% Copyright 2006 by Till Tantau and Mark Wibrow
%
% 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.

\ProvidesFileRCS[v\pgfversion] $Header: /cvsroot/pgf/pgf/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex,v 1.1 2008/06/26 16:55:55 tantau Exp $

\pgfdeclareshape{ellipse}
%
% Draws a circle around the text
%
{
  \savedanchor\centerpoint{%
    \pgf@x=.5\wd\pgfnodeparttextbox%
    \pgf@y=.5\ht\pgfnodeparttextbox%
    \advance\pgf@y by-.5\dp\pgfnodeparttextbox%
  }
  \savedanchor\radius{%
    % 
    % Caculate ``height radius''
    % 
    \pgf@y=.5\ht\pgfnodeparttextbox%
    \advance\pgf@y by.5\dp\pgfnodeparttextbox%
    \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/inner ysep}}%
    \advance\pgf@y by\pgf@yb%
    % 
    % Caculate ``width radius''
    % 
    \pgf@x=.5\wd\pgfnodeparttextbox%
    \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/inner xsep}}%
    \advance\pgf@x by\pgf@xb%
    % 
    % Adjust
    % 
    \pgf@x=1.4142136\pgf@x%
    \pgf@y=1.4142136\pgf@y%
    % 
    % Adjust hieght, if necessary
    % 
    \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/minimum height}}%
    \ifdim\pgf@y<.5\pgf@yc%
      \pgf@y=.5\pgf@yc%
    \fi%
    % 
    % Adjust width, if necessary
    % 
    \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum width}}%
    \ifdim\pgf@x<.5\pgf@xc%
      \pgf@x=.5\pgf@xc%
    \fi%
    % 
    % Add outer sep
    % 
    \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}%  
    \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}%  
    \advance\pgf@x by\pgf@xb%
    \advance\pgf@y by\pgf@yb%
  }

  %
  % Anchors
  % 
  \anchor{center}{\centerpoint}
  \anchor{mid}{\centerpoint\pgfmathsetlength\pgf@y{.5ex}}
  \anchor{base}{\centerpoint\pgf@y=0pt}
  \anchor{north}
  {
    \pgf@process{\radius}
    \pgf@ya=\pgf@y%
    \pgf@process{\centerpoint}
    \advance\pgf@y by\pgf@ya
  }
  \anchor{south}
  {
    \pgf@process{\radius}
    \pgf@ya=\pgf@y%
    \pgf@process{\centerpoint}
    \advance\pgf@y by-\pgf@ya
  }
  \anchor{west}
  {
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@process{\centerpoint}
    \advance\pgf@x by-\pgf@xa
  }
  \anchor{mid west}
  {%
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@process{\centerpoint}
    \advance\pgf@x by-\pgf@xa%
    \pgfmathsetlength\pgf@y{.5ex}
  }
  \anchor{base west}
  {%
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@process{\centerpoint}
    \advance\pgf@x by-\pgf@xa%
    \pgf@y=0pt
  }
  \anchor{north west}
  {
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \pgf@process{\centerpoint}
    \advance\pgf@x by-0.707107\pgf@xa
    \advance\pgf@y by0.707107\pgf@ya
  }
  \anchor{south west}
  {
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \pgf@process{\centerpoint}
    \advance\pgf@x by-0.707107\pgf@xa
    \advance\pgf@y by-0.707107\pgf@ya
  }
  \anchor{east}
  {%
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@process{\centerpoint}
    \advance\pgf@x by\pgf@xa
  }
  \anchor{mid east}
  {%
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@process{\centerpoint}
    \advance\pgf@x by\pgf@xa%
    \pgfmathsetlength\pgf@y{.5ex}
  }
  \anchor{base east}
  {%
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@process{\centerpoint}
    \advance\pgf@x by\pgf@xa%
    \pgf@y=0pt
  }
  \anchor{north east}
  {
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \pgf@process{\centerpoint}
    \advance\pgf@x by0.707107\pgf@xa
    \advance\pgf@y by0.707107\pgf@ya
  }
  \anchor{south east}
  {
    \pgf@process{\radius}
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \pgf@process{\centerpoint}
    \advance\pgf@x by0.707107\pgf@xa
    \advance\pgf@y by-0.707107\pgf@ya
  }
  \anchorborder{
    \edef\pgf@marshal{%
      \noexpand\pgfpointborderellipse
      {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
      {\noexpand\radius}%
    }%
    \pgf@marshal%
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \centerpoint%
    \advance\pgf@x by\pgf@xa%
    \advance\pgf@y by\pgf@ya%
  }

  %
  % Background path
  %
  \backgroundpath
  {
    \pgf@process{\radius}%
    \pgfutil@tempdima=\pgf@x%
    \pgfutil@tempdimb=\pgf@y%
    \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}%  
    \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}%  
    \advance\pgfutil@tempdima by-\pgf@xb%
    \advance\pgfutil@tempdimb by-\pgf@yb%
    \pgfpathellipse{\centerpoint}{\pgfqpoint{\pgfutil@tempdima}{0pt}}{\pgfqpoint{0pt}{\pgfutil@tempdimb}}%
  }
}




% Set the recommended shape aspect ratio
%
% #1 = aspect ratio
%
% Example:
%
% \pgfsetshapeaspect{1.5}

% Keys for shape aspect ratio.
%
% /pgf/aspect         : recommended width/height quotient.
%
\pgfkeys{/pgf/.cd,
	aspect/.code={\pgfsetshapeaspect{#1}},% this for tikz...
	shape aspect/.initial=1,% but this is consistent with other pgfset stuff. 
	shape aspect/.code={%
		\pgfkeys{/pgf/aspect=#1}%
		\pgfkeyssetvalue{/pgf/shape aspect}{#1}
	}%
}
	

\def\pgfsetshapeaspect#1{%
  \def\pgfshapeaspect{#1}%
  % Invert
  \pgfutil@tempdima=#1pt%
  \pgfutil@tempdima=.125\pgfutil@tempdima%
  \c@pgf@counta=\pgfutil@tempdima\relax% 8192*determinant
  \pgfutil@tempdima=8192pt%
  \divide\pgfutil@tempdima by\c@pgf@counta%
  \edef\pgfshapeaspectinverse{\pgf@sys@tonumber{\pgfutil@tempdima}}
}

\pgfsetshapeaspect{1}

\pgfdeclareshape{diamond}
{
  \savedanchor\outernortheast{%
    %
    % Calculate width and height of the inner rectangle
    %
    \pgf@xa=.5\wd\pgfnodeparttextbox%
    \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/inner xsep}}%
    \advance\pgf@xa by\pgf@xc%
    \pgf@ya=.5\ht\pgfnodeparttextbox%
    \advance\pgf@ya by.5\dp\pgfnodeparttextbox%
    \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}%
    \advance\pgf@ya by\pgf@yc%
    %
    % Calculate width and height of diamond
    %
    \pgf@x=\pgf@xa%
    \advance\pgf@x by\pgfshapeaspect\pgf@ya%
    \pgf@y=\pgfshapeaspectinverse\pgf@xa%
    \advance\pgf@y by\pgf@ya%
    %
    % Check against minimum height/width
    %
    \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}%
    \pgf@xb=.5\pgf@xb%   
    \ifdim\pgf@x<\pgf@xb%
      % yes, too small. Enlarge...
      \pgf@x=\pgf@xb%
    \fi%
    \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}%
    \pgf@yb=.5\pgf@yb%   
    \ifdim\pgf@y<\pgf@yb%
      % yes, too small. Enlarge...
      \pgf@y=\pgf@yb%
    \fi%
    %
    % Add outer border
    %
    \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}%
    \advance\pgf@x by\pgf@xa%
    \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}%
    \advance\pgf@y by\pgf@ya%
  }
  \savedanchor\text{%
    \pgf@x=-.5\wd\pgfnodeparttextbox%
    \pgf@y=-.5\ht\pgfnodeparttextbox%
    \advance\pgf@y by.5\dp\pgfnodeparttextbox%
  }

  %
  % Anchors
  %
  \anchor{text}{\text}%
  \anchor{center}{\pgfpointorigin}%
  \anchor{mid}{%
    \pgf@process{\text}%
    \pgf@x=0pt%
    \pgfmathsetlength\pgf@ya{.5ex}
    \advance\pgf@y by\pgf@ya%
  }
  \anchor{base}{\pgf@process{\text}\pgf@x=0pt  }
  \anchor{north}{\pgf@process{\outernortheast}\pgf@x=0pt}
  \anchor{south}{\pgf@process{\outernortheast}\pgf@x=0pt\pgf@y=-\pgf@y}
  \anchor{west}{\pgf@process{\outernortheast}\pgf@x=-\pgf@x\pgf@y=0pt}
  \anchor{north west}{\pgf@process{\outernortheast}\pgf@x=-.5\pgf@x\pgf@y=.5\pgf@y}
  \anchor{south west}{\pgf@process{\outernortheast}\pgf@x=-.5\pgf@x\pgf@y=-.5\pgf@y}
  \anchor{east}{\pgf@process{\outernortheast}\pgf@y=0pt}
  \anchor{north east}{\pgf@process{\outernortheast}\pgf@x=.5\pgf@x\pgf@y=.5\pgf@y}
  \anchor{south east}{\pgf@process{\outernortheast}\pgf@x=.5\pgf@x\pgf@y=-.5\pgf@y}
  \anchorborder{%
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \pgf@process{\outernortheast}%
    \ifdim\pgf@xa>0pt%
    \else%
      \pgf@x=-\pgf@x%
    \fi%
    \ifdim\pgf@ya>0pt%
    \else%
      \pgf@y=-\pgf@y%
    \fi%
    \edef\pgf@marshal{%
      \noexpand\pgfpointintersectionoflines
      {\noexpand\pgfpointorigin}
      {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}
      {\noexpand\pgfqpoint{\the\pgf@x}{0pt}}
      {\noexpand\pgfqpoint{0pt}{\the\pgf@y}}%
    }%
    \pgf@process{\pgf@marshal}%
  }

  %
  % Background path
  %
  \backgroundpath{
    \pgf@process{\outernortheast}%
    \pgf@xc=\pgf@x%
    \pgf@yc=\pgf@y%
    \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/outer xsep}}%
    \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/outer ysep}}%
    \advance\pgf@xc by-1.414213\pgf@xa%
    \advance\pgf@yc by-1.414213\pgf@ya%
    \pgfpathmoveto{\pgfqpoint{\pgf@xc}{0pt}}%
    \pgfpathlineto{\pgfqpoint{0pt}{\pgf@yc}}%
    \pgfpathlineto{\pgfqpoint{-\pgf@xc}{0pt}}%
    \pgfpathlineto{\pgfqpoint{0pt}{-\pgf@yc}}%
    \pgfpathclose%
  }
}






\newif\ifpgf@lib@shapes@starouterradiususesratio
\pgf@lib@shapes@starouterradiususesratiotrue

% Keys for star shape
%
% /pgf/star points       : Number of points on the star.
% /pgf/star point height : The height of the outer star points.
% /pgf/star point ratio  : The ratio of the outer point and inner point radii.

\pgfkeys{/pgf/.cd,
	star points/.initial=5,
	star point height/.initial=.5cm,
	star point height/.code={%
		\def\pgf@lib@temp{#1}%
		\pgfkeyslet{/pgf/star point height}{\pgf@lib@temp}%
		\pgf@lib@shapes@starouterradiususesratiofalse%	
	},
	star point ratio/.initial=1.5,
	star point ratio/.code={%
		\def\pgf@lib@temp{#1}%
		\pgfkeyslet{/pgf/star point ratio}{\pgf@lib@temp}%
		\pgf@lib@shapes@starouterradiususesratiotrue%	
	},%
	star rotate/.style={/pgf/shape border rotate=#1}% For compatability with 1.18
}


% Shape star.
%
\pgfdeclareshape{star}{
	\savedmacro\totalstarpoints{%
		\pgfmathsetcounter{pgf@counta}{\pgfkeysvalueof{/pgf/star points}}%
		\multiply\c@pgf@counta2\relax%
		\edef\totalstarpoints{\the\c@pgf@counta}%
	}
	\savedmacro\anglestep{%
		\pgfmathdivide{180}{\pgfkeysvalueof{/pgf/star points}}%
		\let\anglestep\pgfmathresult%
	}
	\savedmacro\calculateradii{%
		%
		% Get the node dimensions.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		\ifdim\pgf@y>\pgf@x%
			\pgf@x\pgf@y%
		\fi%
		%
		% Calculate the incircle radius.
		%
		\pgf@x1.41421\pgf@x%
		\edef\innerradius{\the\pgf@x}%
		%
		% Calculate the circumcircle radius.
		%
		% Use the star point height or the star point ratio?
		%
		\ifpgf@lib@shapes@starouterradiususesratio%
			\pgfmathparse{\pgfkeysvalueof{/pgf/star point ratio}}%
			\expandafter\pgf@x\pgfmathresult\pgf@x%
		\else%
			\pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/star point height}}%
		\fi%
		\pgf@xc\pgf@x%
		%
		% Accommodate the larger of the minimum height/width.
		%
		\pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@ya>\pgf@xa%
			\pgf@xa\pgf@ya%
		\fi%
		\ifdim\pgf@x<.5\pgf@xa%
	   	\pgf@x.5\pgf@xa%
	   \fi%
	   \edef\outerradius{\the\pgf@x}%
	   %
	   % If the outer radius has been enlarged, adjust the inner radius...
	   %
	   \ifdim\pgf@x>\pgf@xc%
	   	%
	   	% ...using the star point ratio, or...
	   	%
	   	\ifpgf@lib@shapes@starouterradiususesratio%
	   		\pgfmathreciprocal{\pgfkeysvalueof{/pgf/star point ratio}}%
	   		\pgf@xa\pgfmathresult\pgf@x\relax%
	   		\edef\innerradius{\the\pgf@xa}%
			\else%
				%
				% The star point height.
				%
				\pgf@xa\pgf@x\relax%
				\pgfmathaddtolength\pgf@xa{-\pgfkeysvalueof{/pgf/star point height}}%
				\edef\innerradius{\the\pgf@xa}%
			\fi%
		\fi%
		\edef\outerradius{\the\pgf@x}%
		%
		% Now calculate the anchor radii from the outer sep.
		%
		\pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@ya>\pgf@xa%
			\pgf@xa\pgf@ya%
		\fi
		%
		% Take into account the miter length...
		%
		\pgfmathdivide{180}{\pgfkeysvalueof{/pgf/star points}}%
		\let\angletofirstpoint\pgfmathresult%
		\pgfmathmultiply@{\angletofirstpoint}{2}%
		\let\angletosecondpoint\pgfmathresult%
		%
		% ...for the outer radius...
		%
		\pgfmathanglebetweenlines%
			{\pgfqpointpolar{\angletofirstpoint}{\outerradius}}%
			{\pgfqpointpolar{\angletosecondpoint}{\innerradius}}%
			{\pgfqpointpolar{\angletofirstpoint}{\outerradius}}%		
			{\pgfqpointpolar{0}{\innerradius}}%		
		\pgfmathdivide@{\pgfmathresult}{2}%
		\pgfmathcosec@{\pgfmathresult}%
		\pgf@x\outerradius\relax%
		\advance\pgf@x\pgfmathresult\pgf@xa%
		\edef\anchorouterradius{\the\pgf@x}%
		%
		% ...and for the inner radius.
		%
		\pgfmathanglebetweenlines%
			{\pgfqpointpolar{\angletofirstpoint}{\innerradius}}%		
			{\pgfqpointpolar{0}{\outerradius}}%	
			{\pgfqpointpolar{\angletofirstpoint}{\innerradius}}%
			{\pgfqpointpolar{\angletosecondpoint}{\outerradius}}%						
		\pgfmathdivide@{\pgfmathresult}{2}%
		\pgfmathcosec@{\pgfmathresult}%
		\pgf@x\innerradius\relax%
		\advance\pgf@x\pgfmathresult\pgf@xa%
		\edef\anchorinnerradius{\the\pgf@x}%
		%	
		% Save all radii.
		%
		\addtosavedmacro{\innerradius}%
		\addtosavedmacro{\outerradius}%
		\addtosavedmacro{\anchorinnerradius}%
		\addtosavedmacro{\anchorouterradius}%
	}
	\savedmacro\startangle{%
		\pgfmathadd{90}{\pgfkeysvalueof{/pgf/shape border rotate}}%
		\let\startangle\pgfmathresult%
	}
	%
	% Saved anchors.
	%
	\savedanchor{\centerpoint}{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor{\midpoint}{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%	
	%
	% Other anchors.
	%
%
	% Other anchors.
	%
	\anchor{center}{\centerpoint}%
	\anchor{mid}{\centerpoint\pgfmathsetlength\pgf@y{.5ex}}%
 	\anchor{base}{\centerpoint\pgf@y=0pt}%
 	\anchor{north}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{0pt}{\anchorouterradius}}}%
 	\anchor{south}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{0pt}{-\anchorouterradius}}}%
 	\anchor{east}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{\anchorouterradius}{0pt}}}%
 	\anchor{west}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{-\anchorouterradius}{0pt}}}%
 	\anchor{north east}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{\anchorouterradius}{\anchorouterradius}}}%
 	\anchor{north west}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{-\anchorouterradius}{\anchorouterradius}}}%
 	\anchor{south east}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{\anchorouterradius}{-\anchorouterradius}}}%
 	\anchor{south west}{%
 		\calculateradii%
 		\csname pgf@anchor@star@border\endcsname{\pgfqpoint{-\anchorouterradius}{-\anchorouterradius}}}%	 	
 	%
 	% Background path.
 	%
	\backgroundpath{%
		\calculateradii%
		\let\angle\startangle%
		\pgfpathmoveto{\pgfpointadd{\centerpoint}{\pgfqpointpolar{\startangle}{\outerradius}}}%
		\pgfmathloop%
			\pgfmathadd@{\angle}{\anglestep}%
			\let\angle\pgfmathresult%
		\ifnum\pgfmathcounter=\totalstarpoints%
			\pgfpathclose%
		\else%
			\ifodd\pgfmathcounter
				\pgfpathlineto{\pgfpointadd{\centerpoint}{\pgfqpointpolar{\angle}{\innerradius}}}%
			\else%
				\pgfpathlineto{\pgfpointadd{\centerpoint}{\pgfqpointpolar{\angle}{\outerradius}}}%
			\fi%
		\repeatpgfmathloop%
	}%
	%
	% Define points on the anchor border.
	%
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% Adjust the location of the external 
		% point relative to \centerpoint.
		%
		\centerpoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Get the angle of the external point to the \centerpoint.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}%
		%
		% Locate the appropriate sides on the star border...
		%
		\pgfmathsubtract@{\pgfmathresult}{\startangle}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\pgfmathdivide@{\pgfmathresult}{\anglestep}%
		\pgfmathfloor@{\pgfmathresult}%
		\afterassignment\pgfmath@gobbletilpgfmath@
		\c@pgf@counta\pgfmathresult\relax\pgfmath@
		\pgfmathmultiply@{\pgfmathresult}{\anglestep}%
		\pgfmathadd@{\pgfmathresult}{\startangle}%
		\let\firstangle\pgfmathresult%
		\pgfmathadd@{\pgfmathresult}{\anglestep}%
		\let\secondangle\pgfmathresult%
		\calculateradii%
		%
		% ...and thus, the point on the star border.
		%
		\ifodd\c@pgf@counta
			\pgfpointintersectionoflines{\centerpoint}{\pgfpoint{+\externalx}{+\externaly}}%
				{%
					\pgfpointadd{\centerpoint}%
						{\pgfqpointpolar{+\firstangle}{+\anchorinnerradius}}%
					}%	
					{%
						\pgfpointadd{\centerpoint}%
							{\pgfqpointpolar{+\secondangle}{+\anchorouterradius}}%
					}%	
		\else%
			\pgfpointintersectionoflines{\centerpoint}{\pgfpoint{+\externalx}{+\externaly}}%
				{%
					\pgfpointadd{\centerpoint}%
						{\pgfqpointpolar{+\firstangle}{+\anchorouterradius}}%
					}%	
					{%
						\pgfpointadd{\centerpoint}%
							{\pgfqpointpolar{+\secondangle}{+\anchorinnerradius}}%
					}%	
		\fi%
	}
	%
	% Some hackery. This is needed if a star is positioned using 
	% a `...point <n+1>' anchor, where n is the maximum number of 
	% points of any previously drawn star.
	%
	\pgfutil@g@addto@macro\pgf@sh@s@star{%
		\c@pgf@counta\totalstarpoints\relax%
		\divide\c@pgf@counta2\relax%
		\pgfmathloop%
			\ifnum\c@pgf@counta>0\relax%
				\c@pgf@countb\c@pgf@counta\relax%
				\advance\c@pgf@countb-1\relax%
				\pgfutil@ifundefined{pgf@anchor@star@inner point\space\the\c@pgf@counta}{%
					\expandafter\xdef\csname pgf@anchor@star@inner point\space\the\c@pgf@counta\endcsname{%
						\noexpand\calculateradii%
						\noexpand\pgfmathmultiply@{\the\c@pgf@countb}{\noexpand\anglestep}%
						\noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{2}%
						\noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\anglestep}%
						\noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}%
						\noexpand\let\noexpand\angle\noexpand\pgfmathresult%
						\noexpand\pgfpointadd{\noexpand\centerpoint}%
							{\noexpand\pgfqpointpolar{\noexpand\angle}{\noexpand\anchorinnerradius}}%
					}%
					\expandafter\xdef\csname pgf@anchor@star@outer point\space\the\c@pgf@counta\endcsname{%
						\noexpand\calculateradii%
						\noexpand\pgfmathmultiply@{\the\c@pgf@countb}{\noexpand\anglestep}%
						\noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{2}%
						\noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}%
						\noexpand\let\noexpand\angle\noexpand\pgfmathresult%
						\noexpand\pgfpointadd{\noexpand\centerpoint}%
							{\noexpand\pgfqpointpolar{\noexpand\angle}{\noexpand\anchorouterradius}}%
					}%
				}{\c@pgf@counta0\relax}%
			\advance\c@pgf@counta-1\relax%
		\repeatpgfmathloop%	
	}%
}




% Keys for shape regular polygon
%
% /pgf/regular polygon sides 
%
\pgfkeys{/pgf/.cd,
	regular polygon sides/.initial=5,
	regular polygon rotate/.style={/pgf/shape border rotate=#1}% For compatability with 1.18
}


% Shape Regular Polygon.
%
\pgfdeclareshape{regular polygon}{
	\savedmacro\sides{%
		\pgfmathtruncatemacro\sides{\pgfkeysvalueof{/pgf/regular polygon sides}}%
	}
	\savedmacro\anglestep{%
		\pgfmathdivide{360}{\pgfkeysvalueof{/pgf/regular polygon sides}}%
		\let\anglestep\pgfmathresult%
	}
	\savedmacro\calculateradii{%
		%
		% Get the node dimensions.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		\ifdim\pgf@y>\pgf@x%
			\pgf@x\pgf@y%
		\fi%
		%
		% Calculate i, the incircle radius 
		%
		\pgf@x1.41421\pgf@x%
		%
		% Calculate r, the polygon radius
		%
		% r = i / cos(360 / s / 2)
		%
		% (s = polygon sides)
		%
		\pgfmathdivide{180}{\pgfkeysvalueof{/pgf/regular polygon sides}}%
		\pgfmathsec@{\pgfmathresult}%
		\pgf@x\pgfmathresult\pgf@x%
		%
		% Accommodate the minimum width/height.
		%
		\pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@ya>\pgf@xa%
			\pgf@xa\pgf@ya%
		\fi%
		\ifdim\pgf@x<.5\pgf@xa%
			\pgf@x.5\pgf@xa%
		\fi%
		\edef\radius{\the\pgf@x}%
		%
		% Now calculate the anchor radius from the outer sep.
		%
		\pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@ya>\pgf@xa%
			\pgf@xa\pgf@ya%
		\fi
		%
		% Take into account the miter length.
		%
		% m = o / sin (90 - (360 / s / 2))
		%
		% (o = outer sep, s = sides)
		%
		\pgfmathdivide{180}{\pgfkeysvalueof{/pgf/regular polygon sides}}%
		\pgfmathsubtract@{90}{\pgfmathresult}%
		\pgfmathcosec@{\pgfmathresult}%
		\advance\pgf@x\pgfmathresult\pgf@xa%
		\edef\anchorradius{\the\pgf@x}%
		%
		% Save both radii.
		%
		\addtosavedmacro{\radius}%
		\addtosavedmacro{\anchorradius}%
	}
	\savedmacro\startangle{%
		\pgfmathdivide{360}{\pgfkeysvalueof{/pgf/regular polygon sides}}%
		\let\anglestep\pgfmathresult%
		\pgfmathtruncatemacro\sides{\pgfkeysvalueof{/pgf/regular polygon sides}}%
		\expandafter\ifodd\sides\relax%
			\edef\pgfmathresult{90}%
		\else%
			\pgfmathdivide@{\anglestep}{2}%
			\pgfmathsubtract@{90}{\pgfmathresult}%
		\fi%
		\pgfmathadd{\pgfmathresult}{\pgfkeysvalueof{/pgf/shape border rotate}}%
		\let\startangle\pgfmathresult%
	}
	%
	% Saved anchors.
	%
	\savedanchor{\centerpoint}{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor{\midpoint}{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%	
	%
	% Other anchors.
	%
	\anchor{center}{\centerpoint}%
	\anchor{mid}{\midpoint}%
 	\anchor{base}{\centerpoint\pgf@y=0pt}%
 	\anchor{north}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{0pt}{\anchorradius}}}%
 	\anchor{south}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{0pt}{-\anchorradius}}}%
 	\anchor{east}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{\anchorradius}{0pt}}}%
 	\anchor{west}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{-\anchorradius}{0pt}}}%
 	\anchor{north east}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{\anchorradius}{\anchorradius}}}%
 	\anchor{north west}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{-\anchorradius}{\anchorradius}}}%
 	\anchor{south east}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{\anchorradius}{-\anchorradius}}}%
 	\anchor{south west}{%
 		\calculateradii%
 		\csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{-\anchorradius}{-\anchorradius}}}%	
 	%
 	% Background path.
 	%
	\backgroundpath{%
		\calculateradii%
		\pgfpathmoveto{%
			\pgfpointadd{\centerpoint}{\pgfqpointpolar{\startangle}{\radius}}%
		}%
		\let\angle\startangle%
		\pgfmathloop%
			\ifnum\pgfmathcounter=\sides\relax% 
				\pgfpathclose%
			\else%
				\pgfmathadd@{\angle}{\anglestep}%
				\let\angle\pgfmathresult%
				\pgfpathlineto{%
					\pgfpointadd{\centerpoint}{\pgfqpointpolar{\angle}{\radius}}%
				}%
		\repeatpgfmathloop%	
	}%
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% Adjust the location of the external 
		% point relative to \centerpoint.
		%
		\centerpoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Get the angle of the external point to the \centerpoint.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}%
		%
		% Locate the appropriate sides on the polygon border...
		%
		\pgfmathsubtract@{\pgfmathresult}{\startangle}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\pgfmathdivide@{\pgfmathresult}{\anglestep}%
		\pgfmathfloor@{\pgfmathresult}%
		\pgfmathmultiply@{\pgfmathresult}{\anglestep}%
		\pgfmathadd@{\pgfmathresult}{\startangle}%
		\let\firstangle\pgfmathresult%
		\pgfmathadd@{\pgfmathresult}{\anglestep}%
		\let\secondangle\pgfmathresult%
		\calculateradii%
		%
		% ...and thus, the point on the polygon border.
		%
		\pgfpointintersectionoflines{\centerpoint}{\pgfpoint{+\externalx}{+\externaly}}%
			{%
				\pgfpointadd{\centerpoint}%
					{\pgfqpointpolar{+\firstangle}{+\anchorradius}}%
				}%	
				{%
					\pgfpointadd{\centerpoint}%
						{\pgfqpointpolar{+\secondangle}{+\anchorradius}}%
				}%	
	}
	%
	% More hackery for when the recuglar polygon is positioned using 
	% a `corner <n+1>' or `side <n+1>' anchor, where n is the maximum 
	% number of sides of any previously drawn regular polygon.
	%
	\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@regular polygon\endcsname{%
		\c@pgf@counta\sides\relax%
		\pgfmathloop%
			\ifnum\c@pgf@counta>0\relax%
				\pgfutil@ifundefined{pgf@anchor@regular polygon@corner\space\the\c@pgf@counta}{%
				%
				% ...(manually \xdef as \gdef is normally used by \anchor)...
				%
				\expandafter\xdef\csname pgf@anchor@regular polygon@corner\space\the\c@pgf@counta\endcsname{%
					\noexpand\calculateradii%
					\noexpand\pgfmathsubtract@{\the\c@pgf@counta}{1}%
					\noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{\noexpand\anglestep}%
					\noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}%
					\noexpand\let\noexpand\angle\noexpand\pgfmathresult%
					\noexpand\pgfpointadd{\noexpand\centerpoint}%
						{\noexpand\pgfqpointpolar{\noexpand\angle}{\noexpand\anchorradius}}%
				}%
				\expandafter\xdef\csname pgf@anchor@regular polygon@side\space\the\c@pgf@counta\endcsname{%
					\noexpand\calculateradii%
					\noexpand\pgfmathsubtract@{\the\c@pgf@counta}{1}%
					\noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{\noexpand\anglestep}%
					\noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}%
					\noexpand\let\noexpand\firstangle\noexpand\pgfmathresult%
					\noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\anglestep}%
					\noexpand\let\noexpand\secondangle\noexpand\pgfmathresult%
					\noexpand\pgfpointlineattime{0.5}%
						{\noexpand\pgfpointadd{\noexpand\centerpoint}%
							{\noexpand\pgfqpointpolar{\noexpand\firstangle}{\noexpand\anchorradius}}}%
						{\noexpand\pgfpointadd{\noexpand\centerpoint}%
							{\noexpand\pgfqpointpolar{\noexpand\secondangle}{\noexpand\anchorradius}}}%
				}%
			}{\c@pgf@counta0\relax}% 
			\advance\c@pgf@counta-1\relax%
		\repeatpgfmathloop%	
	}%
}



% Keys for shape trapezium
%
% /pgf/trapezium left angle  : angle of the left side.
% /pgf/trapezium right angle : angle of the right side.

\pgfkeys{/pgf/.cd,
	trapezium left angle/.initial=60,
	trapezium right angle/.initial=60,
	trapezium angle/.style={
		/pgf/trapezium left angle=#1,
		/pgf/trapezium right angle=#1
	},%
	trapezium stretches/.is if=pgf@lib@sh@trapeziumstretches,%
	trapezium stretches body/.is if=pgf@lib@sh@trapeziumstretchesbody%
}

\newif\ifpgf@lib@sh@trapeziumstretchesbody
\newif\ifpgf@lib@sh@trapeziumstretches


% Shape trapezium.
%
\pgfdeclareshape{trapezium}{
	\savedmacro\installtrapeziumparameters{%
		%
		% Get the node dimensions.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		\ifpgfshapeborderusesincircle%
			%
			% Get the rotation (no rounding).
			%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			%
			% Use the radius of the incircle if required...
			%
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\fi%			
			\pgf@x1.41421\pgf@x%
			\pgf@y\pgf@x%
		\else%
			%
			% Get the rotation (with rounding).
			%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\afterassignment\pgfmath@gobbletilpgfmath@%
			\expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\ifnum\c@pgf@counta<0\relax%
				\advance\c@pgf@counta360\relax%
			\fi%
			\edef\rotate{\the\c@pgf@counta}%
			%
			% Calculate the width and height of the node
			% contents, according to any border rotation.
			%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xc\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xc%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xc\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xc%
				\fi%
			\fi%
		\fi%
		\pgfmathmod{\pgfkeysvalueof{/pgf/trapezium left angle}}{360}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\leftangle\pgfmathresult%
		\ifdim\leftangle pt=0pt\relax%
			\def\pgfmathresult{0}%
		\else%
			\pgfmathcot@{\leftangle}%
		\fi%
		\pgf@xa2\pgf@y%
		\pgf@xa\pgfmathresult\pgf@xa%
		\pgfmathmod{\pgfkeysvalueof{/pgf/trapezium right angle}}{360}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\rightangle\pgfmathresult%
		\ifdim\rightangle pt=0pt\relax%
			\def\pgfmathresult{0}%
		\else%
			\pgfmathcot@{\rightangle}%
		\fi%
		\pgf@xb2\pgf@y%
		\pgf@xb\pgfmathresult\pgf@xb%
		%
		% Take into account minimum height and width.
		%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@y<.5\pgf@ya%
			\ifpgf@lib@sh@trapeziumstretches%
				\pgf@y.5\pgf@ya%
			\else%
				\ifpgf@lib@sh@trapeziumstretchesbody%
					\pgf@y.5\pgf@ya%
				\else%
					\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}%
					\pgf@yb.5\pgf@ya%
					\pgf@yb\pgfmathresult\pgf@yb%
					\pgf@y.5\pgf@ya%
					\pgf@x\pgfmath@tonumber{\pgf@yb}\pgf@x%
					\pgf@xa\pgfmath@tonumber{\pgf@yb}\pgf@xa%
					\pgf@xb\pgfmath@tonumber{\pgf@yb}\pgf@xb%
				\fi%
			\fi%
		\fi%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum width}}%
		\pgf@xc2\pgf@x%
		\ifdim\pgf@xa<0pt\relax%
			\advance\pgf@xc-\pgf@xa%
		\else%
			\advance\pgf@xc\pgf@xa%
		\fi%
		\ifdim\pgf@xb<0pt\relax%
			\advance\pgf@xc-\pgf@xb%
		\else%
			\advance\pgf@xc\pgf@xb%
		\fi%
		\ifdim\pgf@xc<\pgf@ya%
			\ifpgf@lib@sh@trapeziumstretchesbody%
				\pgf@xc-\pgf@xc%
				\advance\pgf@xc\pgf@ya%
				\advance\pgf@x.5\pgf@xc%
			\else%
				\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@xc}}%
				\pgf@ya\pgfmathresult\pgf@ya%
				\pgf@x\pgfmath@tonumber{\pgf@ya}\pgf@x%
				\pgf@xa\pgfmath@tonumber{\pgf@ya}\pgf@xa%
				\pgf@xb\pgfmath@tonumber{\pgf@ya}\pgf@xb%
				\ifpgf@lib@sh@trapeziumstretches%	
				\else%					
					\pgf@y\pgfmath@tonumber{\pgf@ya}\pgf@y%
				\fi%				
			\fi%
		\fi%
		\edef\halfheight{\the\pgf@y}%
		\edef\halfwidth{\the\pgf@x}%
		\edef\leftextension{\the\pgf@xa}%
		\edef\rightextension{\the\pgf@xb}%
		\pgf@xc2\pgf@x%
		%
		% Take the larger of the outer sep.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@y>\pgf@x%
			\pgf@x\pgf@y%
		\fi%
		\edef\outersep{\the\pgf@x}%
		%
		% The \externalradius is a length that is
		% guarenteed to produce a point outside the trapezium.
		%
		\advance\pgf@xc2.0\pgf@x%
		\pgf@yc\halfheight\relax%
		\multiply\pgf@yc2\relax%
		\advance\pgf@yc2.0\pgf@x%
		\ifdim\pgf@xc<\pgf@yc%
			\edef\externalradius{\the\pgf@yc}%
		\else%
			\edef\externalradius{\the\pgf@xc}%
		\fi%
		%
		% Calculate the centre base and mid poins of the node.
		%
		\pgfextract@process\centerpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y.5\ht\pgfnodeparttextbox%
			\advance\pgf@y-.5\dp\pgfnodeparttextbox%
		}%
		\pgfextract@process\basepoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y0pt\relax%
		}%
		\pgfextract@process\midpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgfmathsetlength\pgf@y{+.5ex}%
		}%
		%
		% Calculate each point on the trapezium (without rotation).
		%
		\pgfextract@process\lowerleftpoint{%
			\centerpoint%
			\advance\pgf@x-\halfwidth\relax%
			\ifdim\leftextension>0pt\relax%
				\advance\pgf@x-\leftextension\relax%
			\fi%
			\advance\pgf@y-\halfheight\relax%
		}%
		\pgfextract@process\upperleftpoint{%
			\centerpoint%
			\advance\pgf@x-\halfwidth\relax%
			\ifdim\leftextension<0pt\relax%
				\advance\pgf@x\leftextension\relax%
			\fi%
			\advance\pgf@y\halfheight\relax%
		}%
		\pgfextract@process\upperrightpoint{%
			\centerpoint%
			\advance\pgf@x\halfwidth\relax%
			\ifdim\rightextension<0pt\relax%
				\advance\pgf@x-\rightextension\relax%
			\fi%
			\advance\pgf@y\halfheight\relax%
		}%
		\pgfextract@process\lowerrightpoint{%
			\centerpoint%
			\advance\pgf@x\halfwidth\relax%
			\ifdim\rightextension>0pt\relax%
				\advance\pgf@x\rightextension\relax%
			\fi%
			\advance\pgf@y-\halfheight\relax%
		}%
		%
		% Now calculate the adjustment for the miter length at each corner 
		% of the trapezium. This ensures more accurate anchor positioning
		% when the line width is particularly thick.
		%
		\pgfextract@process\lowerleftmiter{%
			\pgfmathanglebetweenlines{\lowerleftpoint}{\lowerrightpoint}{\lowerleftpoint}{\upperleftpoint}%
			\pgfmathmultiply@{\pgfmathresult}{.5}%
			\pgfmathtan@{\pgfmathresult}%	
			\pgfmathreciprocal@{\pgfmathresult}%
			\pgf@x-\outersep\relax%
			\pgf@x\pgfmathresult\pgf@x%
			\pgf@y-\outersep\relax%
		}%
		\pgfextract@process\upperleftmiter{%
			\pgfmathanglebetweenlines{\upperleftpoint}{\lowerleftpoint}{\upperleftpoint}{\upperrightpoint}%
			\pgfmathmultiply@{\pgfmathresult}{.5}%
			\pgfmathtan@{\pgfmathresult}%
			\pgfmathreciprocal@{\pgfmathresult}%
			\pgf@x-\outersep\relax%
			\pgf@x\pgfmathresult\pgf@x%
			\pgf@y\outersep\relax%
		}%
		\pgfextract@process\upperrightmiter{%
			\pgfmathanglebetweenlines{\upperrightpoint}{\upperleftpoint}{\upperrightpoint}{\lowerrightpoint}%
			\pgfmathmultiply@{\pgfmathresult}{.5}%
			\pgfmathtan@{\pgfmathresult}%
			\pgfmathreciprocal@{\pgfmathresult}%
			\pgf@x\outersep\relax%
			\pgf@x\pgfmathresult\pgf@x%
			\pgf@y\outersep\relax%
		}%
		\pgfextract@process\lowerrightmiter{%
			\pgfmathanglebetweenlines{\lowerrightpoint}{\upperrightpoint}{\lowerrightpoint}{\lowerleftpoint}%
			\pgfmathmultiply@{\pgfmathresult}{.5}%
			\pgfmathtan@{\pgfmathresult}%
			\pgfmathreciprocal@{\pgfmathresult}%
			\pgf@x\outersep\relax%
			\pgf@x\pgfmathresult\pgf@x%
			\pgf@y-\outersep\relax%
		}%
		%
		% Now calculate the corners for determining anchor border
		% points, by adding the adjustment for the miter length.
		%
		\pgfextract@process\lowerleftborderpoint{%
			\pgfpointadd{\lowerleftpoint}{\lowerleftmiter}%
		}%
		\pgfextract@process\upperleftborderpoint{%
			\pgfpointadd{\upperleftpoint}{\upperleftmiter}%
		}%
		\pgfextract@process\upperrightborderpoint{%
			\pgfpointadd{\upperrightpoint}{\upperrightmiter}%
		}%
		\pgfextract@process\lowerrightborderpoint{%
			\pgfpointadd{\lowerrightpoint}{\lowerrightmiter}%
		}%
		%
		% Calulate the angle from the centerpoint to each corner.
		% Rotation is not important here (see \anchorborder code).
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\lowerleftborderpoint}%
		\let\angletolowerleft\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\upperleftborderpoint}%
		\let\angletoupperleft\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\upperrightborderpoint}%
		\let\angletoupperright\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\lowerrightborderpoint}%
		\let\angletolowerright\pgfmathresult%
		%
		% Do the same for the *inversely rotated* base point...
		%
		\pgfextract@process\rotatedbasepoint{%
			\pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\lowerleftborderpoint}%
		\let\baseangletolowerleft\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\upperleftborderpoint}%
		\let\baseangletoupperleft\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\upperrightborderpoint}%
		\let\baseangletoupperright\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\lowerrightborderpoint}%
		\let\baseangletolowerright\pgfmathresult%
		%
		% And the *inversely rotated* mid point...
		%
		\pgfextract@process\rotatedmidpoint{%
			\pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\lowerleftborderpoint}%
		\let\midangletolowerleft\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\upperleftborderpoint}%
		\let\midangletoupperleft\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\upperrightborderpoint}%
		\let\midangletoupperright\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\lowerrightborderpoint}%
		\let\midangletolowerright\pgfmathresult%
		%
		% Now rotate the border points around the centerpoint...
		%
		\pgfextract@process\lowerleftborderpoint{%
			\pgfmathrotatepointaround%
				{\lowerleftborderpoint}%
				{\centerpoint}%
				{\rotate}%
		}%
		\pgfextract@process\upperleftborderpoint{%
			\pgfmathrotatepointaround%
				{\upperleftborderpoint}%
				{\centerpoint}%
				{\rotate}%
		}%
		\pgfextract@process\upperrightborderpoint{%
			\pgfmathrotatepointaround%
				{\upperrightborderpoint}%
				{\centerpoint}%
				{\rotate}%
		}%
		\pgfextract@process\lowerrightborderpoint{%
			\pgfmathrotatepointaround%
				{\lowerrightborderpoint}%
				{\centerpoint}%
				{\rotate}%
		}%
		%
		% ...and the points for drawing the border (i.e. no outer sep).
		%
		\pgfextract@process\lowerleftpoint{%
			\pgfmathrotatepointaround{\lowerleftpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\upperleftpoint{%
			\pgfmathrotatepointaround{\upperleftpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\upperrightpoint{%
			\pgfmathrotatepointaround{\upperrightpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\lowerrightpoint{%
			\pgfmathrotatepointaround{\lowerrightpoint}{\centerpoint}{\rotate}%
		}%			
		%
		% And finally, save all the relevant stuff.
		%
		\addtosavedmacro{\lowerleftpoint}%
		\addtosavedmacro{\upperleftpoint}%
		\addtosavedmacro{\upperrightpoint}%
		\addtosavedmacro{\lowerrightpoint}%
    %
		\addtosavedmacro{\lowerleftborderpoint}%
		\addtosavedmacro{\upperleftborderpoint}%
		\addtosavedmacro{\upperrightborderpoint}%
		\addtosavedmacro{\lowerrightborderpoint}%
    %
		\addtosavedmacro{\angletolowerleft}%
		\addtosavedmacro{\angletoupperleft}%
		\addtosavedmacro{\angletoupperright}%
		\addtosavedmacro{\angletolowerright}%
		%
		\addtosavedmacro{\baseangletolowerleft}%
		\addtosavedmacro{\baseangletoupperleft}%
		\addtosavedmacro{\baseangletoupperright}%
		\addtosavedmacro{\baseangletolowerright}%
		%
		\addtosavedmacro{\midangletolowerleft}%
		\addtosavedmacro{\midangletoupperleft}%
		\addtosavedmacro{\midangletoupperright}%
		\addtosavedmacro{\midangletolowerright}%
    %
    \addtosavedmacro{\rotate}%
    \addtosavedmacro{\externalradius}%
	}
	\savedanchor\centerpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor\basepoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y0pt\relax%
	}%
	\savedanchor\midpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%
	\anchor{center}{\centerpoint}%
	\anchor{base}{\basepoint}%
	\anchor{base east}{%
		\installtrapeziumparameters%
		\let\pgf@trapeziumanchorborderreferencepoint\basepoint%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{base west}{%
		\installtrapeziumparameters%
		\let\pgf@trapeziumanchorborderreferencepoint\basepoint%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{mid}{\midpoint}%
	\anchor{mid east}{%
		\installtrapeziumparameters%
		\let\pgf@trapeziumanchorborderreferencepoint\midpoint%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{mid west}{%
		\installtrapeziumparameters%
		\let\pgf@trapeziumanchorborderreferencepoint\midpoint%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{north}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{0pt}{\externalradius}}%
	}
	\anchor{south}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}%
	}
	\anchor{east}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{west}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}
	\anchor{north east}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}%
	}
	\anchor{south west}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}%
	}
	\anchor{south east}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}%
	}
	\anchor{north west}{%
		\installtrapeziumparameters%
		\csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}%
	}
	\anchor{bottom left corner}{%
		\installtrapeziumparameters%
		\lowerleftborderpoint%
	}%
	\anchor{top left corner}{%
		\installtrapeziumparameters%
		\upperleftborderpoint%
	}%
	\anchor{top right corner}{%
		\installtrapeziumparameters%
		\upperrightborderpoint%
	}%
	\anchor{bottom right corner}{%
		\installtrapeziumparameters%
		\lowerrightborderpoint%
	}%	
	\anchor{left side}{%
		\installtrapeziumparameters%
		\pgfpointlineattime{0.5}{\lowerleftborderpoint}{\upperleftborderpoint}%
	}%	
	\anchor{right side}{%
		\installtrapeziumparameters%
		\pgfpointlineattime{0.5}{\lowerrightborderpoint}{\upperrightborderpoint}%
	}%	
	\anchor{top side}{%
		\installtrapeziumparameters%
		\pgfpointlineattime{0.5}{\upperleftborderpoint}{\upperrightborderpoint}%
	}%	
	\anchor{bottom side}{%
		\installtrapeziumparameters%
		\pgfpointlineattime{0.5}{\lowerleftborderpoint}{\lowerrightborderpoint}%
	}%		
	\backgroundpath{%
		\installtrapeziumparameters%
		\pgfpathmoveto{\lowerleftpoint}%
		\pgfpathlineto{\upperleftpoint}%
		\pgfpathlineto{\upperrightpoint}%
		\pgfpathlineto{\lowerrightpoint}%
		\pgfpathclose%			
	}
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% This allows anchors base east, base west, mid east and mid west,
		% to redefine the `center' of the node to correctly calculate the
		% border points.
		%
		\pgfutil@ifundefined{pgf@trapeziumanchorborderreferencepoint}%
			{\let\referencepoint\centerpoint}%
			{\let\referencepoint\pgf@trapeziumanchorborderreferencepoint}%
		%
		% Adjust the location of the external 
		% point relative to the reference point.
		%
		\referencepoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Install the required points and angles.
		%
		\installtrapeziumparameters%
		%
		% Get the angle of the external point to the \referencepoint.
		%
		\pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
		%
		% *Subtract* the rotation from the external angle. This is 
		% why the border point angles do not neeed to be rotated.
		%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		%
		% Get the relevant angles for the reference point.
		%
		\let\externalangle\pgfmathresult%
		\ifx\referencepoint\basepoint%
			\let\angletoupperright\baseangletoupperright%
			\let\angletoupperleft\baseangletoupperleft%
			\let\angletolowerright\baseangletolowerright%
			\let\angletolowerleft\baseangletolowerleft%
		\else%
			\ifx\referencepoint\midpoint%
				\let\angletoupperright\midangletoupperright%
				\let\angletoupperleft\midangletoupperleft%
				\let\angletolowerright\midangletolowerright%
				\let\angletolowerleft\midangletolowerleft%
		\fi\fi%
		%
		% Find the line on the border...
		%			
		\ifdim\externalangle pt<\angletoupperright pt\relax%
			\let\firstpoint\upperrightborderpoint%
			\let\secondpoint\lowerrightborderpoint%
		\else%
			\ifdim\externalangle pt<\angletoupperleft pt\relax%
				\let\firstpoint\upperleftborderpoint%
				\let\secondpoint\upperrightborderpoint%
			\else%
				\ifdim\externalangle pt<\angletolowerleft pt\relax%
					\let\firstpoint\upperleftborderpoint%
					\let\secondpoint\lowerleftborderpoint%
				\else%
					\ifdim\externalangle pt<\angletolowerright pt\relax%
						\let\firstpoint\lowerleftborderpoint%
						\let\secondpoint\lowerrightborderpoint%
					\else%
						\let\firstpoint\upperrightborderpoint%
						\let\secondpoint\lowerrightborderpoint%
					\fi%
				\fi%
			\fi%
		\fi%
		%
		% ...and thus the point on the border.
		%
		\pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\firstpoint}{\secondpoint}%
	}%
}




% Shape semicircle.
%
\pgfdeclareshape{semicircle}{
	\savedmacro\installsemicircleparameters{%
		%
		% Get the larger of the outer sep.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@x<\pgf@y%
			\pgf@x\pgf@y%
		\fi%
		\edef\outersep{\the\pgf@x}%
		%
		% Get the node dimensions.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x+.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y+.5\ht\pgfnodeparttextbox%
		\advance\pgf@y+.5\dp\pgfnodeparttextbox%
		%
		% Use the radius of the incircle if required...
		%
		\ifpgfshapeborderusesincircle%
			%
			% Get the rotation (no rounding).
			%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\fi%			
			\pgf@x1.41421\pgf@x%
			\edef\halfheight{\the\pgf@x}%
			\advance\pgf@x\pgf@x%
		\else%
			%
			% Get the rotation (with rounding).
			%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\afterassignment\pgfmath@gobbletilpgfmath@%
			\expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\ifnum\c@pgf@counta<0\relax%
				\advance\c@pgf@counta360\relax%
			\fi%
			\edef\rotate{\the\c@pgf@counta}%
			%
			% Calculate the width and height of the node
			% contents, according to any border rotation.
			%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xc\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xc%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xc\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xc%
				\fi%
			\fi%
			\advance\pgf@y\pgf@y%
			\pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}%
			\pgf@x\pgfmathresult pt\relax%
			\pgf@y.5\pgf@y%
			\edef\halfheight{\the\pgf@y}%
		\fi%
		\edef\defaultradius{\the\pgf@x}%
		%
		% Take into account minimum height and width.
		%
		\pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}%
		\ifdim\pgf@x<.5\pgf@xa%
			\pgf@x.5\pgf@xa%
		\fi%
		\pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@x<\pgf@ya%
			\pgf@x\pgf@ya%
		\fi%
		\edef\semicircleradius{\the\pgf@x}%
		%
		% Find the center/base/mid of the semi circle node.
		%		
		\pgfextract@process\centerpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y.5\ht\pgfnodeparttextbox%
			\advance\pgf@y+-.5\dp\pgfnodeparttextbox%
		}%
		\pgfextract@process\basepoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y0pt\relax%
		}%
		\pgfextract@process\midpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgfmathsetlength\pgf@y{+.5ex}%
		}%
		\pgfextract@process\semicirclecenterpoint{%
			\centerpoint%
			\pgf@ya\semicircleradius\relax%
			\advance\pgf@ya-\defaultradius\relax%
			%
			% The point is adjusted to make the node contents
			% appear more centered if the node is enlarged to
			% some minimum size. The factor .4 just seems OK.
			%
			\pgf@ya.4\pgf@ya% 
			\advance\pgf@y-\pgf@ya%
			\pgf@ya\halfheight\relax%
			\advance\pgf@y-\pgf@ya%	
		}%
		%
		% Add the outer sep to the radius here.
		%
		\pgf@x\semicircleradius\relax%
		\advance\pgf@x\outersep\relax%
		\edef\semicircleradius{\the\pgf@x}%
		\pgfpointdiff{\centerpoint}{\semicirclecenterpoint}%
		\ifdim\pgf@y<0pt\pgf@y-\pgf@y\fi%
		\edef\centerpointdiff{\the\pgf@y}%
		%
		% Calculate the start and end points on the border.
		%		
		\pgfextract@process\arcstartborder{%
			\semicirclecenterpoint%
			\advance\pgf@x\semicircleradius\relax%
		}%
		\pgfextract@process\arcendborder{%
			\semicirclecenterpoint%
			\advance\pgf@x-\semicircleradius\relax%
		}%
		%
		% Calculate the start and end *corner* points on the border.
		% This is needed to accommodate the outer sep.
		%
		\pgfextract@process\arcstartcorner{%
			\arcstartborder%
			\advance\pgf@y-\outersep\relax%
		}%
		\pgfextract@process\arcendcorner{%
			\arcendborder%
			\advance\pgf@y-\outersep\relax%
		}
		%
		% Now calculate all the relevant angles.
		%
		% For the center point.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcstartborder}%
		\let\angletoarcstartborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcendborder}%
		\let\angletoarcendborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcstartcorner}%
		\let\angletoarcstartcorner\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcendcorner}%
		\let\angletoarcendcorner\pgfmathresult%
		%
		% For the basepoint (rotated about the center point).
		%
		\pgfextract@process\rotatedbasepoint{%
			\pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcstartborder}%
		\let\baseangletoarcstartborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcendborder}%
		\let\baseangletoarcendborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcstartcorner}%
		\let\baseangletoarcstartcorner\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcendcorner}%
		\let\baseangletoarcendcorner\pgfmathresult%
		%
		% For the midpoint (rotated about the center point).
		%
		\pgfextract@process\rotatedmidpoint{%
			\pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcstartborder}%
		\let\midangletoarcstartborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcendborder}%
		\let\midangletoarcendborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcstartcorner}%
		\let\midangletoarcstartcorner\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcendcorner}%
		\let\midangletoarcendcorner\pgfmathresult%
		%
		% Now, rotate the semicircle points around the centerpoint.
		%
		\pgfextract@process\semicirclecenterpoint{%
			\pgfmathrotatepointaround{\semicirclecenterpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcstartborder{%
			\pgfmathrotatepointaround{\arcstartborder}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcendborder{%
			\pgfmathrotatepointaround{\arcendborder}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcstartcorner{%
			\pgfmathrotatepointaround{\arcstartcorner}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcendcorner{%
			\pgfmathrotatepointaround{\arcendcorner}{\centerpoint}{\rotate}%
		}%
		%
		% Calculate the distance between the base point and the (rotated) semicircle center.
		%
		\pgfpointdiff{\basepoint}{\semicirclecenterpoint}%
		\pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}%
		\edef\basesemicirclecenterdiff{\pgfmathresult pt}%
		%
		% Calculate the distance between the base point and the (rotated) semicircle center.
		%
		\pgfpointdiff{\midpoint}{\semicirclecenterpoint}%
		\pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}%
		\edef\midsemicirclecenterdiff{\pgfmathresult pt}%
		%
		% And save all the stuff.
		%
		\addtosavedmacro{\rotate}%
		\addtosavedmacro{\outersep}%
		\addtosavedmacro{\semicircleradius}%
		%
		\addtosavedmacro{\arcstartborder}%
		\addtosavedmacro{\arcendborder}%
		\addtosavedmacro{\arcstartcorner}%
		\addtosavedmacro{\arcendcorner}%
		\addtosavedmacro{\semicirclecenterpoint}%
		%
		\addtosavedmacro{\angletoarcstartborder}%
		\addtosavedmacro{\angletoarcendborder}%
		\addtosavedmacro{\angletoarcstartcorner}%
		\addtosavedmacro{\angletoarcendcorner}%
		%
		\addtosavedmacro{\centerpointdiff}%
		\addtosavedmacro{\basesemicirclecenterdiff}%
		\addtosavedmacro{\midsemicirclecenterdiff}%
		%
		\addtosavedmacro{\baseangletoarcstartborder}%
		\addtosavedmacro{\baseangletoarcendborder}%
		\addtosavedmacro{\baseangletoarcstartcorner}%
		\addtosavedmacro{\baseangletoarcendcorner}%
		%
		\addtosavedmacro{\midangletoarcstartborder}%
		\addtosavedmacro{\midangletoarcendborder}%
		\addtosavedmacro{\midangletoarcstartcorner}%
		\addtosavedmacro{\midangletoarcendcorner}%
	}
	\savedanchor{\centerpoint}{%
		\pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}%
		\pgfmathsetlength\pgf@y{+.5\ht\pgfnodeparttextbox}%
		\pgfmathaddtolength\pgf@y{-.5\dp\pgfnodeparttextbox}%	
	}
	\savedanchor{\basepoint}{%
		\pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}%
		\pgf@y0pt\relax%
	}
	\savedanchor{\midpoint}{%
		\pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}
	\anchor{center}{\centerpoint}
	\anchor{base}{\basepoint}
	\anchor{base west}{%
		\installsemicircleparameters%
		\let\pgf@semicirclereferencepoint\basepoint%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{-\semicircleradius}{0pt}}%
	}
	\anchor{base east}{%
		\installsemicircleparameters%
		\let\pgf@semicirclereferencepoint\basepoint%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{\semicircleradius}{0pt}}%
	}
	\anchor{mid}{\midpoint}
	\anchor{mid west}{%
		\installsemicircleparameters%
		\let\pgf@semicirclereferencepoint\midpoint%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{-\semicircleradius}{0pt}}%
	}
	\anchor{mid east}{%
		\installsemicircleparameters%
		\let\pgf@semicirclereferencepoint\midpoint%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{\semicircleradius}{0pt}}%
	}
	\anchor{apex}{%
		\installsemicircleparameters%
		\pgfmathadd@{\rotate}{90}%
		\let\angle\pgfmathresult%
		\pgfpointadd{\semicirclecenterpoint}{\pgfqpointpolar{\angle}{\semicircleradius}}%
	}
	\anchor{arc start}{%
		\installsemicircleparameters%
		\arcstartcorner%
	}
	\anchor{arc end}{%
		\installsemicircleparameters%
		\arcendcorner%
	}
	\anchor{chord center}{%
		\installsemicircleparameters%
		\pgfpointlineattime{0.5}{\arcstartcorner}{\arcendcorner}%
	}
	\anchor{north}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{90}{\semicircleradius}}%
	}
	\anchor{south}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{270}{\semicircleradius}}%
	}
	\anchor{east}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{0}{\semicircleradius}}%
	}
	\anchor{west}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{180}{\semicircleradius}}%
	}
	\anchor{north west}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{135}{\semicircleradius}}%
	}
	\anchor{south west}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{225}{\semicircleradius}}%
	}
	\anchor{north east}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{45}{\semicircleradius}}%
	}
	\anchor{south east}{%
		\installsemicircleparameters%
		\csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{315}{\semicircleradius}}%
	}
	\backgroundpath{%
		\installsemicircleparameters%
		\pgf@x\semicircleradius\relax%
		\advance\pgf@x-\outersep\relax%
		\edef\semicircleradius{\the\pgf@x}%
		\pgfpathmoveto{\pgfpointadd{\semicirclecenterpoint}{\pgfqpointpolar{\rotate}{\semicircleradius}}}%
		{%
			\pgftransformrotate{\rotate}%
			\pgfpatharc{0}{180}{\semicircleradius}%
			\pgfpathclose%	
		}%
	}
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% Check if a reference point has been defined (i.e. \midpoint or \basepoint).
		%
		\pgfutil@ifundefined{pgf@semicirclereferencepoint}%
			{\let\referencepoint\centerpoint}%
			{\let\referencepoint\pgf@semicirclereferencepoint}%
		%
		% Adjust the location of the external  point relative to the reference point.
		%
		\referencepoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Install the required points and angles.
		%
		\installsemicircleparameters%
		%
		% Get the angle of the external point to the \referencepoint.
		%
		\pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
		\let\externalangle\pgfmathresult%
		%
		% *Subtract* the rotation from the external angle.
		%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\angle\pgfmathresult%
		\ifx\referencepoint\basepoint%
			\let\angletoarcstartborder\baseangletoarcstartborder%
			\let\angletoarcendborder\baseangletoarcendborder%
			\let\angletoarcstartcorner\baseangletoarcstartcorner%
			\let\angletoarcendcorner\baseangletoarcendcorner%
			\let\centerpointdiff\basesemicirclecenterdiff%
		\else%
			\ifx\referencepoint\midpoint%
				\let\angletoarcstartborder\midangletoarcstartborder%
				\let\angletoarcendborder\midangletoarcendborder%
				\let\angletoarcstartcorner\midangletoarcstartcorner%
				\let\angletoarcendcorner\midangletoarcendcorner%
				\let\centerpointdiff\midsemicirclecenterdiff%
		\fi\fi%
		%
		% Determine if the line will cross the semicircle arc, or the chord.
		% 
		\ifdim\angle pt>\angletoarcstartborder pt\relax%
			\let\firstpoint\pgfutil@empty%
			\let\secondpoint\pgfutil@empty%
		\else%
			\ifdim\angle pt>\angletoarcstartcorner pt\relax%
				\let\firstpoint\arcstartcorner%
				\let\secondpoint\arcstartborder%
			\else%
				\ifdim\angle pt>\angletoarcendcorner pt\relax%
					\let\firstpoint\arcendcorner%
					\let\secondpoint\arcstartcorner%
				\else%
					\ifdim\angle pt>\angletoarcendborder pt\relax%
						\let\firstpoint\arcendborder%
						\let\secondpoint\arcendcorner%
					\else%
						\let\firstpoint\pgfutil@empty%
						\let\secondpoint\pgfutil@empty%
					\fi%
				\fi%
			\fi%
		\fi%
		\ifx\firstpoint\pgfutil@empty
			%
			% Calculate the angle from the centre of the semicircle to the
			% point on the semicircle arc which intersects the line from 
			% the external point to the reference point...
			%
			\pgfmathanglebetweenlines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\semicirclecenterpoint}{\referencepoint}%
			\pgfmathsin@{\pgfmathresult}%
			\let\sineangle\pgfmathresult%
			\pgf@x\semicircleradius\relax%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@x}}%
			\let\reciprocalradius\pgfmathresult%
			\pgf@x\centerpointdiff\relax%
			\pgf@x\sineangle\pgf@x%
			\pgf@x\reciprocalradius\pgf@x%
			\pgfmathasin@{\pgfmath@tonumber{\pgf@x}}%
			\pgf@x\pgfmathresult pt\relax%
			\advance\pgf@x\externalangle pt\relax%
			\edef\angle{\pgfmath@tonumber{\pgf@x}}%
			%
			% ...and thus the point on the border.
			%
			\pgfpointadd{\semicirclecenterpoint}{\pgfqpointpolar{\angle}{\semicircleradius}}%
		\else%
			%
			% Calculate the the point where the semicircle chord intersects 
			% the line from the external point to the reference point.
			%
			\pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\firstpoint}{\secondpoint}%
		\fi%
	}		
}


% Keys for shape isosceles triangle
%
% /pgf/isosceles triangle apex angle : angle at the apex of the triangle.
\pgfkeys{/pgf/.cd,
	isosceles triangle apex angle/.initial=45,
	isosceles triangle stretches/.is if=pgf@lib@sh@isosceslestrianglestretches
}
\newif\ifpgf@lib@sh@isosceslestrianglestretches

\pgfdeclareshape{isosceles triangle}{
	\savedmacro\trianglepoints{%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/isosceles triangle apex angle}}%
		\divide\pgf@x2\relax%
		\edef\halfapexangle{\pgfmath@tonumber{\pgf@x}}%
		\addtosavedmacro\halfapexangle%
		%
		\pgfmathtan@{\halfapexangle}%
		\let\tanhalfapexangle\pgfmathresult%
		%
		\pgfmathcot@{\halfapexangle}%
		\let\cothalfapexangle\pgfmathresult%
		%
		\pgfmathsin@{\halfapexangle}%
		\let\sinhalfapexangle\pgfmathresult%
		%
		\pgfmathreciprocal@{\pgfmathresult}%
		\let\cosechalfapexangle\pgfmathresult%
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		%
		\ifpgfshapeborderusesincircle%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\else%
				\pgf@y\pgf@x%
			\fi%
			\pgf@x1.414213\pgf@x%
			\pgf@y1.414213\pgf@y%
			%
			\pgf@xa\pgf@x%
			\advance\pgf@xa\cosechalfapexangle\pgf@x%
			\pgf@ya\tanhalfapexangle\pgf@xa%
		\else%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\ifdim\pgfmathresult pt<0pt\relax%
				\pgfmathadd@{\pgfmathresult}{360}%
			\fi%
			\pgfmathsetcount\c@pgf@counta{+\pgfmathresult}%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\edef\rotate{\the\c@pgf@counta}%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xa\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xa%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xa\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xa%
				\fi%
			\fi%
			%
			\pgf@xa2.0\pgf@x%
			\pgf@ya\tanhalfapexangle\pgf@xa%
			\advance\pgf@xa\cothalfapexangle\pgf@y%
			\advance\pgf@ya\pgf@y%			
		\fi%
		\addtosavedmacro\rotate%
		\ifdim\pgf@xa=0pt\relax%
			\pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum height}}%
		\fi%
		% Adjust for minimum height and width.
		%
		\pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum width}}%
		\ifdim\pgf@ya<.5\pgf@yb%
			\ifpgf@lib@sh@isosceslestrianglestretches%
				\pgf@ya.5\pgf@yb%
				%
				\pgfmathdivide@{\pgfmath@tonumber{\pgf@ya}}{\pgfmath@tonumber{\pgf@xa}}%
				\pgfmathatan@{\pgfmathresult}%
				\let\halfapexangle\pgfmathresult%
				%				
			\else%
				\pgf@ya.5\pgf@yb%
				\pgf@xa\cothalfapexangle\pgf@ya%
			\fi%
		\fi%
		%
		\pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@xa<\pgf@xb%
			\ifpgf@lib@sh@isosceslestrianglestretches%
				\pgf@xa\pgf@xb%
				%
				\pgfmathdivide@{\pgfmath@tonumber{\pgf@ya}}{\pgfmath@tonumber{\pgf@xa}}%
				\pgfmathatan@{\pgfmathresult}%
				\let\halfapexangle\pgfmathresult%
				%		
			\else%
				\pgf@xa\pgf@xb%
				\pgf@ya\tanhalfapexangle\pgf@xa%
			\fi%
		\fi%
		%
		%
		% Now find the ``offset height'' (h'). This is the distance from the
		% center of the node contents to the base of the triangle. 
		%
		\ifpgfshapeborderusesincircle%
			%
			% h' = H*sin(a/2) / (1+sin(a/2))
			%
			% where:
			%   H = the height of the triangle.
			%   a = the apex angle.
			%
			\pgf@xc\pgf@xa%
			\pgfmathsin@{\halfapexangle}%
			\pgf@xc\pgfmathresult\pgf@xc%
			\pgf@yc1pt\relax%
			\advance\pgf@yc\pgfmathresult pt\relax%
			\pgfmathdivide@{\pgfmath@tonumber{\pgf@xc}}{\pgfmath@tonumber{\pgf@yc}}
			\pgfutil@tempdima\pgfmathresult pt\relax%
		\else%
			%
			% h' = 0.5*h + (0.5*(W-w)*cos(a/2) - h*sin(a/2))/(1+sin(a/2))
			%
			% where:
			%   h = the height of the node contents.
			%   w = the width of the node contents.
			%   W = the width of the triangle.
			%   a = the apex angle.
			%
			\pgf@xc\pgf@ya%
			\advance\pgf@xc-\pgf@y%
			\pgfmathcos@{\halfapexangle}%
			\pgf@xc\pgfmathresult\pgf@xc%
			\pgfmathsin@{\halfapexangle}%
			\advance\pgf@xc-\pgfmathresult\pgf@x%
			\advance\pgf@xc-\pgfmathresult\pgf@x%
			\pgf@yc\pgfmathresult pt\relax%
			\advance\pgf@yc1pt\relax%
			\pgfmathdivide@{\pgfmath@tonumber{\pgf@xc}}{\pgfmath@tonumber{\pgf@yc}}%
			\pgfutil@tempdima\pgfmathresult pt\relax%
			\advance\pgfutil@tempdima\pgf@x%	
		\fi%
		\pgfextract@process\apex{%
			\pgf@y0pt%
			\pgf@x\pgf@xa%
			\advance\pgf@x-\pgfutil@tempdima%
		}%
		\addtosavedmacro\apex%
		%
		\pgfextract@process\lowerleft{%
			\pgf@y\pgf@ya%
			\pgf@x-\pgfutil@tempdima%
		}%
		\addtosavedmacro\lowerleft%
		%
		\pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@xb<\pgf@yb%
			\pgf@xb\pgf@yb%
		\fi%
		\pgfextract@process\apexanchor{%
			\apex%
			\advance\pgf@x\cosechalfapexangle\pgf@xb%
		}%
		\addtosavedmacro\apexanchor%
		%
		\pgf@yc-\halfapexangle pt\relax%
		\advance\pgf@yc90pt\relax%
		\divide\pgf@yc2\relax%
		\pgfmathcot@{\pgfmath@tonumber{\pgf@yc}}%
		\pgfextract@process\lowerleftanchor{%
			\lowerleft%
			\advance\pgf@y\pgfmathresult\pgf@xb%
			\advance\pgf@x-\pgf@xb%
		}%
		\addtosavedmacro\lowerleftanchor%	
		%
		\pgfextract@process\lowerrightanchor{%
			\lowerleftanchor%
			\pgf@y-\pgf@y%
		}%	
		\addtosavedmacro\lowerrightanchor%	
	}
	\anchor{apex}{%
		\trianglepoints%
		\pgfpointadd{\centerpoint}{%
			\pgfmathrotatepointaround{\apexanchor}{\pgfpointorigin}{\rotate}%
		}%
	}%
	\anchor{left corner}{%
		\trianglepoints%
		\pgfpointadd{\centerpoint}{%
			\pgfmathrotatepointaround{\lowerleftanchor}{\pgfpointorigin}{\rotate}%
		}%
	}%
	\anchor{right corner}{%
		\trianglepoints%
		\pgfpointadd{\centerpoint}{%
			\pgfmathrotatepointaround{\lowerrightanchor}{\pgfpointorigin}{\rotate}%
		}%
	}%
	\savedanchor\centerpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor\midpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%
	\savedanchor\basepoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y0pt%
	}%
	\anchor{center}{\centerpoint}%
	\anchor{mid}{\midpoint}%
	\anchor{mid west}{%
		\trianglepoints%
		\let\pgf@isoscelestriangle@referencepoint\midpoint%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{0pt}}%
	}%
	\anchor{mid east}{%
		\trianglepoints%
		\let\pgf@isoscelestriangle@referencepoint\midpoint%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{0pt}}%
	}%
	\anchor{base}{\basepoint}%
	\anchor{base west}{%
		\trianglepoints%
		\let\pgf@isoscelestriangle@referencepoint\basepoint%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{0pt}}%
	}%
	\anchor{base east}{%
		\trianglepoints%
		\let\pgf@isoscelestriangle@referencepoint\basepoint%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{0pt}}%
	}%
	\anchor{north}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{0pt}{1pt}}%
	}
	\anchor{south}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{0pt}{-1pt}}%
	}
	\anchor{east}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{0pt}}%
	}
	\anchor{west}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{0pt}}%
	}
	\anchor{north east}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{1pt}}%
	}
	\anchor{south west}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{-1pt}}%
	}
	\anchor{south east}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{-1pt}}%
	}
	\anchor{north west}{%
		\trianglepoints%
		\csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{1pt}}%
	}
	\anchor{left side}{%
		\trianglepoints%
		\pgfmathrotatepointaround{%
			\pgfpointadd{\pgfpointlineattime{0.5}{\lowerleftanchor}{\apexanchor}}{\centerpoint}}%
				{\centerpoint}{\rotate}%
	}
	\anchor{right side}{%
		\trianglepoints%
		\pgfmathrotatepointaround{%
			\pgfpointadd{\pgfpointlineattime{0.5}{\lowerrightanchor}{\apexanchor}}{\centerpoint}}%
				{\centerpoint}{\rotate}%
	}
	\anchor{lower side}{%
		\trianglepoints%
		\pgfmathrotatepointaround{%
			\pgfpointadd{\pgfpointlineattime{0.5}{\lowerleftanchor}{\lowerrightanchor}}{\centerpoint}}%
				{\centerpoint}{\rotate}%
	}
	\backgroundpath{%
		\trianglepoints%
		{%
			\pgftransformshift{\centerpoint}%
			\pgftransformrotate{\rotate}%
			\pgfpathmoveto{\apex}%
			\pgfpathlineto{\lowerleft}%
			\pgfpathlineto{\lowerleft\pgf@y-\pgf@y}%
			\pgfpathclose%
		}%
	}
	\anchorborder{%
		\pgfutil@ifundefined{pgf@isoscelestriangle@referencepoint}{\let\referencepoint\centerpoint}%
			{\let\referencepoint\pgf@isoscelestriangle@referencepoint}%
		\pgfextract@process\externalpoint{%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\referencepoint%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%		
		\trianglepoints%
		\pgfmathanglebetweenpoints{\referencepoint}{\externalpoint}%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
			\pgfmathmod@{\pgfmathresult}{360}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\externalangle\pgfmathresult%
		%
		\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\centerpoint}{\lowerrightanchor}}%
		\ifdim\externalangle pt<\pgfmathresult pt\relax%
			\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\centerpoint}{\lowerleftanchor}}%
			\ifdim\externalangle pt<\pgfmathresult pt\relax%
				\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\centerpoint}{\apexanchor}}%
				\ifdim\externalangle pt>\pgfmathresult pt\relax%
					\let\firstpoint\apexanchor%
					\let\secondpoint\lowerleftanchor%
				\else%
					\let\firstpoint\apexanchor%
					\let\secondpoint\lowerrightanchor%
				\fi%
			\else%
				\let\firstpoint\lowerleftanchor%
				\let\secondpoint\lowerrightanchor%
			\fi%
		\else%
			\let\firstpoint\lowerrightanchor%
			\let\secondpoint\apexanchor%
		\fi%
		\pgfpointintersectionoflines{\referencepoint}{\externalpoint}%
			{\pgfmathrotatepointaround{\pgfpointadd{\centerpoint}{\firstpoint}}{\centerpoint}{\rotate}}%
			{\pgfmathrotatepointaround{\pgfpointadd{\centerpoint}{\secondpoint}}{\centerpoint}{\rotate}}%	
	}%
}




% Keys for shape kite
%
%
\pgfkeys{/pgf/.cd,
	kite upper vertex angle/.initial=120,
	kite lower vertex angle/.initial=60,
	kite vertex angles/.code={%
		\pgfutil@in@{and}{#1}%
		\ifpgfutil@in@%
			\def\pgf@marshal##1and##2\@@{%
				\pgfkeys{/pgf/kite upper vertex angle=##1}%
				\pgfkeys{/pgf/kite lower vertex angle=##2}%
			}%
			\expandafter\pgf@marshal#1\@@%
		\else%
			\pgfkeys{/pgf/kite upper vertex angle=#1}%
			\pgfkeys{/pgf/kite lower vertex angle=#1}%
		\fi%
	}%
}

% Shape kite.
%
\pgfdeclareshape{kite}{
	\savedmacro\installkiteparameters{%
		%
		% Get the larger of the outer sep.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@x<\pgf@y%
			\pgf@x\pgf@y%
		\fi%
		\edef\outersep{\the\pgf@x}%
		%
		% Calculate the centre, base and mid points of the node.
		%
		\pgfextract@process\centerpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y.5\ht\pgfnodeparttextbox%
			\advance\pgf@y-.5\dp\pgfnodeparttextbox%
		}%
		\pgfextract@process\basepoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y0pt\relax%
		}%
		\pgfextract@process\midpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgfmathsetlength\pgf@y{+.5ex}%
		}%
		%
		% Halve the vertex angles.
		%
		\pgfmathdivide{\pgfkeysvalueof{/pgf/kite upper vertex angle}}{2}%
		\let\halfuppervertexangle\pgfmathresult%
		\pgfmathdivide{\pgfkeysvalueof{/pgf/kite lower vertex angle}}{2}%
		\let\halflowervertexangle\pgfmathresult%
		%
		% Get the node dimensions.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		\ifpgfshapeborderusesincircle%
			%
			% Get the rotation.
			%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			%
			% Get the radis of the incircle.
			%
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\fi%			
			\pgf@x1.41421\pgf@x%
			%
			% Get the distances from the upper and lower verticies
			% to the center of the incircle.
			%
			\pgfmathsin@{\halfuppervertexangle}%
			\let\sinehalfuppervertexangle\pgfmathresult%
			\pgfmathreciprocal@{\pgfmathresult}%
			\let\cosechalfuppervertexangle\pgfmathresult%
			\pgf@ya\pgfmathresult\pgf@x%
			\pgfmathsin@{\halflowervertexangle}%
			\let\sinehalflowervertexangle\pgfmathresult%
			\pgfmathreciprocal@{\pgfmathresult}%
			\pgf@yb\pgfmathresult\pgf@x%
			%
			% Now calculate vertical offset (yc) between the center of 
			% the incircle, and the intersection of the kite diagonals.
			%
		   % yc = x * cosec(a/2) - x * cot(a/2) * (sin(a/2) + sin(b/2)) * cosec(a/2 + b/2)
		   %
		   % where:
		   %   x = the incircle radius.
		   %   a = the upper vertex angle.
		   %   b = the lower vertex angle.
		   %
		   \pgf@yc\pgf@x%
		   \pgfmathadd@{\halfuppervertexangle}{\halflowervertexangle}%
		   \pgfmathcosec@{\pgfmathresult}%
		   \pgf@yc\pgfmathresult\pgf@yc%
		   \pgfmathadd@{\sinehalfuppervertexangle}{\sinehalflowervertexangle}%
        \pgf@yc\pgfmathresult\pgf@yc%
		  	\pgfmathcos@{\halfuppervertexangle}%
		  	\pgf@yc\pgfmathresult\pgf@yc%
		  	\pgf@yc-\cosechalfuppervertexangle\pgf@yc%
		  	\advance\pgf@yc\cosechalfuppervertexangle\pgf@x%
			\edef\deltay{\the\pgf@yc}%
			%
			% Now calculate the height of the kite...
			%
			\advance\pgf@ya-\pgf@yc%
			%
			% ...and the depth.
			%
			\advance\pgf@yb\pgf@yc%
			%
			% Get the half width of the widest part of the kite.
			%
			\pgfmathtan@{\halfuppervertexangle}%
			\pgf@xa\pgfmathresult\pgf@ya%			
		\else%
			\multiply\pgf@x2\relax%
			\multiply\pgf@y2\relax%
			%
			% Get the rotation (with rounding).
			%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\afterassignment\pgfmath@gobbletilpgfmath@%
			\expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\ifnum\c@pgf@counta<0\relax%
				\advance\c@pgf@counta360\relax%
			\fi%
			\edef\rotate{\the\c@pgf@counta}%
			%
			% Calculate the width and height of the node
			% contents, according to any border rotation.
			%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xc\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xc%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xc\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xc%
				\fi%
			\fi%
			%
			% The node contents (total height y) extends a distance ya into the 
			% upper isosceles triangle of the kite and a distance yb into the 
			% lower isosceles triangle. Thus, the following relationships hold:
			%
			%   ya/yb = tan(b/2)/tan(a/2)
			%
			% and   y = ya + yb
			%
			% so   ya = y * sin(a/2 + b/2) / (cos(a/2) * sin(b/2))
			%
			% where:
			%   a = upper vertex angle.
			%   b = lower vertex angle.
			%
			\pgfmathadd@{\halfuppervertexangle}{\halflowervertexangle}%
			\pgfmathsin@{\pgfmathresult}%
			\pgfmathreciprocal@{\pgfmathresult}%
			\pgf@ya\pgfmathresult\pgf@y%
			\pgfmathcos@{\halfuppervertexangle}%
			\pgf@ya\pgfmathresult\pgf@ya%
			\pgfmathsin@{\halflowervertexangle}%
			\pgf@ya\pgfmathresult\pgf@ya%
			\pgf@yb\pgf@y%
			\advance\pgf@yb-\pgf@ya%
			%
			% The vertical offset between the center of the node, and
			% the intersection of the kite diagonals is given by:
			% 
			% yc = y/2 - ya
			%
			\pgf@yc.5\pgf@y%
			\advance\pgf@yc-\pgf@ya%
			\edef\deltay{\the\pgf@yc}%
			%
			% Get the half width of the widest part of the kite.
			%
			\pgfmathtan@{\halfuppervertexangle}%
			\pgf@xa.5\pgf@x%
			\advance\pgf@xa\pgfmathresult\pgf@ya%
			%
			% Now calculate the height of the kite...
			%
			\pgf@xb.5\pgf@x%
			\pgfmathreciprocal@{\pgfmathresult}%
			\advance\pgf@ya\pgfmathresult\pgf@xb%
			%
			% ...and the depth.
			%
			\pgfmathtan@{\halflowervertexangle}%
			\pgfmathreciprocal@{\pgfmathresult}%
			\advance\pgf@yb\pgfmathresult\pgf@xb%
		\fi%
		%
		% Take into account minimum height and width.
		%
		% ya is the kite height.
		% yb is the kite depth.
		% xa is the kite (half) width.
		%
		\pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/minimum height}}%
		\pgf@y\pgf@ya%
		\advance\pgf@y\pgf@yb%
		\ifdim\pgf@y<\pgf@yc%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}%
			\pgf@yc\pgfmathresult\pgf@yc%
			\pgf@xa\pgfmath@tonumber{\pgf@yc}\pgf@xa%
			\pgf@ya\pgfmath@tonumber{\pgf@yc}\pgf@ya%
			\pgf@yb\pgfmath@tonumber{\pgf@yc}\pgf@yb%
		\fi%
		\pgf@x2.0\pgf@xa%	
		\pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum width}}%
		\ifdim\pgf@x<\pgf@xc%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@x}}%
			\pgf@xc\pgfmathresult\pgf@xc%
			\pgf@xa\pgfmath@tonumber{\pgf@xc}\pgf@xa%
			\pgf@ya\pgfmath@tonumber{\pgf@xc}\pgf@ya%
			\pgf@yb\pgfmath@tonumber{\pgf@xc}\pgf@yb%
		\fi%
		\edef\kitehalfwidth{\the\pgf@xa}%
		\edef\kiteheight{\the\pgf@ya}%
		\edef\kitedepth{\the\pgf@yb}%
		%
		% Calculate the basic points on the kite (for the background path).
		%
		\pgfextract@process\toppoint{%
			\centerpoint%
			\advance\pgf@y\deltay\relax%
			\advance\pgf@y\kiteheight%
		}%
		\pgfextract@process\bottompoint{%
			\centerpoint%
			\advance\pgf@y\deltay\relax%
			\advance\pgf@y-\kitedepth%
		}%
		\pgfextract@process\leftpoint{%
			\centerpoint%
			\advance\pgf@y\deltay\relax%
			\advance\pgf@x-\kitehalfwidth%
		}%
		\pgfextract@process\rightpoint{%
			\centerpoint%
			\advance\pgf@y\deltay\relax%
				\advance\pgf@x\kitehalfwidth%
		}%
		%
		% Now calculate the miter length. At the top...
		%
		\pgfmathsin@{\halfuppervertexangle}%
		\pgfmathreciprocal@{\pgfmathresult}%
		\pgf@y\outersep\relax%
		\pgf@y\pgfmathresult\pgf@y%
		\edef\topmiter{\the\pgf@y}%
		%
		% ...at the bottom...
		%
		\pgfmathsin@{\halflowervertexangle}%
		\pgfmathreciprocal@{\pgfmathresult}%
		\pgf@y\outersep\relax%
		\pgf@y\pgfmathresult\pgf@y%
		\edef\bottommiter{\the\pgf@y}%
		%
		% ...to the right...
		%
		\pgfmathsubtract@{180}{\halflowervertexangle}%
		\pgfmathsubtract@{\pgfmathresult}{\halfuppervertexangle}%
		\pgfmathdivide@{\pgfmathresult}{2}%
		\pgfmathsin@{\pgfmathresult}%
		\pgfmathreciprocal@{\pgfmathresult}%
		\pgf@xa\outersep\relax%
		\pgf@xa\pgfmathresult\pgf@xa%
		\pgfmathsubtract@{\halfuppervertexangle}{\halflowervertexangle}%
		\pgfmathdivide@{\pgfmathresult}{2}%
		\let\angle\pgfmathresult%
		\pgfextract@process\rightmiter{%
			\pgfqpointpolar{\angle}{\the\pgf@xa}%
		}%
		%
		% ...and to the left.
		%
		\pgfmathsubtract@{180}{\angle}%
		\let\angle\pgfmathresult%
		\pgfextract@process\leftmiter{%
			\pgfqpointpolar{\angle}{\the\pgf@xa}%
		}%
		%
		% Create the border points.
		%
		\pgfextract@process\topborderpoint{%
			\toppoint%
			\advance\pgf@y\topmiter\relax%
		}%
		\pgfextract@process\bottomborderpoint{%
			\bottompoint%
			\advance\pgf@y-\bottommiter\relax%
		}%
		\pgfextract@process\leftborderpoint{%
			\leftpoint%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\leftmiter%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		\pgfextract@process\rightborderpoint{%
			\rightpoint%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\rightmiter%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		%
		% Get the angle from the \centerpoint to the *unrotated points*.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\topborderpoint}%
		\let\angletotoppoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\leftborderpoint}%
		\let\angletoleftpoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\bottomborderpoint}%
		\let\angletobottompoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\rightborderpoint}%
		\let\angletorightpoint\pgfmathresult%
		%
		% ...from the *inversly rotated* \basepoint...
		%
		\pgfextract@process\rotatedbasepoint{%
			\pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\topborderpoint}%
		\let\baseangletotoppoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\leftborderpoint}%
		\let\baseangletoleftpoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\bottomborderpoint}%
		\let\baseangletobottompoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\rightborderpoint}%
		\let\baseangletorightpoint\pgfmathresult%
		%
		% ...and from the *inversely rotated* \midpoint.
		%
		\pgfextract@process\rotatedmidpoint{%
			\pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\topborderpoint}%
		\let\midangletotoppoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\leftborderpoint}%
		\let\midangletoleftpoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\bottomborderpoint}%
		\let\midangletobottompoint\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\rightborderpoint}%
		\let\midangletorightpoint\pgfmathresult%
		%
		% Calculate a radius guaranteed to be outside the kite.
		%
		\pgfextractx\pgf@xa{\pgfpointdiff{\leftborderpoint}{\rightborderpoint}}%
		\ifdim\pgf@xa<0pt\relax%
			\pgf@xa-\pgf@xa%
		\fi%
		\pgfextracty\pgf@ya{\pgfpointdiff{\topborderpoint}{\bottomborderpoint}}%
		\ifdim\pgf@ya<0pt\relax%
			\pgf@ya-\pgf@ya%
		\fi%
		\ifdim\pgf@ya>\pgf@xa%
			\edef\externalradius{\the\pgf@ya}%
		\else%
			\edef\externalradius{\the\pgf@xa}%
		\fi%
		%
		% Now rotate the points...
		%
		\pgfextract@process\toppoint{%
			\pgfmathrotatepointaround{\toppoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\bottompoint{%
			\pgfmathrotatepointaround{\bottompoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\leftpoint{%
			\pgfmathrotatepointaround{\leftpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\rightpoint{%
			\pgfmathrotatepointaround{\rightpoint}{\centerpoint}{\rotate}%
		}%
		%
		% ...and the border points.
		%
		\pgfextract@process\topborderpoint{%
			\pgfmathrotatepointaround{\topborderpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\bottomborderpoint{%
			\pgfmathrotatepointaround{\bottomborderpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\leftborderpoint{%
			\pgfmathrotatepointaround{\leftborderpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\rightborderpoint{%
			\pgfmathrotatepointaround{\rightborderpoint}{\centerpoint}{\rotate}%
		}%
		%
		% Now save it all.
		%
		\addtosavedmacro{\rotate}%
		\addtosavedmacro{\externalradius}%
		%
		\addtosavedmacro\toppoint%
		\addtosavedmacro\bottompoint%
		\addtosavedmacro\leftpoint%
		\addtosavedmacro\rightpoint%
		%
		\addtosavedmacro\topborderpoint%
		\addtosavedmacro\bottomborderpoint%
		\addtosavedmacro\leftborderpoint%
		\addtosavedmacro\rightborderpoint%
		%
		\addtosavedmacro\angletotoppoint%
		\addtosavedmacro\angletobottompoint%
		\addtosavedmacro\angletoleftpoint%
		\addtosavedmacro\angletorightpoint%
		%
		\addtosavedmacro\baseangletotoppoint%
		\addtosavedmacro\baseangletobottompoint%
		\addtosavedmacro\baseangletoleftpoint%
		\addtosavedmacro\baseangletorightpoint%
		%
		\addtosavedmacro\midangletotoppoint%
		\addtosavedmacro\midangletobottompoint%
		\addtosavedmacro\midangletoleftpoint%
		\addtosavedmacro\midangletorightpoint%			
	}
	\savedanchor\centerpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor\basepoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y0pt\relax%
	}%
	\savedanchor\midpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%
	\anchor{center}{\centerpoint}%
	\anchor{base}{\basepoint}%
	\anchor{base west}{%
		\installkiteparameters%
		\let\pgf@kiteanchorborderreferencepoint\basepoint%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{base east}{%
		\installkiteparameters%
		\let\pgf@kiteanchorborderreferencepoint\basepoint%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}%
	\anchor{mid}{\midpoint}%
	\anchor{mid west}{%
		\installkiteparameters%
		\let\pgf@kiteanchorborderreferencepoint\midpoint%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{mid east}{%
		\installkiteparameters%
		\let\pgf@kiteanchorborderreferencepoint\midpoint%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}%
	\anchor{north}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{0pt}{\externalradius}}%
	}
	\anchor{south}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}%
	}
	\anchor{east}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{west}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}
	\anchor{north east}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}%
	}
	\anchor{south west}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}%
	}
	\anchor{south east}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}%
	}
	\anchor{north west}{%
		\installkiteparameters%
		\csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}%
	}
	\anchor{upper vertex}{%
		\installkiteparameters%
		\topborderpoint}
	\anchor{lower vertex}{%
		\installkiteparameters%
		\bottomborderpoint}
	\anchor{left vertex}{%
		\installkiteparameters%
		\leftborderpoint}
	\anchor{right vertex}{%
		\installkiteparameters%
		\rightborderpoint}
	\anchor{upper left side}{%
		\installkiteparameters%
		\pgfpointlineattime{0.5}{\topborderpoint}{\leftborderpoint}}
	\anchor{lower left side}{%
		\installkiteparameters%
		\pgfpointlineattime{0.5}{\bottomborderpoint}{\leftborderpoint}}
	\anchor{upper right side}{%
		\installkiteparameters%
		\pgfpointlineattime{0.5}{\topborderpoint}{\rightborderpoint}}
	\anchor{lower right side}{%
		\installkiteparameters%
		\pgfpointlineattime{0.5}{\bottomborderpoint}{\rightborderpoint}}
	\backgroundpath{%
		\installkiteparameters%
		\pgfpathmoveto{\toppoint}%
		\pgfpathlineto{\leftpoint}%
		\pgfpathlineto{\bottompoint}%
		\pgfpathlineto{\rightpoint}%
		\pgfpathclose%
	}
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% This allows anchors base east, base west, mid east and mid west,
		% to redefine the `center' of the node to correctly calculate the
		% border points.
		%
		\pgfutil@ifundefined{pgf@kiteanchorborderreferencepoint}%
			{\let\referencepoint\centerpoint}%
			{\let\referencepoint\pgf@kiteanchorborderreferencepoint}%
		%
		% Adjust the location of the external 
		% point relative to the reference point.
		%
		\referencepoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Install the required points and angles.
		%
		\installkiteparameters%
		%
		% Get the angle of the external point relative to \referencepoint.
		%
		\pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
		%
		% *Subtract* the rotation from the external angle.
		%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\externalangle\pgfmathresult%
		\ifx\referencepoint\basepoint%
			\let\angletotoppoint\baseangletotoppoint%
			\let\angletobottompoint\baseangletobottompoint%
			\let\angletoleftpoint\baseangletoleftpoint%
			\let\angletorightpoint\baseangletorightpoint%
		\else%
			\ifx\referencepoint\midpoint%
				\let\angletotoppoint\midangletotoppoint%
				\let\angletobottompoint\midangletobottompoint%
				\let\angletoleftpoint\midangletoleftpoint%
				\let\angletorightpoint\midangletorightpoint%
		\fi\fi%
		%
		%  Depending on the rotation, the angle to \rightborderpoint
		%  may be smaller than the angle to \topborderpoint.
		%
		\ifdim\angletorightpoint pt<\angletotoppoint pt\relax%
			\ifdim\externalangle pt<\angletorightpoint pt\relax%
				\let\firstpoint\rightborderpoint%
				\let\secondpoint\bottomborderpoint%
			\else%
				\ifdim\externalangle pt<\angletotoppoint pt\relax%
					\let\firstpoint\rightborderpoint%
					\let\secondpoint\topborderpoint%
				\else%
					\ifdim\externalangle pt<\angletoleftpoint pt\relax%
						\let\firstpoint\topborderpoint%
						\let\secondpoint\leftborderpoint%
					\else%
						\ifdim\externalangle pt<\angletobottompoint pt\relax%
							\let\firstpoint\leftborderpoint%
							\let\secondpoint\bottomborderpoint%
						\else%
							\let\firstpoint\rightborderpoint%
							\let\secondpoint\bottomborderpoint%
						\fi%
					\fi%
				\fi%
			\fi%
		\else%
			\ifdim\externalangle pt<\angletotoppoint pt\relax%
				\let\firstpoint\rightborderpoint%
				\let\secondpoint\topborderpoint%
			\else%
				\ifdim\externalangle pt<\angletoleftpoint pt\relax%
					\let\firstpoint\leftborderpoint%
					\let\secondpoint\topborderpoint%
				\else%
					\ifdim\externalangle pt<\angletobottompoint pt\relax%
						\let\firstpoint\bottomborderpoint%
						\let\secondpoint\leftborderpoint%
					\else%
						\ifdim\externalangle pt<\angletorightpoint pt\relax%
							\let\firstpoint\rightborderpoint%
							\let\secondpoint\bottomborderpoint%
						\else%
							\let\firstpoint\rightborderpoint%
							\let\secondpoint\topborderpoint%
						\fi%
					\fi%
				\fi%
			\fi%
		\fi%
		\pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\firstpoint}{\secondpoint}%
	}
}




% Keys for shape dart.
%
%

\pgfkeys{/pgf/.cd,
	dart tip angle/.initial=45,
	dart tail angle/.initial=135
}

% Shape dart.
%
\pgfdeclareshape{dart}{%
	\savedmacro\installdartparameters{%
		%
		% Get the halved angles (more useful).
		%
		\pgfmathdivide{\pgfkeysvalueof{/pgf/dart tip angle}}{2}%
		\let\halftipangle\pgfmathresult%
		\pgfmathdivide{\pgfkeysvalueof{/pgf/dart tail angle}}{2}%
		\let\halftailangle\pgfmathresult%
		%
		% Calculate some common results.
		%
		\pgfmathcot@{\halftipangle}%
		\let\cothalftipangle\pgfmathresult%
		%
		% Get the larger of the outer sep.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@x<\pgf@y%
			\pgf@x\pgf@y%
		\fi%
		\edef\outersep{\the\pgf@x}%
		%
		% Calculate the centre, base and mid points of the node.
		%
		\pgfextract@process\centerpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y.5\ht\pgfnodeparttextbox%
			\advance\pgf@y-.5\dp\pgfnodeparttextbox%
		}%
		\pgfextract@process\basepoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y0pt\relax%
		}%
		\pgfextract@process\midpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgfmathsetlength\pgf@y{+.5ex}%
		}%
		%
		% Get the (halved) dimension of the node.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		%
		% Get the length of the dart tip.
		%
		\ifpgfshapeborderusesincircle%
			%
			% Get the (unrounded) rotation.
			%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			%
			% Get the radius of the incircle.
			%
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\fi%			
			\pgf@x1.41421\pgf@x%
			%
			% Calculate the length of the dart tip.
			%
			\pgf@xa\cothalftipangle\pgf@x%
			\advance\pgf@xa\pgf@x%
		\else%
			%
			% Get the rotation (with rounding).
			%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\afterassignment\pgfmath@gobbletilpgfmath@%
			\expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\ifnum\c@pgf@counta<0\relax%
				\advance\c@pgf@counta360\relax%
			\fi%
			\edef\rotate{\the\c@pgf@counta}%
			%
			% Flip the width and height of the node contents, 
			% according to the appropriate border rotation.
			%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xc\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xc%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xc\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xc%
				\fi%
			\fi%
			%
			% Calculate the length of the dart tip.
			%
			\pgf@xa\cothalftipangle\pgf@y%
			\advance\pgf@xa2.0\pgf@x% 
		\fi%
		%
		% Get the (half) separation of the dart tails.
		%
		\pgfmathsubtract@{\halftailangle}{\halftipangle}%
		\pgfmathcosec@{\pgfmathresult}%
		\pgf@ya\pgfmathresult\pgf@xa%
		\pgfmathsin@{\halftipangle}%
		\pgf@ya\pgfmathresult\pgf@ya%
		\pgfmathcos@{\halftipangle}%
		\pgf@ya\pgfmathresult\pgf@ya%
		%
		% Get the total length of the dart...
		%
		\pgf@xb\cothalftipangle\pgf@ya%
		%
		% and hence the length of the tails. 
		%
		\pgf@xc-\pgf@xa%
		\advance\pgf@xc\pgf@xb%
		%
		% Adjust for minimum height (length of the dart).
		%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@xb<\pgf@y%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@xb}}%
			\pgf@y\pgfmathresult\pgf@y%
			\pgf@xa\pgfmath@tonumber{\pgf@y}\pgf@xa%
			\pgf@xc\pgfmath@tonumber{\pgf@y}\pgf@xc%
			\pgf@ya\pgfmath@tonumber{\pgf@y}\pgf@ya%
			\pgf@x\pgfmath@tonumber{\pgf@y}\pgf@x%
		\fi%
		%
		% Adjust for minimum width (tail separation length).
		%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum width}}%
		\pgf@y.5\pgf@y%
		\ifdim\pgf@ya<\pgf@y%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@ya}}%
			\pgf@ya\pgf@y%
			\pgf@y\pgfmathresult\pgf@y%
			\pgf@xa\pgfmath@tonumber{\pgf@y}\pgf@xa%
			\pgf@xc\pgfmath@tonumber{\pgf@y}\pgf@xc%
			\pgf@x\pgfmath@tonumber{\pgf@y}\pgf@x%
		\fi%
		\edef\dartlength{\the\pgf@xa}%
		\edef\deltax{\the\pgf@x}%
		\edef\taillength{\the\pgf@xc}%
		\edef\halftailseparation{\the\pgf@ya}
		%
		% Create the basic points on the dart (for the backgroundo path).
		%
		\pgfextract@process\tippoint{%
			\centerpoint%
			\advance\pgf@x\dartlength\relax%
			\advance\pgf@x-\deltax\relax%
		}%
		\pgfextract@process\tailcenterpoint{%
			\centerpoint%
			\advance\pgf@x-\deltax\relax%
		}%
		\pgfextract@process\lefttailpoint{%
			\centerpoint%
			\advance\pgf@x-\deltax\relax%
			\advance\pgf@x-\taillength\relax%
			\advance\pgf@y\halftailseparation\relax%
		}%
		\pgfextract@process\righttailpoint{%
			\centerpoint%
			\advance\pgf@x-\deltax\relax%
			\advance\pgf@x-\taillength\relax%
			\advance\pgf@y-\halftailseparation\relax%
		}%
		%
		% Calculate the miter vectors. At the dart tip...
		%
		\pgfextract@process\tipmiter{%
			\pgfmathcosec@{\halftipangle}%
			\pgf@x\outersep\relax%
			\pgf@x\pgfmathresult\pgf@x%
			\pgf@y0pt\relax%
		}%
		%
		% ...at the tail center...
		%
		\pgfextract@process\tailcentermiter{%
			\pgfmathcosec@{\halftailangle}%
			\pgf@x-\outersep\relax%
			\pgf@x\pgfmathresult\pgf@x%
			\pgf@y0pt\relax%
		}%
		%
		% ...at the left tail...
		%
		\pgfmathsubtract@{\halftailangle}{\halftipangle}%
		\pgfmathdivide@{\pgfmathresult}{2}%
		\let\angle\pgfmathresult%
		\pgfmathcosec@{\pgfmathresult}%
		\pgf@x\outersep\relax%
		\pgf@x\pgfmathresult\pgf@x%
		\pgfmathadd@{\angle}{90}%
		\pgfmathsubtract{\pgfmathresult}{\halftailangle}%
		\pgfmathsincos@{\pgfmathresult}%
		\pgf@ya\pgfmathresultx\pgf@x%
		\pgf@xa\pgfmathresulty\pgf@x%
		\pgfextract@process\lefttailmiter{%
			\pgf@x-\pgf@xa%
			\pgf@y\pgf@ya%
		}%
		%
		% ...and the right tail.
		%
		\pgfextract@process\righttailmiter{%
			\pgf@x-\pgf@xa%
			\pgf@y-\pgf@ya%
		}%
		%
		% Create the border points.
		%
		\pgfextract@process\tipborderpoint{%
			\pgfpointadd{\tippoint}{\tipmiter}
		}%
		\pgfextract@process\tailcenterborderpoint{%
			\pgfpointadd{\tailcenterpoint}{\tailcentermiter}%
		}%
		\pgfextract@process\lefttailborderpoint{%
			\pgfpointadd{\lefttailpoint}{\lefttailmiter}%
		}%
		\pgfextract@process\righttailborderpoint{%
			\pgfpointadd{\righttailpoint}{\righttailmiter}%
		}%
		%
		% Calculate the angles between the centerpoint
		% and the *unrotated* borderpoints.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\tipborderpoint}%
		\let\angletotip\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\tailcenterborderpoint}%
		\let\angletotailcenter\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\lefttailborderpoint}%
		\let\angletolefttail\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\righttailborderpoint}%
		\let\angletorighttail\pgfmathresult%
		%
		% Calculate the angles between the *inversly rotated* 
		% basepoint and the *unrotated* borderpoints.
		%
		\pgfextract@process\rotatedbasepoint{%
			\pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\tipborderpoint}%
		\let\baseangletotip\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\tailcenterborderpoint}%
		\let\baseangletotailcenter\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\lefttailborderpoint}%
		\let\baseangletolefttail\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedbasepoint}{\righttailborderpoint}%
		\let\baseangletorighttail\pgfmathresult%
		%
		% Calculate the angles between the *inversly rotated* 
		% midpoint and the *unrotated* borderpoints.
		%
		\pgfextract@process\rotatedmidpoint{%
			\pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}%
		}%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\tipborderpoint}%
		\let\midangletotip\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\tailcenterborderpoint}%
		\let\midangletotailcenter\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\lefttailborderpoint}%
		\let\midangletolefttail\pgfmathresult%
		\pgfmathanglebetweenpoints{\rotatedmidpoint}{\righttailborderpoint}%
		\let\midangletorighttail\pgfmathresult%
		%
		% Rotate the background path points.
		%
		\pgfextract@process\tippoint{%
			\pgfmathrotatepointaround{\tippoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\tailcenterpoint{%
			\pgfmathrotatepointaround{\tailcenterpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\lefttailpoint{%
			\pgfmathrotatepointaround{\lefttailpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\righttailpoint{%
			\pgfmathrotatepointaround{\righttailpoint}{\centerpoint}{\rotate}%
		}%
		%
		% Calculate a radius guaranteed to be outside the dart.
		%
		\pgfextractx\pgf@xa{\pgfpointdiff{\lefttailborderpoint}{\tipborderpoint}}%
		\pgfextracty\pgf@ya{\pgfpointdiff{\lefttailborderpoint}{\righttailborderpoint}}%
		\ifdim\pgf@xa<0pt\relax%
			\pgf@xa-\pgf@xa%
		\fi%
		\ifdim\pgf@ya<0pt\relax%
			\pgf@ya-\pgf@ya%
		\fi%
		\ifdim\pgf@xa>\pgf@ya%
			\edef\externalradius{\the\pgf@xa}%
		\else%
			\edef\externalradius{\the\pgf@ya}%
		\fi%
		%
		% Rotate the border anchor points.
		%
		\pgfextract@process\tipborderpoint{%
			\pgfmathrotatepointaround{\tipborderpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\tailcenterborderpoint{%
			\pgfmathrotatepointaround{\tailcenterborderpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\lefttailborderpoint{%
			\pgfmathrotatepointaround{\lefttailborderpoint}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\righttailborderpoint{%
			\pgfmathrotatepointaround{\righttailborderpoint}{\centerpoint}{\rotate}%
		}%
		%
		% Save everything.
		%
		\addtosavedmacro{\rotate}%
		\addtosavedmacro{\externalradius}%
		%
		\addtosavedmacro{\tippoint}%
		\addtosavedmacro{\tailcenterpoint}%
		\addtosavedmacro{\lefttailpoint}%
		\addtosavedmacro{\righttailpoint}%
		%
		\addtosavedmacro{\tipborderpoint}%
		\addtosavedmacro{\tailcenterborderpoint}%
		\addtosavedmacro{\lefttailborderpoint}%
		\addtosavedmacro{\righttailborderpoint}%
		%
		\addtosavedmacro{\angletotip}%
		\addtosavedmacro{\angletotailcenter}%
		\addtosavedmacro{\angletolefttail}%
		\addtosavedmacro{\angletorighttail}%
		%
		\addtosavedmacro{\baseangletotip}%
		\addtosavedmacro{\baseangletotailcenter}%
		\addtosavedmacro{\baseangletolefttail}%
		\addtosavedmacro{\baseangletorighttail}%
		%
		\addtosavedmacro{\midangletotip}%
		\addtosavedmacro{\midangletotailcenter}%
		\addtosavedmacro{\midangletolefttail}%
		\addtosavedmacro{\midangletorighttail}%
	}
	\savedanchor\centerpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor\basepoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y0pt\relax%
	}%
	\savedanchor\midpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%
	\anchor{center}{\centerpoint}%
	\anchor{base}{\basepoint}%
	\anchor{base west}{%
		\installdartparameters%
		\let\pgf@dartanchorborderreferencepoint\basepoint%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}
	\anchor{base east}{%
		\installdartparameters%
		\let\pgf@dartanchorborderreferencepoint\basepoint%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{mid}{\midpoint}%
	\anchor{mid west}{%
		\installdartparameters%
		\let\pgf@dartanchorborderreferencepoint\midpoint%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}
	\anchor{mid east}{%
		\installdartparameters%
		\let\pgf@dartanchorborderreferencepoint\midpoint%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{north}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{0pt}{\externalradius}}%
	}
	\anchor{south}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}%
	}
	\anchor{east}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{0pt}}%
	}
	\anchor{west}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}%
	}
	\anchor{north east}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}%
	}
	\anchor{south west}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}%
	}
	\anchor{south east}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}%
	}
	\anchor{north west}{%
		\installdartparameters%
		\csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}%
	}
	\anchor{tip}{%
		\installdartparameters%
		\tipborderpoint}
	\anchor{left tail}{%
		\installdartparameters%
		\lefttailborderpoint}
	\anchor{right tail}{%
		\installdartparameters%
		\righttailborderpoint}
	\anchor{tail center}{%
		\installdartparameters%
		\tailcenterborderpoint}
	\anchor{left side}{%
		\installdartparameters%
		\pgfpointlineattime{0.5}{\tipborderpoint}{\lefttailborderpoint}}
	\anchor{right side}{%
		\installdartparameters%
		\pgfpointlineattime{0.5}{\tipborderpoint}{\righttailborderpoint}}
	\backgroundpath{%
		\installdartparameters%
		\pgfpathmoveto{\tippoint}%
		\pgfpathlineto{\lefttailpoint}%
		\pgfpathlineto{\tailcenterpoint}%
		\pgfpathlineto{\righttailpoint}%
		\pgfpathclose%
	}
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% This allows anchors base east, base west, mid east and mid west,
		% to redefine the `center' of the node to correctly calculate the
		% border points.
		%
		\pgfutil@ifundefined{pgf@dartanchorborderreferencepoint}%
			{\let\referencepoint\centerpoint}%
			{\let\referencepoint\pgf@dartanchorborderreferencepoint}%
		%
		% Adjust the location of the external 
		% point relative to the reference point.
		%
		\referencepoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Install the required points and angles.
		%
		\installdartparameters%
		%
		% Get the angle of the external point relative to \referencepoint.
		%
		\pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
		%
		% *Subtract* the rotation from the external angle.
		%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\externalangle\pgfmathresult%
		%
		% Get the set of angles for the appropriate border point.
		%
		\ifx\referencepoint\basepoint%
			\let\angletotip\baseangletotip%
			\let\angletotailcenter\baseangletotailcenter%
			\let\angletolefttail\baseangletolefttail%
			\let\angletorighttail\baseangletorighttail%
		\else%
			\ifx\referencepoint\midpoint%
				\let\angletotip\midangletotip%
				\let\angletotailcenter\midangletotailcenter%
				\let\angletolefttail\midangletolefttail%
				\let\angletorighttail\midangletorighttail%
		\fi\fi%
		%
		% Locate the appropriate line on the border...
		%
		\ifdim\externalangle pt<\angletotip pt\relax%
			\let\firstpoint\tipborderpoint%
			\let\secondpoint\righttailborderpoint%
		\else%
			\ifdim\externalangle pt<\angletolefttail pt\relax%
				\let\firstpoint\lefttailborderpoint%
				\let\secondpoint\tipborderpoint%
			\else%
				\ifdim\externalangle pt<\angletotailcenter pt\relax%
					\let\firstpoint\lefttailborderpoint%
					\let\secondpoint\tailcenterborderpoint%
				\else%
					\ifdim\externalangle pt<\angletorighttail pt\relax%
						\let\firstpoint\righttailborderpoint%
						\let\secondpoint\tailcenterborderpoint%
					\else%
						\let\firstpoint\tipborderpoint%
						\let\secondpoint\righttailborderpoint%
					\fi%
				\fi%
			\fi%
		\fi%
		%
		% ...and thus the point on the border.
		%
		\pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\firstpoint}{\secondpoint}%
	}%
}



% Keys for shape circular sector:
%
% /pgf/circular sector angle : the angle at the center of the sector.
%
\pgfkeys{/pgf/circular sector angle/.initial=60}

% Shape circular sector
%
\pgfdeclareshape{circular sector}{%
	\savedmacro\installcircularsectorparameters{%
		%
		% Define a \centerpoint, \basepoint and \midpoint.
		%
		\pgfextract@process\centerpoint{%
			\pgf@x.5\wd\pgfnodeparttextbox%
			\pgf@y.5\ht\pgfnodeparttextbox%
			\advance\pgf@y-.5\dp\pgfnodeparttextbox%
		}%
		%
		% Get the larger of the outer sep.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@x<\pgf@y%
			\pgf@x\pgf@y%
		\fi%
		\edef\outersep{\the\pgf@x}%
		%
		% Half of the sector angle is more useful.
		%
		\pgfmathmod{\pgfkeysvalueof{/pgf/circular sector angle}}{360}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\angle\pgfmathresult%
		\pgfmathdivide@{\pgfmathresult}{2}%
		\let\halfangle\pgfmathresult%
		%
		% Get some useful trigonometric stuff.
		%
		\pgfmathsin@{\halfangle}%
		\let\sinehalfangle\pgfmathresult%
		\pgfmathreciprocal@{\pgfmathresult}%
		\let\cosechalfangle\pgfmathresult%
		\pgfmathabs@{\halfangle}%
		\pgfmathcos@{\pgfmathresult}%
		\let\coshalfangle\pgfmathresult%
		\pgf@x\pgfmathresult pt\relax%
		\pgf@x\cosechalfangle\pgf@x%
		\edef\cothalfangle{\pgfmath@tonumber{\pgf@x}}%
		%
		% Calculate the miter length at the center, 
		% according to the outer sep.
		%
		\pgf@x\outersep\relax%
		\pgf@x\cosechalfangle\pgf@x%
		\edef\centermiter{\the\pgf@x}%
		%
		% Get the start and end angles of the arc.
		%
		\pgfmathsubtract@{180}{\halfangle}%
		\let\startangle\pgfmathresult%
		\pgfmathadd@{180}{\halfangle}%
		\let\endangle\pgfmathresult%
		%
		% Get (half) the node dimensions.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		%
		% Calculate the radius of the sector and the `center offset', 
		% which is the distance between the center of the node and the 
		% center of the sector.
		%
		\ifpgfshapeborderusesincircle%
			%
			% Get the rotation.
			%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			%
			% Calculate the incircle radius.
			%	
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\fi%
			\pgf@x1.41421\pgf@x%
			\pgf@xa\cosechalfangle\pgf@x% 
			%
			% xa is the radius, xb the offset.
			%
			\pgf@xb\pgf@xa%
			\advance\pgf@xa\pgf@x%
		\else%
			%
			% Get the rotation (with rounding).
			%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\afterassignment\pgfmath@gobbletilpgfmath@%
			\expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\ifnum\c@pgf@counta<0\relax%
				\advance\c@pgf@counta360\relax%
			\fi%
			\edef\rotate{\the\c@pgf@counta}%
			%
			% Swap the height and width for relevant angles.
			%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xc\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xc%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xc\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xc%
				\fi%
			\fi%
			%
			% xa is the radius, xb the offset.
			%
			\pgf@xa\cosechalfangle\pgf@y%
			\pgf@xa\coshalfangle\pgf@xa%
			\advance\pgf@xa\pgf@x%
			\pgf@xb\pgf@xa% 
			\advance\pgf@xa\pgf@x%
			\pgfmathveclen@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@y}}%
			\pgf@xa\pgfmathresult pt\relax% 
		\fi%
		%
		% Adjust for minimum height and width.
		%
		\pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/minimum width}}%
		\pgf@x.5\pgf@x%
		\pgfmathsec@{\halfangle}%
		\pgf@xc\pgfmathresult\pgf@xb%
		\ifdim\pgf@xc<0pt\relax%
			\pgf@xc-\pgf@xc%
		\fi%
		\ifdim\pgf@xc<\pgf@x%
			\pgfmathreciprocal{\pgfmath@tonumber{\pgf@xc}}% 
			\pgf@xc\pgfmathresult\pgf@x% Increase by ratio.
			\pgf@xa\pgfmath@tonumber{\pgf@xc}\pgf@xa%
			\pgf@xb\pgfmath@tonumber{\pgf@xc}\pgf@xb%
		\fi%
		\pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@xa<\pgf@y%
			\pgfmathreciprocal{\pgfmath@tonumber{\pgf@xa}}%
			\pgf@xc\pgfmathresult\pgf@y% Increase by ratio.
			\pgf@xa\pgf@y%
			\pgf@xb\pgfmath@tonumber{\pgf@xc}\pgf@xb%
		\fi%
		\edef\centeroffset{\the\pgf@xb}%
		\edef\radius{\the\pgf@xa}%
		%
		% Calculate the radius at sector border and the arc corners.
		%
		\advance\pgf@xa\outersep\relax%
		\edef\borderradius{\the\pgf@xa}%
		\pgf@x\outersep\relax%
		\pgf@x\cosechalfangle\pgf@x%
		\pgf@x\coshalfangle\pgf@x%
		\advance\pgf@xa\pgf@x%		
		\edef\cornerradius{\the\pgf@xa}%
		%
		% Calculate the *unrotated* points for the background path.
		%
		\pgfextract@process\sectorcenter{%
			\centerpoint%
			\advance\pgf@x\centeroffset%
		}%
		\pgfextract@process\arcstart{%
			\pgfqpointpolar{\startangle}{\radius}%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\sectorcenter%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		%
		% Calculate the *unrotated* points for the anchor border.
		%
		\pgfextract@process\sectorcenterborder{%
			\sectorcenter%
			\advance\pgf@x\centermiter\relax%
		}%
		\pgfextract@process\arcstartborder{%
			\pgfqpointpolar{\startangle}{\borderradius}%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\sectorcenter%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		\pgfextract@process\arcendborder{%
			\pgfqpointpolar{\endangle}{\borderradius}%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\sectorcenter%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		\pgfextract@process\arcstartcorner{%
			\pgfqpointpolar{\startangle}{\cornerradius}%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\sectorcenterborder%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		\pgfextract@process\arcendcorner{%
			\pgfqpointpolar{\endangle}{\cornerradius}%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\sectorcenterborder%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		%
		% Calculate the *unrotated* corner angles to the \centerpoint.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\sectorcenterborder}%
		\let\angletosectorcenterborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcstartborder}%
		\let\angletoarcstartborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcendborder}%
		\let\angletoarcendborder\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcstartcorner}%
		\let\angletoarcstartcorner\pgfmathresult%
		\pgfmathanglebetweenpoints{\centerpoint}{\arcendcorner}%
		\let\angletoarcendcorner\pgfmathresult%
		%
		% Rotate the background path points around the note center.
		%
		\pgfextract@process\sectorcenter{%
			\pgfmathrotatepointaround{\sectorcenter}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcstart{%
			\pgfmathrotatepointaround{\arcstart}{\centerpoint}{\rotate}%
		}%
		%
		% Rotate the border points around the note center.
		%
		\pgfextract@process\sectorcenterborder{%
			\pgfmathrotatepointaround{\sectorcenterborder}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcstartborder{%
			\pgfmathrotatepointaround{\arcstartborder}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcendborder{%
			\pgfmathrotatepointaround{\arcendborder}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcstartcorner{%
			\pgfmathrotatepointaround{\arcstartcorner}{\centerpoint}{\rotate}%
		}%
		\pgfextract@process\arcendcorner{%
			\pgfmathrotatepointaround{\arcendcorner}{\centerpoint}{\rotate}%
		}%
		%
		% Add the rotation to the start and end angles.
		%
		\pgfmathadd@{\startangle}{\rotate}%
		\let\startangle\pgfmathresult%
		\pgfmathadd@{\endangle}{\rotate}%
		\let\endangle\pgfmathresult%
		%
		% Save everything. 
		%
		% NB \addtosavedmacro is currently experimental. May get changed.
		%
		\addtosavedmacro{\rotate}%
		\addtosavedmacro{\centeroffset}%
		%
		\addtosavedmacro{\radius}%
		\addtosavedmacro{\borderradius}%
		\addtosavedmacro{\cornerradius}%
		%
		\addtosavedmacro{\endangle}%
		\addtosavedmacro{\startangle}%
		%
		\addtosavedmacro{\sectorcenter}%
		\addtosavedmacro{\arcstart}%
		%
		\addtosavedmacro{\sectorcenterborder}%
		\addtosavedmacro{\arcstartborder}%
		\addtosavedmacro{\arcendborder}%
		\addtosavedmacro{\arcstartcorner}%
		\addtosavedmacro{\arcendcorner}%
		%
		\addtosavedmacro{\angletosectorcenterborder}%
		\addtosavedmacro{\angletoarcstartborder}%
		\addtosavedmacro{\angletoarcendborder}%
		\addtosavedmacro{\angletoarcstartcorner}%
		\addtosavedmacro{\angletoarcendcorner}%
	}%
	\savedanchor\centerpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor\basepoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y0pt\relax%
	}%
	\savedanchor\midpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+.5ex}%
	}%
	\anchor{center}{\centerpoint}
	\anchor{base}{\basepoint}
	\anchor{mid}{\midpoint}	
	\anchor{arc start}{%
		\installcircularsectorparameters%
		\arcstartcorner%
	}
	\anchor{arc end}{%
		\installcircularsectorparameters%
		\arcendcorner%
	}
	\anchor{sector center}{%
		\installcircularsectorparameters%
		\sectorcenterborder%
	}
	\anchor{arc center}{%
		\installcircularsectorparameters%
		\pgfmathadd@{\rotate}{180}%
		\let\angle\pgfmathresult%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpointpolar{\angle}{\cornerradius}}%
	}
	\anchor{north}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{0pt}{\cornerradius}}%
	}
	\anchor{south}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{0pt}{-\cornerradius}}%
	}
	\anchor{east}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{\cornerradius}{0pt}}%
	}
	\anchor{west}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{-\cornerradius}{0pt}}%
	}
	\anchor{north west}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{-\cornerradius}{\cornerradius}}%
	}
	\anchor{south west}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{-\cornerradius}{-\cornerradius}}%
	}
	\anchor{north east}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{\cornerradius}{\cornerradius}}%
	}
	\anchor{south east}{%
		\installcircularsectorparameters%
		\csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{\cornerradius}{-\cornerradius}}%
	}
	\backgroundpath{%
		\installcircularsectorparameters%
		\pgfpathmoveto{\sectorcenter}%
		\pgfpathlineto{\arcstart}%
		\ifdim\endangle pt>360pt\relax%
			\ifdim\startangle pt>360pt\relax%
				\pgfpatharc{\startangle}{\endangle}{\radius}%
			\else%
				\pgfpatharc{\startangle}{360}{\radius}%
				\pgfpatharc{0}{\endangle}{\radius}%
			\fi%
		\else%
			\pgfpatharc{\startangle}{\endangle}{\radius}%
		\fi%
		\pgfpathclose%
	}%
	\anchorborder{%
		%
		% Save x and y.
		%
		\edef\externalx{\the\pgf@x}%
		\edef\externaly{\the\pgf@y}%
		%
		% Adjust the location of the external  point relative to \centerpoint.
		%
		\centerpoint%
		\pgf@xa\externalx\relax%
		\pgf@ya\externaly\relax%
		\advance\pgf@xa\pgf@x%
		\advance\pgf@ya\pgf@y%
		\edef\externalx{\the\pgf@xa}%
		\edef\externaly{\the\pgf@ya}%
		%
		% Install the required points and angles.
		%
		\installcircularsectorparameters%
		%
		% Get the angle of the external point to the \centerpoint.
		%
		\pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}%
		\let\externalangle\pgfmathresult%
		%
		% *Subtract* the rotation from the external angle.
		%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\angle\pgfmathresult%
		%
		% Determine if the line will cross the sector arc.
		% 
		\ifdim\angle pt>\angletoarcendcorner pt\relax%
			\let\firstpoint\arcendcorner%
			\let\secondpoint\sectorcenterborder%
		\else%
			\ifdim\angle pt>\angletoarcendborder pt\relax%
				\let\firstpoint\arcendborder%
				\let\secondpoint\arcendcorner%
			\else%
				\ifdim\angle pt>\angletoarcstartborder pt\relax%
					\let\firstpoint\pgfutil@empty%
					\let\secondpoint\pgfutil@empty%
				\else%
					\ifdim\angle pt>\angletoarcstartcorner pt\relax%
						\let\firstpoint\arcstartborder
						\let\secondpoint\arcstartcorner
					\else%		
						\let\firstpoint\sectorcenterborder%
						\let\secondpoint\arcstartcorner%
					\fi%
				\fi%
			\fi%
		\fi%
		\ifx\firstpoint\pgfutil@empty
			%
			% Calculate the angle from the centre of the semicircle to the
			% point on the semicircle arc which intersects the line from 
			% the external point to the reference point...
			%
			\pgfmathanglebetweenlines{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\sectorcenter}{\centerpoint}%
			\pgfmathsin@{\pgfmathresult}%
			\let\sineangle\pgfmathresult%
			\pgf@x\borderradius\relax%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@x}}%
			\let\reciprocalradius\pgfmathresult%
			\pgf@x\centeroffset\relax%
			\pgf@x\sineangle\pgf@x%
			\pgf@x\reciprocalradius\pgf@x%
			\pgfmathasin@{\pgfmath@tonumber{\pgf@x}}%
			\pgf@x\pgfmathresult pt\relax%
			\advance\pgf@x\externalangle pt\relax%
			\edef\angle{\pgfmath@tonumber{\pgf@x}}%
			%
			% ...and thus the point on the border.
			%
			\pgfpointadd{\sectorcenter}{\pgfqpointpolar{\angle}{\borderradius}}%
		\else%
			%
			% Calculate the the point where the semicircle chord intersects 
			% the line from the external point to the reference point.
			%
			\pgfpointintersectionoflines{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}%
				{\firstpoint}{\secondpoint}%
		\fi%		
	}%
}



% Keys for shape cylinder
%
% /pgf/shape aspect              : Ratio between the x and y radii of the cylinder end.
% /pgf/cylinder uses custom fill : Use a custom fill for the cylinder.
% /pgf/cylinder end fill         : Custom color for the cylinder end.
% /pgf/cylinder body fill        : Custom color for the cylinderbody.
%

\newif\ifpgfcylinderusescustomfill
\pgfkeys{/pgf/.cd,
	cylinder uses custom fill/.is if=pgfcylinderusescustomfill,
	cylinder end fill/.initial=white,
	cylinder body fill/.initial=white
}


\pgfdeclareshape{cylinder}{%
	\savedmacro\getcylinderpoints{%
		\pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/inner xsep}}%
		\pgf@x\pgf@xc%
		\advance\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}%
		\pgf@y\pgf@yc%
		\advance\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y.5\dp\pgfnodeparttextbox%
		\ifpgfshapeborderusesincircle%
			\pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}%
			\ifdim\pgf@x<\pgf@y%
				\pgf@x\pgf@y%
			\else%
				\pgf@y\pgf@x%
			\fi%
			\pgf@x1.414213\pgf@x%
			\pgf@y1.414213\pgf@y%			
		\else%
			\pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}%
			\ifdim\pgfmathresult pt<0pt\relax%
				\pgfmathadd@{\pgfmathresult}{360}%
			\fi%
			\pgfmathsetcount\c@pgf@counta{+\pgfmathresult}%
			\advance\c@pgf@counta45\relax%
			\divide\c@pgf@counta90\relax%
			\multiply\c@pgf@counta90\relax%
			\edef\rotate{\the\c@pgf@counta}%
			\ifnum\c@pgf@counta=90\relax%
				\pgf@xa\pgf@x%
				\pgf@x\pgf@y%
				\pgf@y\pgf@xa%
				\pgf@yc\pgf@xc%
			\else%
				\ifnum\c@pgf@counta=270\relax%
					\pgf@xa\pgf@x%
					\pgf@x\pgf@y%
					\pgf@y\pgf@xa%
					\pgf@yc\pgf@xc%
				\fi%
			\fi%
		\fi%
		\addtosavedmacro\rotate%
		\pgf@xa\pgf@x%
		\pgf@ya\pgf@y%
		\pgfutil@tempdima\pgfshapeaspect\pgf@ya%
		\pgfutil@tempdimb\pgf@ya%
		%
		% Adjust for minimum height.
		%
		\pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum width}}%
		\ifdim\pgfutil@tempdimb<.5\pgf@xc\relax%
			\pgfutil@tempdimb.5\pgf@xc%
			\pgf@ya\pgfutil@tempdimb%
		\fi%
		%
		% Calculate how far the node contents can extend into the cylinder bottom.
		%
		\pgf@yb\pgfutil@tempdimb%
		\advance\pgf@yb-\pgf@yc%
		\pgfmathdivide@{\pgfmath@tonumber{\pgf@yb}}{\pgfmath@tonumber{\pgfutil@tempdimb}}%
		\pgfmathasin@{\pgfmathresult}%
		\pgfmathcos@{\pgfmathresult}%
		\let\angle\pgfmathresult%
		\pgf@xb\pgfmathresult\pgfutil@tempdima%
		%
		% Adjust for minimum width.
		%
		\pgf@x.5\pgflinewidth%
		\advance\pgf@x2.0\pgf@xa%
		\advance\pgf@x3.0\pgfutil@tempdima%
		\advance\pgf@x-\pgf@xb%
		\pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum height}}%
		\ifdim\pgf@x<\pgf@xc%
			\advance\pgf@xc-\pgf@x%
			\advance\pgf@xa.5\pgf@xc%
		\fi%		
		%
		% Add the larger of the outer sep to the radii.
		%
		\pgf@x\pgfutil@tempdima\relax%
		\pgf@y\pgfutil@tempdimb\relax%
		\pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/outer xsep}}%
		\pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/outer ysep}}%
		\ifdim\pgf@xc>\pgf@yc%
			\advance\pgf@x\pgf@xc%
			\advance\pgf@y\pgf@xc%
			\edef\outersep{\the\pgf@xc}%
		\else%
			\advance\pgf@x\pgf@yc%
			\advance\pgf@y\pgf@yc%
			\edef\outersep{\the\pgf@yc}%
		\fi%
		\edef\xradius{\the\pgf@x}%
		\edef\yradius{\the\pgf@y}%
		\addtosavedmacro\xradius%
		\addtosavedmacro\yradius%
		\addtosavedmacro\outersep%
		%
		\pgfextract@process\cylindercenter{%
			\pgf@x\pgfutil@tempdima%
			\advance\pgf@x.5\pgflinewidth%
			\advance\pgf@x\pgf@xb%
			\pgf@x.5\pgf@x%	
			\pgf@y0pt%
		}%
		\addtosavedmacro\cylindercenter%
		%
		\pgfextract@process\beforetop{%
			\pgf@x\pgf@xa%
			\advance\pgf@x\pgfutil@tempdima%
			\advance\pgf@x.5\pgflinewidth%
			\pgf@y\pgf@ya%
		}%
		\pgfextract@process\afterbottom{%
			\pgf@x-\pgf@xa%
			\advance\pgf@x\pgf@xb%
			\pgf@y\pgf@ya%
		}%
		\addtosavedmacro\beforetop%
		\addtosavedmacro\afterbottom%		
		\pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/outer ysep}}%
		\pgfextract@process\beforetopanchor{%
			\beforetop%
			\advance\pgf@y\pgf@yc%
		}%
		\pgfextract@process\afterbottomanchor{%
			\afterbottom%
			\advance\pgf@y\pgf@yc%
		}%
		\addtosavedmacro\beforetopanchor%		
		\addtosavedmacro\afterbottomanchor%	
		%
		\beforetopanchor%
		\advance\pgf@x\xradius\relax%
		\ifdim\pgf@x>\pgf@y%
			\edef\externalradius{\the\pgf@x}%
		\else%
			\edef\externalradius{\the\pgf@y}%
		\fi%
		\addtosavedmacro\externalradius%
	}
	\savedanchor\centerpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y.5\ht\pgfnodeparttextbox%
		\advance\pgf@y-.5\dp\pgfnodeparttextbox%
	}%
	\savedanchor\midpoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgfmathsetlength\pgf@y{+0.5ex}%
	}%
	\savedanchor\basepoint{%
		\pgf@x.5\wd\pgfnodeparttextbox%
		\pgf@y0pt%
	}%
	\anchor{center}{\centerpoint}
	\anchor{shape center}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{\pgfpointadd{\cylindercenter}{\centerpoint}}%
			{\centerpoint}{\rotate}%	
	}%
	\anchor{mid}{\midpoint}%
	\anchor{mid east}{%
		\getcylinderpoints%
		\let\pgf@cylinder@referencepoint\midpoint%
		\pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{0pt}}%
	}%
	\anchor{mid west}{%
		\getcylinderpoints%
		\let\pgf@cylinder@referencepoint\midpoint%
		\pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{base}{\basepoint}%
	\anchor{base east}{%
		\getcylinderpoints%
		\let\pgf@cylinder@referencepoint\basepoint%
		\pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{0pt}}%
	}%
	\anchor{base west}{%
		\getcylinderpoints%
		\let\pgf@cylinder@referencepoint\basepoint%
		\pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{north}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{0pt}{\externalradius}}%
	}%
	\anchor{south}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{0pt}{-\externalradius}}%
	}%
	\anchor{east}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{0pt}}%
	}%
	\anchor{west}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{0pt}}%
	}%
	\anchor{north east}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{\externalradius}}%
	}%
	\anchor{south west}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{-\externalradius}}%
	}%
	\anchor{south east}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{-\externalradius}}%
	}%
	\anchor{north west}{%
		\getcylinderpoints%
		\pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{\externalradius}}%
	}%
	\anchor{before top}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor}{\centerpoint}}{\centerpoint}{\rotate}%
	}
	\anchor{top}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{%
			\pgfpointadd{%
				\beforetop%
				\pgf@y0pt\relax%
				\advance\pgf@x\xradius\relax%
			}{\centerpoint}}{\centerpoint}{\rotate}%
	}
	\anchor{after top}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor\pgf@y-\pgf@y}{\centerpoint}}{\centerpoint}{\rotate}%
	}
	\anchor{before bottom}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor\pgf@y-\pgf@y}{\centerpoint}}{\centerpoint}{\rotate}%
	}
	\anchor{bottom}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{%
			\pgfpointadd{%
				\afterbottom%
				\pgf@y0pt\relax%
				\advance\pgf@x-\xradius\relax%
			}{\centerpoint}}{\centerpoint}{\rotate}%
	}
	\anchor{after bottom}{%
		\getcylinderpoints%
		\pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor}{\centerpoint}}{\centerpoint}{\rotate}%
	}	
	\backgroundpath{%
		\getcylinderpoints%
		{%
			\pgf@x\xradius\relax%
			\advance\pgf@x-\outersep\relax%
			\edef\xradius{\the\pgf@x}%
			\pgf@y\yradius\relax%
			\advance\pgf@y-\outersep\relax%
			\edef\yradius{\the\pgf@y}%
			\pgftransformshift{\centerpoint}%
			\pgftransformrotate{\rotate}%
			\pgfpathmoveto{\afterbottom}%
			\pgfpatharc{90}{270}{\xradius and \yradius}%
			\pgfpathlineto{\beforetop\pgf@y-\pgf@y}%
			\pgfpatharc{-90}{90}{\xradius and \yradius}%
			\pgfpathclose%
			\pgfpathmoveto{\beforetop}%
			\pgfpatharc{90}{270}{\xradius and \yradius}%
		}%
	}%
	\behindbackgroundpath{%
		\ifpgfcylinderusescustomfill%
			\getcylinderpoints%
			\pgf@x\xradius\relax%
			\advance\pgf@x-\outersep\relax%
			\edef\xradius{\the\pgf@x}%
			\pgf@y\yradius\relax%
			\advance\pgf@y-\outersep\relax%
			\edef\yradius{\the\pgf@y}%
			{%				
				\pgftransformshift{\centerpoint}%
				\pgftransformrotate{\rotate}%
				\pgfpathmoveto{\afterbottom}%
				\pgfpatharc{90}{270}{\xradius and \yradius}%
				\pgfpathlineto{\beforetop\pgf@y-\pgf@y}%
				\pgfpatharc{270}{90}{\xradius and \yradius}%
				\pgfpathclose%
				\expandafter\pgfsetfillcolor\expandafter{\pgfkeysvalueof{/pgf/cylinder body fill}}%
				\pgfusepath{fill}%
				%
				\pgfpathmoveto{\beforetop}%
				\pgfpatharc{90}{-270}{\xradius and \yradius}%
				\pgfpathclose
				\expandafter\pgfsetfillcolor\expandafter{\pgfkeysvalueof{/pgf/cylinder end fill}}%
				\pgfusepath{fill}%
			}%		
		\fi%	
	}%
	\anchorborder{%
		\pgfextract@process\externalpoint{}%
		\getcylinderpoints%
		\pgfutil@ifundefined{pgf@cylinder@referencepoint}{\let\referencepoint\centerpoint}{%
			\let\referencepoint\pgf@cylinder@referencepoint}%
		\pgfextract@process\externalpoint{%
			\externalpoint%
			\pgf@xa\pgf@x%
			\pgf@ya\pgf@y%
			\referencepoint%
			\advance\pgf@x\pgf@xa%
			\advance\pgf@y\pgf@ya%
		}%
		\pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}%
		\pgfmathsubtract@{\pgfmathresult}{\rotate}%
		\ifdim\pgfmathresult pt<0pt\relax%
			\pgfmathadd@{\pgfmathresult}{360}%
		\fi%
		\let\externalangle\pgfmathresult%
		%
		\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\afterbottomanchor}{\centerpoint}}%
		\ifdim\externalangle pt<\pgfmathresult pt\relax%
			\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\beforetopanchor}{\centerpoint}}%
			\ifdim\externalangle pt<\pgfmathresult pt\relax%
				\pgfmathrotatepointaround{%
					\pgfmathpointintersectionoflineandarc%
						{\pgfmathrotatepointaround{\externalpoint}{\centerpoint}{-\rotate}}%
						{\pgfmathrotatepointaround{\referencepoint}{\centerpoint}{-\rotate}}%
						{%
							\beforetop%
							\pgf@xa\pgf@x%
							\centerpoint%
							\advance\pgf@x\pgf@xa%
						}%
						{0}{90}{\xradius and \yradius}%
					}{\centerpoint}{\rotate}%
			\else%
				\pgfpointintersectionoflines{%
					\pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor}{\centerpoint}}%
						{\centerpoint}{\rotate}}{%
					\pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor}{\centerpoint}}%
						{\centerpoint}{\rotate}}%
					{\referencepoint}{\externalpoint}%
			\fi%
		\else%
			\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\afterbottomanchor\pgf@y-\pgf@y}{\centerpoint}}%
			\ifdim\externalangle pt>\pgfmathresult pt\relax%
				\pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\beforetopanchor\pgf@y-\pgf@y}{\centerpoint}}%
				\ifdim\externalangle pt>\pgfmathresult pt\relax%
					\pgfmathrotatepointaround{%
						\pgfmathpointintersectionoflineandarc%
							{\pgfmathrotatepointaround{\externalpoint}{\centerpoint}{-\rotate}}%
							{\pgfmathrotatepointaround{\referencepoint}{\centerpoint}{-\rotate}}%
							{%
								\beforetop%
								\pgf@xa\pgf@x%
								\centerpoint
								\advance\pgf@x\pgf@xa%
							}%
							{270}{360}{\xradius and \yradius}%
						}{\centerpoint}{\rotate}%
				\else%
					\pgfpointintersectionoflines{%
						\pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor\pgf@y-\pgf@y}{\centerpoint}}%
							{\centerpoint}{\rotate}}{%
						\pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor\pgf@y-\pgf@y}{\centerpoint}}%
							{\centerpoint}{\rotate}}%
						{\referencepoint}{\externalpoint}%
				\fi%
			\else%
				\pgfmathrotatepointaround{%
					\pgfmathpointintersectionoflineandarc%
						{\pgfmathrotatepointaround{\externalpoint}{\centerpoint}{-\rotate}}%
						{\pgfmathrotatepointaround{\referencepoint}{\centerpoint}{-\rotate}}%
						{%
							\afterbottom%
							\pgf@xa\pgf@x%
							\centerpoint
							\advance\pgf@x\pgf@xa%
						}%
						{90}{270}{\xradius and \yradius}%
					}{\centerpoint}{\rotate}%
			\fi%
		\fi%
	}
}