path: root/Master/texmf-dist/source/latex/tqft/tqft.dtx

% \iffalse meta-comment
%<*internal>
\iffalse
%</internal>
%<*readme>
----------------------------------------------------------------
tqft --- a style file for drawing TQFT diagrams with TikZ/PGF
E-mail: stacey@math.ntnu.no
Released under the LaTeX Project Public License v1.3c or later
See http://www.latex-project.org/lppl.txt
----------------------------------------------------------------

This package defines some node shapes useful for drawing TQFT diagrams with TikZ/PGF.
%</readme>
%<*internal>
\fi
\def\nameofplainTeX{plain}
\ifx\fmtname\nameofplainTeX\else
  \expandafter\begingroup
\fi
%</internal>
%<*install>
\input docstrip.tex
\keepsilent
\askforoverwritefalse
\preamble
----------------------------------------------------------------
tqft --- a style file for drawing TQFT diagrams with TikZ/PGF
E-mail: stacey@math.ntnu.no
Released under the LaTeX Project Public License v1.3c or later
See http://www.latex-project.org/lppl.txt
----------------------------------------------------------------

\endpreamble
\postamble

Copyright (C) 2011 by Andrew Stacey <stacey@math.ntnu.no>

This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License (LPPL), either
version 1.3c of this license or (at your option) any later
version.  The latest version of this license is in the file:

http://www.latex-project.org/lppl.txt

This work is "maintained" (as per LPPL maintenance status) by
Andrew Stacey.

This work consists of the file  tqft.dtx
and the derived files           tqft.ins,
                                tqft.pdf, and
                                tqft.sty.

\endpostamble
\usedir{tex/latex/tqft}
\generate{
  \file{\jobname.sty}{\from{\jobname.dtx}{package}}
}
%</install>
%<install>\endbatchfile
%<*internal>
\usedir{source/latex/tqft}
\generate{
  \file{\jobname.ins}{\from{\jobname.dtx}{install}}
}
\nopreamble\nopostamble
\usedir{doc/latex/demopkg}
\generate{
  \file{README.txt}{\from{\jobname.dtx}{readme}}
}
\ifx\fmtname\nameofplainTeX
  \expandafter\endbatchfile
\else
  \expandafter\endgroup
\fi
%</internal>
%<*package>
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tqft}[2011/05/03 v1.0 Tikz/PGF commands for drawing TQFT diagrams]
%</package>
%<*driver>
\documentclass{ltxdoc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
%\usepackage{morefloats}
\usepackage{tikz}
\usepackage{\jobname}
\usepackage[numbered]{hypdoc}
\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} 
 
\usepackage{listings}
\lstloadlanguages{[LaTeX]TeX}
\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
 
\usepackage{fancyvrb}
\EnableCrossrefs
\CodelineIndex
\RecordChanges
\begin{document}
  \DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
% \CheckSum{1595}
%
% \CharacterTable
%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%   Digits        \0\1\2\3\4\5\6\7\8\9
%   Exclamation   \!     Double quote  \"     Hash (number) \#
%   Dollar        \$     Percent       \%     Ampersand     \&
%   Acute accent  \'     Left paren    \(     Right paren   \)
%   Asterisk      \*     Plus          \+     Comma         \,
%   Minus         \-     Point         \.     Solidus       \/
%   Colon         \:     Semicolon     \;     Less than     \<
%   Equals        \=     Greater than  \>     Question mark \?
%   Commercial at \@     Left bracket  \[     Backslash     \\
%   Right bracket \]     Circumflex    \^     Underscore    \_
%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%   Right brace   \}     Tilde         \~}
%
%
% \changes{1.0}{2011/05/03}{Converted to DTX file}
%
% \DoNotIndex{\newcommand,\newenvironment}
%
% \providecommand*{\url}{\texttt}
% \GetFileInfo{tqft.dtx}
% \title{The \textsf{tqft} package: codebase}
% \author{Andrew Stacey \\ \url{stacey@math.ntnu.no}}
% \date{\fileversion~from \filedate}
%
% \maketitle
%
%
% \begin{tikzpicture}[every node/.style={tqft/cobordism style={draw,thick,red}}]
% \node[
%   tqft,
%   fill=orange,
%   fill opacity=.5,
%   boundary style={fill=purple},
%   cobordism style={draw,thick,red},
%   boundary lower style={draw,dashed,thick,blue},
%   boundary upper style={draw,green,thick},
%   incoming boundary components=4,
%   outgoing boundary components=6,
%   offset=-1.5,
% ] (a) {};
% \node[pin=north:1] at (a.incoming boundary 1) {};
% \node[pin=north:3] at (a.incoming boundary 3) {};
% \node[pin=south:1] at (a.outgoing boundary 1) {};
% \node[pin=south:4] at (a.outgoing boundary 4) {};
% \node[pin=south:6] at (a.outgoing boundary 6) {};
% \end{tikzpicture}
%
% \section{Introduction}
%
% This is a package for drawing TQFT diagrams using PGF/TikZ.
% Its inspiration was a question and answer on the website \url{http://tex.stackexchance.com}.
%
%
% \StopEventually{}
%
% \section{Implementation}
%
% \iffalse
%<*package>
% \fi
%    \begin{macrocode}
\RequirePackage{pgfkeys}
\RequirePackage{pgf}
%    \end{macrocode}
%
% We can view the cobordisms from the \emph{input} or \emph{output} ends, the implementation of the choice is to draw an arc from 0 to 180 or from 0 to -180 so we just need to track minus signs.
% These macros are for that.
%    \begin{macrocode}
\def\pgf@tqft@minus{-}
\let\pgf@tqft@upper\@empty
\let\pgf@tqft@lower\pgf@tqft@minus
%    \end{macrocode}
% Some helpful extra functions.
%
% \Verb+\tqftset+ is our equivalent of \Verb+\tikzset+.
%    \begin{macrocode}
\def\tqftset#1{\pgfkeys{/pgf/tqft/.cd,#1}}
%    \end{macrocode}
% \begin{macro}{\tqft@process}
% This macro applies our flow transformation to the given coordinates, % with the result stored in \Verb+\pgf@x+ and \Verb+\pgf@y+.
%    \begin{macrocode}
\def\tqft@process#1#2{%
  \edef\tqft@px{#1}
  \edef\tqft@py{#2}
  \pgf@process{
    \pgftransformreset
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
    \pgfpointtransformed{\pgfqpoint{\tqft@px}{\tqft@py}}
  }
}
%    \end{macrocode}
% \end{macro}
%
% Declare some dimension registers to hold the specifications of the cobordism.
%    \begin{macrocode}
\newdimen\tqft@xa
\newdimen\tqft@xb
\newdimen\tqft@c
\newdimen\tqft@ch
\newdimen\tqft@h
\newdimen\tqft@s
\newdimen\tqft@w
\newif\iftqft@within@node
%    \end{macrocode}
% Now we set up all the keys that we'll need in the course of this shape
%    \begin{macrocode}
\pgfkeys{
%    \end{macrocode}
% This key is our basic installer key, setting the shape and putting us in the right key family.
%    \begin{macrocode}
  /tikz/tqft/.style={%
    /tikz/shape=tqft cobordism,
    /pgf/tqft,
    /tikz/every tqft
  },
%    \end{macrocode}
% This deals with unknown keys, passing them on to TikZ.
%    \begin{macrocode}
  /pgf/tqft/.unknown/.code={%
    \let\tqft@searchname=\pgfkeyscurrentname%
    \pgfkeysalso{%
      /tikz/\tqft@searchname=#1
    }
  },
%    \end{macrocode}
% Here we have the standard \Verb+every something+ style.
%    \begin{macrocode}
  /tikz/every tqft/.style={},
%    \end{macrocode}
% We might get called in \Verb+/tikz+ or \Verb+/pgf+, this passes off anything in \Verb+/tikz/tqft+ to \Verb+/pgf/tqft+.
%    \begin{macrocode}
  /tikz/tqft/.unknown/.code={%
    \let\tqft@searchname=\pgfkeyscurrentname%
    \pgfkeysalso{%
      /pgf/tqft/\tqft@searchname=#1
    }
  },
%    \end{macrocode}
% Let's play happy families!
%    \begin{macrocode}
  /pgf/tqft/.is family,
  /pgf/tqft,
%    \end{macrocode}
% This sets our shape to be the boundary circle
%    \begin{macrocode}
  boundary circle/.style={
    /tikz/shape=tqft boundary circle
  },
%    \end{macrocode}
% These set our number of boundary components
%    \begin{macrocode}
  incoming boundary components/.initial=5,
  outgoing boundary components/.initial=4,
%    \end{macrocode}
% This is the ``horizontal'' offset of the first outgoing component from the first incoming one.
%    \begin{macrocode}
  offset/.initial=0,
%    \end{macrocode}
% This is the ``vertical'' separation between boundary components.
%    \begin{macrocode}
  cobordism height/.initial=2cm,
%    \end{macrocode}
% This is the ``horizontal'' separation between boundary components.
%    \begin{macrocode}
  boundary separation/.initial=2cm,
%    \end{macrocode}
% These are the ``horizontal'' and ``vertical'' radii, respectively, of the boundary components (perhaps poorly named!).
%    \begin{macrocode}
  circle width/.initial=10pt,
  circle depth/.initial=5pt,
%    \end{macrocode}
% These control the separation between the node and its anchors.
%    \begin{macrocode}
  outer xsep/.initial=0pt,
  outer ysep/.initial=0pt,
  outer sep/.style={
    outer xsep=#1,
    outer ysep=#1
  },
%    \end{macrocode}
% This is our flow control.  The \Verb+flow+ key installs a transformation to be applied to our node shape.
% The possible transformations are stored in the following keys.
% They aren't just rotations so that the numbering is always ``top to bottom'' or ``left to right''.
%    \begin{macrocode}
  flow/.code={%
    \pgfkeys{/pgf/tqft/flow transformation/.expand twice/.expand once=\pgfkeysvalueof{/pgf/tqft/flow transformation #1}}
  },
  flow transformation south/.initial={},
  flow transformation north/.initial={%
    xscale=-1,rotate=180
  },
  flow transformation east/.initial={%
    rotate=90,xscale=-1
  },
  flow transformation west/.initial={%
    rotate=270
  },
  flow transformation/.initial={},
%    \end{macrocode}
% These control the direction from which we view the cobordism.
%    \begin{macrocode}
  view from/.is choice,
  view from/incoming/.code={%
    \let\pgf@tqft@upper\pgf@tqft@minus
    \let\pgf@tqft@lower\@empty
  },
  view from/outgoing/.code={%
  \let\pgf@tqft@lower\pgf@tqft@minus
    \let\pgf@tqft@upper\@empty
  },
%    \end{macrocode}
% The next set of keys are for styling the different pieces of a cobordism.
%    \begin{macrocode}
  boundary lower style contents/.initial={},
  boundary lower style/.code={%
    \pgfkeys{/pgf/tqft/boundary lower style contents/.style={%
        /tikz/.cd,#1
      }
    }
  },
  boundary style contents/.initial={},
  boundary style/.code={%
    \pgfkeys{/pgf/tqft/boundary style contents/.style={%
        /tikz/.cd,#1
      }
    }
  },
  boundary upper style contents/.initial={},
  boundary upper style/.code={%
    \pgfkeys{/pgf/tqft/boundary upper style contents/.style={%
        /tikz/.cd,#1
      }
    }
  },
  cobordism style contents/.initial={},
  cobordism style/.code={%
    \pgfkeys{/pgf/tqft/cobordism style contents/.style={%
        /tikz/.cd,#1%
      }
    }
  },
%    \end{macrocode}
% The next set of keys define some default shapes.
%    \begin{macrocode}
  pair of pants/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=2,
    offset=-.5
  },
  /tikz/tqft pair of pants/.style={
    /pgf/tqft/pair of pants,
  },
  reverse pair of pants/.style={
    /tikz/tqft,
    incoming boundary components=2,
    outgoing boundary components=1,
    offset=.5
  },
  /tikz/tqft reverse pair of pants/.style={
    /pgf/tqft/reverse pair of pants,
  },
  cylinder to prior/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=1,
    offset=-.5
  },
  /tikz/tqft cylinder to prior/.style={
    /pgf/tqft/cylinder to prior,
  },
  cylinder to next/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=1,
    offset=.5
  },
  /tikz/tqft cylinder to next/.style={
    /pgf/tqft/cylinder to next,
  },
  cylinder/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=1
  },
  /tikz/tqft cylinder/.style={
    /pgf/tqft/cylinder,
  },
  cup/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=0
  },
  /tikz/tqft cup/.style={
    /pgf/tqft/cup,
  },
  cap/.style={
    /tikz/tqft,
    incoming boundary components=0,
    outgoing boundary components=1
  },
  /tikz/tqft cap/.style={
    /pgf/tqft/cap,
  },
}
%    \end{macrocode}
%
% \begin{macro}{tqft shape}
% This is a generic cobordism shape
%    \begin{macrocode}
\pgfdeclareshape{tqft cobordism}{
%    \end{macrocode}
% Save our specifications: incoming and outgoing boundary components
%    \begin{macrocode}
  \savedmacro{\tqft@incoming}{\edef\tqft@incoming{\pgfkeysvalueof{/pgf/tqft/incoming boundary components}}}
  \savedmacro{\tqft@outgoing}{\edef\tqft@outgoing{\pgfkeysvalueof{/pgf/tqft/outgoing boundary components}}}
%    \end{macrocode}
% and the offset (in units of boundary components) between the leading incoming and outgoing components (regarded as a shift of the outgoing components relative to the incoming)
%    \begin{macrocode}
  \savedmacro{\tqft@offset}{\edef\tqft@offset{\pgfkeysvalueof{/pgf/tqft/offset}}}
%    \end{macrocode}
% Now we save our dimensions: height, separation, the radii of the boundary circles, and outer seps, and the heights of the control points.
%    \begin{macrocode}
  \saveddimen{\tqft@height}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/cobordism height}}
  \saveddimen{\tqft@separation}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/boundary separation}}
  \saveddimen{\tqft@width}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle width}}
  \saveddimen{\tqft@depth}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle depth}}
  \saveddimen{\tqft@outerxsep}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/outer xsep}}
  \saveddimen{\tqft@outerysep}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/outer ysep}}
  \saveddimen{\tqft@control}{
  \pgfkeysgetvalue{/pgf/tqft/cobordism height}{\tqft@tempa}
  \pgfkeysgetvalue{/pgf/tqft/circle depth}{\tqft@tempb}
  \pgfmathsetlength{\pgf@x}{.5 * \tqft@tempa - 4 * \tqft@tempb}
}
%    \end{macrocode}
% This is the internal transformation that is in place
%    \begin{macrocode}
   \savedmacro{\tqft@transformation}{%
  \pgfkeysgetvalue{/pgf/tqft/flow transformation}{\tqft@transformation}
}
%    \end{macrocode}
% For the externally available anchors, we need to save a few things as well.
%
% Position of first incoming boundary in internal coordinates 
%    \begin{macrocode}
   \savedanchor{\tqft@start@incoming}{%
    \pgfmathsetlength{\pgf@x}{-(max(\pgfkeysvalueof{/pgf/tqft/incoming boundary components} - 1,\pgfkeysvalueof{/pgf/tqft/outgoing boundary components} - 1 + \pgfkeysvalueof{/pgf/tqft/offset}) + min(0,\pgfkeysvalueof{/pgf/tqft/offset}) )*\pgfkeysvalueof{/pgf/tqft/boundary separation}/2}
    \pgfmathsetlength{\pgf@y}{.5 * \pgfkeysvalueof{/pgf/tqft/cobordism height}}
}
%    \end{macrocode}
% Position of first outgoing boundary in internal coordinates 
%    \begin{macrocode}
   \savedanchor{\tqft@start@outgoing}{%
    \pgfmathsetlength{\pgf@x}{-(max(\pgfkeysvalueof{/pgf/tqft/incoming boundary components} - 1,\pgfkeysvalueof{/pgf/tqft/outgoing boundary components} - 1 + \pgfkeysvalueof{/pgf/tqft/offset}) + min(0,\pgfkeysvalueof{/pgf/tqft/offset})- 2*\pgfkeysvalueof{/pgf/tqft/offset})*\pgfkeysvalueof{/pgf/tqft/boundary separation}/2}
    \pgfmathsetlength{\pgf@y}{-.5 * \pgfkeysvalueof{/pgf/tqft/cobordism height}}
}
%    \end{macrocode}
% For completeness, we record the size of the text box (not that we expect any text, but you never know)
%    \begin{macrocode}
\savedanchor{\tqft@textsize}{%
  \pgf@y=-.5\ht\pgfnodeparttextbox%
  \pgf@x=-.5\wd\pgfnodeparttextbox%
}
%    \end{macrocode}
%
% These are our externally available anchors
%    \begin{macrocode}
  \anchor{centre}{\pgfpointorigin}
  \anchor{center}{\pgfpointorigin}
\anchor{text}{
  \tqft@textsize
}
\anchor{north}{%
  \pgf@ya=\tqft@height\relax
  \pgf@yb=.5\pgf@ya
  \advance\pgf@yb by \tqft@outerysep\relax
  \tqft@process{0pt}{\the\pgf@yb}
}
\anchor{south}{%
  \pgf@yb=\tqft@height\relax
  \pgf@ya=.5\pgf@yb
  \advance\pgf@ya by \tqft@outerysep\relax
  \pgf@yb=-\pgf@ya
  \tqft@process{0pt}{\the\pgf@yb}
}
\anchor{west}{%
  \tqft@start@incoming
  \pgf@xa=\pgf@x
  \advance\pgf@xa by -\tqft@width
  \pgf@ya=\pgf@y
  \tqft@start@outgoing
  \pgf@xb=\pgf@x
  \advance\pgf@xb by -\tqft@width
  \pgf@yb=\pgf@y
  \pgf@xc=.5\pgf@xa
  \advance\pgf@xc by .5\pgf@xb
  \pgf@yc=.5\pgf@ya
  \advance\pgf@yc by .5\pgf@yb
  \advance\pgf@xc by -\tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{east}{%
  \tqft@start@incoming
  \pgf@xa=\pgf@x
  \pgfmathsetlength{\pgf@xa}{\pgf@xa + (\tqft@incoming - 1) * \tqft@separation}
  \advance\pgf@xa by \tqft@width\relax
  \pgf@ya=\pgf@y
  \tqft@start@outgoing
  \pgf@xb=\pgf@x
  \pgfmathsetlength{\pgf@xb}{\pgf@xb + (\tqft@outgoing - 1) * \tqft@separation}
  \advance\pgf@xb by \tqft@width\relax
  \pgf@yb=\pgf@y
  \pgf@xc=.5\pgf@xa
  \advance\pgf@xc by .5\pgf@xb
  \pgf@yc=.5\pgf@ya
  \advance\pgf@yc by .5\pgf@yb
  \advance\pgf@xc by \tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{north west}{
  \tqft@start@incoming
  \pgf@xc=\pgf@x
  \pgf@yc=\pgf@y
  \advance\pgf@xc by -\tqft@width\relax
  \advance\pgf@yc by \tqft@outerysep\relax
  \advance\pgf@xc by -\tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{south west}{
  \tqft@start@outgoing
  \pgf@xc=\pgf@x
  \pgf@yc=\pgf@y
  \advance\pgf@xc by -\tqft@width\relax
  \advance\pgf@yc by -\tqft@outerysep\relax
  \advance\pgf@xc by -\tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{north east}{
  \tqft@start@incoming
  \pgf@xc=\pgf@x
  \pgfmathsetlength{\pgf@xc}{\pgf@xc + (\tqft@incoming - 1)*\tqft@separation}
  \pgf@yc=\pgf@y
  \advance\pgf@xc by \tqft@width\relax
  \advance\pgf@yc by \tqft@outerysep\relax
  \advance\pgf@xc by \tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{south east}{
  \tqft@start@outgoing
  \pgf@xc=\pgf@x
  \pgfmathsetlength{\pgf@xc}{\pgf@xc + (\tqft@outgoing - 1)*\tqft@separation}
  \pgf@yc=\pgf@y
  \advance\pgf@xc by \tqft@width\relax
  \advance\pgf@yc by -\tqft@outerysep\relax
  \advance\pgf@xc by \tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
%    \end{macrocode}
% To define anchors at the boundary components requires a bit of trickery borrowed from the ``regular polygon'' shape.
%    \begin{macrocode}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@incoming\relax%
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@incoming boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@incoming boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@incoming
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{\noexpand\pgf@y + \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - 1) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@outgoing\relax%
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@outgoing boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@outgoing boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@outgoing
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{\noexpand\pgf@y - \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - 1) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@incoming\relax%
  \advance\c@pgf@counta-1\relax
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@after incoming boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@after incoming boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@incoming
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{.25 * \noexpand\pgf@y +.75 * \noexpand\tqft@control + \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - .5) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@outgoing\relax%
  \advance\c@pgf@counta-1\relax
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@after outgoing boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@after outgoing boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@outgoing
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{.25 * \noexpand\pgf@y -.75 * \noexpand\tqft@control - \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - .5) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
%    \end{macrocode}
% Now we define the background path.
% This is the upper part of the cobordism.
%    \begin{macrocode}
  \backgroundpath{
%    \end{macrocode}
% Apply the internal transformation
%    \begin{macrocode}
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
%    \end{macrocode}
% Convert the boundary separation and width to lengths
%    \begin{macrocode}
    \pgfmathsetlength{\tqft@s}{\tqft@separation}
    \pgfmathsetlength{\tqft@w}{2*\tqft@width}
%    \end{macrocode}
% Compute the starting position of the incoming boundary components so that we get the centre anchor on the centre of the cobordism
%    \begin{macrocode}
\tqft@start@incoming
\tqft@xa=\pgf@x
    \advance\tqft@xa by -.5\tqft@w\relax
\tqft@h=\pgf@y
    \tqft@xb=\tqft@xa
    \advance\tqft@xb by \tqft@w\relax
\tqft@c=\tqft@control\relax
%    \end{macrocode}
% Do we have any incoming boundary components at all?
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
%    \end{macrocode}
% Yes, so move to the position of the first and draw it
%    \begin{macrocode}
    \pgfpathmoveto{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{\pgf@tqft@upper180}{0}{\tqft@width and \tqft@depth}
%    \end{macrocode}
% Do we have any more incoming boundary components?
%    \begin{macrocode}
   \ifnum\tqft@incoming>1
%    \end{macrocode}
% Yes, so iterate over the remaining incoming boundary components
%    \begin{macrocode}
    \foreach \tqft@k in {2,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \advance\tqft@xb by \tqft@k\tqft@s
     \advance\tqft@xb by -2\tqft@s
     \advance\tqft@xa by -\tqft@s
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{\pgf@tqft@upper180}{0}{\tqft@width and \tqft@depth}
    }
    \fi
%    \end{macrocode}
% If we don't have any outgoing boundary components, may as well close up now.
%    \begin{macrocode}
    \ifnum\tqft@outgoing=0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \fi
    \fi
%    \end{macrocode}
% Shift down to the outgoing components, if we have any
%    \begin{macrocode}
    \ifnum\tqft@outgoing>0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing - 1 + \tqft@offset) * \tqft@separation + 2*\tqft@width}
%    \end{macrocode}
% If we had incoming boundaries, this is a curveto, otherwise it's a moveto
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \else
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
     \tqft@xb=\tqft@xa
     \advance\tqft@xb by -\tqft@w
%    \end{macrocode}
% Now draw the lower components
%    \begin{macrocode}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
%    \end{macrocode}
% Now iterate over the remaining outgoing boundary components
%    \begin{macrocode}
    \ifnum\tqft@outgoing>1
    \foreach \tqft@k in {2,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \advance\tqft@xb by -\tqft@k\tqft@s
     \advance\tqft@xb by 2\tqft@s
     \advance\tqft@xa by \tqft@s
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
    }
    \fi
%    \end{macrocode}
% Shift back up to the incoming components, if we had any, otherwise arc back to our starting point
%    \begin{macrocode}
     \advance\tqft@xb by -\tqft@outgoing\tqft@s
     \advance\tqft@xb by \tqft@s
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa - (\tqft@outgoing -1 + \tqft@offset) * \tqft@separation - 2*\tqft@width}
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \else
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
    \fi
%    \end{macrocode}
% Close the path
%    \begin{macrocode}
     \pgfpathclose
  }
%    \end{macrocode}
% End of background path
% Now we define the behind background path.
% This is the lower part of the boundary circles.
%    \begin{macrocode}
  \behindbackgroundpath{
%    \end{macrocode}
% Apply the internal transformation
%    \begin{macrocode}
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
%    \end{macrocode}
% Convert the boundary separation and width to lengths
%    \begin{macrocode}
    \pgfmathsetlength{\tqft@s}{\tqft@separation}
    \pgfmathsetlength{\tqft@w}{2*\tqft@width}
%    \end{macrocode}
% Compute the starting position of the incoming boundary components so that we get the centre anchor on the centre of the cobordism
%    \begin{macrocode}
    \pgfmathsetlength{\tqft@xa}{-(max(\tqft@incoming - 1,\tqft@outgoing - 1 + \tqft@offset) + min(0,\tqft@offset) + 2)*\tqft@separation/2}
    \pgfmathsetlength{\tqft@h}{.5 * \tqft@height}
%    \end{macrocode}
% This section draws the boundary circles
%    \begin{macrocode}
    {
%    \end{macrocode}
% Initialise the TikZ path settings and read in the style options for the boundary
%    \begin{macrocode}
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{boundary style contents}
      \tikz@mode
      \tikz@options
%    \end{macrocode}
% Do we have any incoming boundary components at all?
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
%    \end{macrocode}
% Yes, so iterate over them
%    \begin{macrocode}
    \foreach \tqft@k in {1,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \pgfpathellipse{\pgfqpoint{\tqft@xa}{\tqft@h}}{\pgfqpoint{\tqft@width}{0pt}}{\pgfqpoint{0pt}{\tqft@depth}}
    }
    \fi
%    \end{macrocode}
% Now iterate over the outgoing boundary components, if we have any
%    \begin{macrocode}
    \ifnum\tqft@outgoing>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing + \tqft@offset + 1) * \tqft@separation}
    \foreach \tqft@k in {1,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
%     \advance\tqft@xa by \tqft@s
     \pgfpathellipse{\pgfqpoint{\tqft@xa}{-\tqft@h}}{\pgfqpoint{\tqft@width}{0pt}}{\pgfqpoint{0pt}{\tqft@depth}}
    }
    \fi
%    \end{macrocode}
%    \begin{macrocode}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
    }
%    \end{macrocode}
% This section draws the lower parts of the boundary circles
%    \begin{macrocode}
    {
%    \end{macrocode}
% Initialise the TikZ path settings and read in the style options for the boundary
%    \begin{macrocode}
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{boundary lower style contents}
      \tikz@mode
      \tikz@options
      \advance\tqft@xa by .5\tqft@w
%    \end{macrocode}
% Do we have any incoming boundary components at all?
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
%    \end{macrocode}
% Yes, so iterate over them
%    \begin{macrocode}
    \foreach \tqft@k in {1,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@lower180}{\tqft@width and \tqft@depth}
    }
    \fi
%    \end{macrocode}
% Now iterate over the outgoing boundary components, if we have any
%    \begin{macrocode}
    \ifnum\tqft@outgoing>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing + \tqft@offset + 1) * \tqft@separation}
    \foreach \tqft@k in {1,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
%     \advance\tqft@xa by \tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@lower180}{\tqft@width and \tqft@depth}
    }
    \fi
%    \end{macrocode}
%    \begin{macrocode}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
    }
  }
%    \end{macrocode}
% End of behind background path.
%
% Now we define the before background path.
% This is the upper part of the boundary circles and the cobordism edge.
%    \begin{macrocode}
  \beforebackgroundpath{
%    \end{macrocode}
% We \emph{don't} apply the internal transformation as it is already in place from the \Verb+\backgroundpath+.
% Convert the boundary separation and width to lengths
%    \begin{macrocode}
    \pgfmathsetlength{\tqft@s}{\tqft@separation}
    \pgfmathsetlength{\tqft@w}{2*\tqft@width}
%    \end{macrocode}
% Compute the starting position of the incoming boundary components so that we get the centre anchor on the centre of the cobordism
%    \begin{macrocode}
    \pgfmathsetlength{\tqft@xa}{-(max(\tqft@incoming - 1,\tqft@outgoing - 1 + \tqft@offset) + min(0,\tqft@offset))*\tqft@s/2 - \tqft@width}
    \tqft@xb=\tqft@xa
    \advance\tqft@xb by \tqft@w
\tqft@c=\tqft@control\relax
    \pgfmathsetlength{\tqft@h}{.5 * \tqft@height}
%    \end{macrocode}
% This section draws the non-boundary part of the cobordism.
%    \begin{macrocode}
   {
%    \end{macrocode}
% Initialise the TikZ path settings and read in the style options for the boundary
%    \begin{macrocode}
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{cobordism style contents}
      \tikz@mode
      \tikz@options
% Do we have any incoming boundary components at all?
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
%    \end{macrocode}
% Do we have more than one?
%    \begin{macrocode}
   \ifnum\tqft@incoming>1
%    \end{macrocode}
% Yes, so iterate over the remaining incoming boundary components
%    \begin{macrocode}
    \foreach \tqft@k in {2,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \advance\tqft@xb by \tqft@k\tqft@s
     \advance\tqft@xb by -2\tqft@s
     \advance\tqft@xa by -\tqft@s
    \pgfpathmoveto{\pgfqpoint{\tqft@xb}{\tqft@h}}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    }
    \fi
%    \end{macrocode}
% If we don't have any outgoing boundary components, may as well close up now.
%    \begin{macrocode}
    \ifnum\tqft@outgoing=0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
    \pgfpathmoveto{\pgfqpoint{\tqft@xb}{\tqft@h}}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \fi
    \fi
%    \end{macrocode}
% Shift down to the outgoing components, if we have any
%    \begin{macrocode}
    \ifnum\tqft@outgoing>0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing - 1 + \tqft@offset) * \tqft@separation + 2*\tqft@width}
%    \end{macrocode}
% If we had incoming boundaries, this is a curveto, otherwise it's a moveto
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathmoveto{\pgfqpoint{\tqft@xb}{\tqft@h}}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \else
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
     \tqft@xb=\tqft@xa
     \advance\tqft@xb by -\tqft@w
%    \end{macrocode}
% Now draw the lower components
%    \begin{macrocode}
     \pgfpathmoveto{\pgfqpoint{\tqft@xb}{-\tqft@h}}
%    \end{macrocode}
% Now iterate over the remaining outgoing boundary components
%    \begin{macrocode}
    \ifnum\tqft@outgoing>1
    \foreach \tqft@k in {2,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \advance\tqft@xb by -\tqft@k\tqft@s
     \advance\tqft@xb by 2\tqft@s
     \advance\tqft@xa by \tqft@s
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \advance\tqft@xa by -\tqft@w
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    }
    \fi
%    \end{macrocode}
% Shift back up to the incoming components, if we had any, otherwise arc back to our starting point
%    \begin{macrocode}
     \advance\tqft@xb by -\tqft@outgoing\tqft@s
     \advance\tqft@xb by \tqft@s
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa - (\tqft@outgoing -1 + \tqft@offset) * \tqft@separation - 2*\tqft@width}
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \else
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
    \fi
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
}
%    \end{macrocode}
% This section draws the upper parts of the boundary circles
%    \begin{macrocode}
    {
%    \end{macrocode}
% Initialise the TikZ path settings and read in the style options for the boundary
%    \begin{macrocode}
\let\tqft@bdry@path=\pgfutil@empty
\let\tqft@bdry@node@path=\pgfutil@empty
\pgfsyssoftpath@setcurrentpath{\tqft@bdry@path}
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{boundary upper style contents}
      \tikz@mode
      \tikz@options
      \advance\tqft@xa by -\tqft@s
      \advance\tqft@xa by \tqft@w
%    \end{macrocode}
% Do we have any incoming boundary components at all?
%    \begin{macrocode}
    \ifnum\tqft@incoming>0
%    \end{macrocode}
% Yes, so iterate over them
%    \begin{macrocode}
    \foreach \tqft@k in {1,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
  \ifx\tikz@fig@name\pgfutil@empty
  \else
  {
    \advance\tqft@xa by -\tqft@width
    \pgftransformshift{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \tqft@within@nodetrue
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@node@path}
    \pgfnode{tqft boundary circle}{centre}{}{\tikz@fig@name\space incoming \tqft@k}{}
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@node@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@path}
  }
  \fi
    }
    \fi
%    \end{macrocode}
% Now iterate over the outgoing boundary components, if we have any
%    \begin{macrocode}
    \ifnum\tqft@outgoing>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing + \tqft@offset + 1) * \tqft@separation}
    \foreach \tqft@k in {1,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
%     \advance\tqft@xa by \tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
  \ifx\tikz@fig@name\pgfutil@empty
  \else
  {
    \pgfmathtruncatemacro{\tqft@l}{\tqft@outgoing + 1 - \tqft@k}
    \advance\tqft@xa by -\tqft@width
    \pgftransformshift{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \tqft@within@nodetrue
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@node@path}
    \pgfnode{tqft boundary circle}{centre}{}{\tikz@fig@name\space outgoing \tqft@l}{}
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@node@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@path}
  }
  \fi
    }
    \fi
%    \end{macrocode}
%    \begin{macrocode}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
    }
  }
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{boundary circle shape}
% This is a the shape of the boundary circles
%    \begin{macrocode}
\pgfdeclareshape{tqft boundary circle}{
%    \end{macrocode}
% Now we save our dimensions: height, separation, and the radii of the boundary circles
%    \begin{macrocode}
  \saveddimen{\tqft@height}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/cobordism height}}
  \saveddimen{\tqft@separation}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/boundary separation}}
  \saveddimen{\tqft@width}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle width}}
  \saveddimen{\tqft@depth}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle depth}}
%    \end{macrocode}
%
% For the externally available anchors, we need to save the declared transformation; we save the actual transformation, not the macro that points to it.
% If we're called within the main cobordism shape, the transformation is already applied so we ignore it.
%    \begin{macrocode}
   \savedmacro{\tqft@transformation}{%
  \iftqft@within@node
  \let\tqft@transformation=\pgfutil@empty
  \else
  \pgfkeysgetvalue{/pgf/tqft/flow transformation}{\tqft@transformation}
  \fi
}
%    \end{macrocode}
%    \begin{macrocode}
   \savedanchor{\tqft@centre}{%
  \pgfpointorigin}
%    \end{macrocode}
% For completeness, we record the size of the text box (not that we expect any text, but you never know)
%    \begin{macrocode}
\savedanchor{\tqft@textsize}{%
  \pgf@y=-.5\ht\pgfnodeparttextbox%
  \pgf@x=-.5\wd\pgfnodeparttextbox%
}
%    \end{macrocode}
% These are our externally available anchors
%    \begin{macrocode}
  \anchor{centre}{\tqft@centre}
  \anchor{center}{\tqft@centre}
\anchor{text}{
  \tqft@textsize
}
  \anchor{next}{%
  \tqft@process{\tqft@separation}{0pt}}%
%    \end{macrocode}
%    \begin{macrocode}
  \anchor{prior}{%
  \tqft@process{-\tqft@separation}{0pt}}%
%    \end{macrocode}
%    \begin{macrocode}
  \anchor{above}{%
  \tqft@process{0pt}{\tqft@height}}%
%    \end{macrocode}
%    \begin{macrocode}
  \anchor{below}{%
  \tqft@process{0pt}{-\tqft@height}}%
%    \end{macrocode}
% The anchor border is the ellipse, but we need to take into account the possible transformation.
% (This isn't right if the origin is shifted.)
% At the moment, '0 degrees' is interpreted in the transformed coordinate system.
% Should provide a system whereby that can be intepreted in the main coordinate system.
%    \begin{macrocode}
  \anchorborder{
%    \end{macrocode}
% This next \Verb+\pgf@process+ makes the angles absolute.
% Comment it out to make the angles relative.
%    \begin{macrocode}
  \tqft@process{\the\pgf@x}{\the\pgf@y}
  \edef\tqft@marshal{%
    \noexpand\pgfpointborderellipse
    {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
    {\noexpand\pgfqpoint{\tqft@width}{\tqft@depth}}
  }%
  \tqft@marshal
  \tqft@process{\the\pgf@x}{\the\pgf@y}
}
%    \end{macrocode}
% Now we define the background path.
% This is the upper part of the cobordism.
%    \begin{macrocode}
  \backgroundpath{
%    \end{macrocode}
% Apply the internal transformation if we're not within a node
%    \begin{macrocode}
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
%    \end{macrocode}
% Draw the boundary circle
%    \begin{macrocode}
  \pgfpathellipse{\pgfqpoint{0pt}{0pt}}{\pgfqpoint{\tqft@width}{0pt}}{\pgfqpoint{0pt}{\tqft@depth}}
  } 
%    \end{macrocode}
% We draw the upper and lower arcs again with the appropriate styles
%    \begin{macrocode}
  \beforebackgroundpath{
  \iftqft@within@node
  \else
    \tikz@mode@fillfalse%
    \tikz@mode@drawfalse%
    \let\tikz@mode=\pgfutil@empty
    \let\tikz@options=\pgfutil@empty
    {
    \pgfsys@beginscope
      \tqftset{boundary lower style contents}
      \tikz@mode
      \tikz@options
      \pgfpathmoveto{\pgfqpoint{\tqft@width}{0pt}}
      \pgfpatharc{0}{\pgf@tqft@lower180}{\tqft@width and \tqft@depth}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
      \pgfsys@endscope
    }
    {
      \pgfsys@beginscope
      \tqftset{boundary upper style contents}
      \tikz@mode
      \tikz@options
      \pgfpathmoveto{\pgfqpoint{\tqft@width}{0pt}}
      \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
      \pgfsys@endscope
    }
    \fi
  }
  }
%    \end{macrocode}
% \end{macro}
% \iffalse
%</package>
% \fi
%
% \Finale

\endinput