#2){%
+ \pgfutil@in@{ -| }{#2}%
+ \ifpgfutil@in@%
+ \let\tikz@next=\tikz@parse@hvboth%
+ \else%
+ \pgfutil@in@{ -|}{#2}%
+ \ifpgfutil@in@%
+ \let\tikz@next=\tikz@parse@hvleft%
+ \else%
+ \pgfutil@in@{-| }{#2}%
+ \ifpgfutil@in@%
+ \let\tikz@next=\tikz@parse@hvright%
+ \else%
+ \let\tikz@next=\tikz@parse@hvdone%
+ \fi%
+ \fi%
+ \fi%
+ \tikz@next#1(#2)}%
+\def\tikz@parse@hvboth#1(#2 -| #3){\tikz@parse@vhdone#1({#3}|-{#2})}%
+\def\tikz@parse@hvleft#1(#2 -|#3){\tikz@parse@vhdone#1({#3}|-{#2})}%
+\def\tikz@parse@hvright#1(#2-| #3){\tikz@parse@vhdone#1({#3}|-{#2})}%
+\def\tikz@parse@hvdone#1(#2-|#3){\tikz@parse@vhdone#1({#3}|-{#2})}%
+
+\def\tikz@parse@vh#1(#2){%
+ \pgfutil@in@{ |- }{#2}%
+ \ifpgfutil@in@%
+ \let\tikz@next=\tikz@parse@vhboth%
+ \else%
+ \pgfutil@in@{ |-}{#2}%
+ \ifpgfutil@in@%
+ \let\tikz@next=\tikz@parse@vhleft%
+ \else%
+ \pgfutil@in@{|- }{#2}%
+ \ifpgfutil@in@%
+ \let\tikz@next=\tikz@parse@vhright%
+ \else%
+ \let\tikz@next=\tikz@parse@vhdone%
+ \fi%
+ \fi%
+ \fi%
+ \tikz@next#1(#2)}%
+\def\tikz@parse@vhboth#1(#2 |- #3){\tikz@parse@vhdone#1({#2}|-{#3})}%
+\def\tikz@parse@vhleft#1(#2 |-#3){\tikz@parse@vhdone#1({#2}|-{#3})}%
+\def\tikz@parse@vhright#1(#2|- #3){\tikz@parse@vhdone#1({#2}|-{#3})}%
+\def\tikz@parse@vhdone#1(#2|-#3){%
+ {%
+ \tikz@@@scan@@absolute\tikz@parse@vh@mid(#2)%
+ \tikz@@@scan@@absolute\tikz@parse@vh@end(#3)%
+ \xdef\tikz@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}}%
+ }%
+ \tikz@marshal%
+}%
+\def\tikz@parse@vh@mid#1{\pgf@process{#1}\pgf@xa=\pgf@x}%
+\def\tikz@parse@vh@end#1{\pgf@process{#1}\pgf@ya=\pgf@y}%
+
+\def\tikz@parse@intersection#1(intersection{%
+ \pgfutil@ifnextchar o{%
+ \tikz@parse@main@intersection#1 1%
+ }{%
+ \tikz@parse@main@intersection#1%
+ }%
+}%
+\def\tikz@parse@main@intersection#1#2of #3 and #4){%
+ \tikzset{cs/solution={#2}}%
+ \pgfutil@in@{--}{#3}%
+ \ifpgfutil@in@%
+ \tikz@reparse@line{first}#3\pgf@stop%
+ \else%
+ \tikzset{cs/first node={#3}}%
+ \fi%
+ \pgfutil@in@{--}{#4}%
+ \ifpgfutil@in@%
+ \tikz@reparse@line{second}#4\pgf@stop%
+ \else%
+ \tikzset{cs/second node={#4}}%
+ \fi%
+ \tikz@parse@cs@intersection()% advanced hackery...
+ \edef\pgf@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
+ \pgf@marshal%
+}%
+\def\tikz@reparse@line#1#2--#3\pgf@stop{%
+ \tikzset{cs/#1 line={(#2)--(#3)}}%
+}%
+
+
+\def\tikz@parse@intersection@a#1{\pgf@process{#1}\pgf@xa=\pgf@x\pgf@ya=\pgf@y}%
+\def\tikz@parse@intersection@b#1{\pgf@process{#1}\pgf@xb=\pgf@x\pgf@yb=\pgf@y}%
+
+\def\tikz@scan@relative#1+{%
+ \pgfutil@ifnextchar+{\tikz@scan@plusplus#1}{\tikz@scan@oneplus#1}}%
+
+\def\tikz@scan@plusplus#1+{%
+ \def\tikz@doafter{#1}%
+ \tikz@scan@absolute\tikz@add%
+}%
+\def\tikz@add#1{%
+ \tikz@doafter{\pgfpointadd{#1}{\tikz@last@position@saved}}%
+}%
+\def\tikz@scan@oneplus#1{%
+ \def\tikz@doafter{#1}%
+ \tikz@updatecurrentfalse%
+ \tikz@scan@absolute\tikz@add%
+}%
+
+
+
+%
+% Quote handling
+%
+
+\let\tikz@enable@node@quotes\relax
+\let\tikz@enable@edge@quotes\relax
+\let\tikz@enable@pic@quotes\relax
+
+
+
+% Loading further libraries
+
+% Include a library file.
+%
+% #1 = List of names of library file.
+%
+% Description:
+%
+% This command includes a list of TikZ library files. For each file X in the
+% list, the file tikzlibraryX.code.tex is included, provided this has
+% not been done earlier.
+%
+% For the convenience of Context users, both round and square brackets
+% are possible for the argument.
+%
+% If no file tikzlibraryX.code.tex exists, the file
+% pgflibraryX.code.tex is tried instead. If this file, also, does not
+% exist, an error message is printed.
+%
+% Example:
+%
+% \usetikzlibrary{arrows}
+% \usetikzlibrary[patterns,topaths]
+
+\def\usetikzlibrary{\pgfutil@ifnextchar[{\use@tikzlibrary}{\use@@tikzlibrary}}%}%
+\def\use@tikzlibrary[#1]{\use@@tikzlibrary{#1}}%
+\def\use@@tikzlibrary#1{%
+ \edef\pgf@list{#1}%
+ \pgfutil@for\pgf@temp:=\pgf@list\do{%
+ \expandafter\pgfkeys@spdef\expandafter\pgf@temp\expandafter{\pgf@temp}%
+ \ifx\pgf@temp\pgfutil@empty
+ \else
+ \expandafter\ifx\csname tikz@library@\pgf@temp @loaded\endcsname\relax%
+ \expandafter\global\expandafter\let\csname tikz@library@\pgf@temp @loaded\endcsname=\pgfutil@empty%
+ \expandafter\edef\csname tikz@library@#1@atcode\endcsname{\the\catcode`\@}
+ \expandafter\edef\csname tikz@library@#1@barcode\endcsname{\the\catcode`\|}
+ \expandafter\edef\csname tikz@library@#1@dollarcode\endcsname{\the\catcode`\$}
+ \catcode`\@=11
+ \catcode`\|=12
+ \catcode`\$=3
+ \pgfutil@InputIfFileExists{tikzlibrary\pgf@temp.code.tex}{}{
+ \pgfutil@IfFileExists{pgflibrary\pgf@temp.code.tex}{%
+ \expandafter\usepgflibrary\expandafter{\pgf@temp}%
+ }{%
+ \tikzerror{I did not find the tikz library
+ '\pgf@temp'. I looked for files named
+ tikzlibrary\pgf@temp.code.tex and
+ pgflibrary\pgf@temp.code.tex, but neither
+ could be found in the current texmf trees.}
+ }}%
+ \catcode`\@=\csname tikz@library@#1@atcode\endcsname
+ \catcode`\|=\csname tikz@library@#1@barcode\endcsname
+ \catcode`\$=\csname tikz@library@#1@dollarcode\endcsname
+ \fi%
+ \fi
+ }%
+}%
+
+
+% Always-present libraries:
+
+\usetikzlibrary{topaths}%
+
+
+
+
+\endinput