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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/tqft
Initial commit
Diffstat (limited to 'macros/latex/contrib/tqft')
-rw-r--r--macros/latex/contrib/tqft/README.txt9
-rw-r--r--macros/latex/contrib/tqft/tqft.dtx2146
-rw-r--r--macros/latex/contrib/tqft/tqft.pdfbin0 -> 460464 bytes
-rw-r--r--macros/latex/contrib/tqft/tqft_code.pdfbin0 -> 281351 bytes
-rw-r--r--macros/latex/contrib/tqft/tqft_doc.tex987
5 files changed, 3142 insertions, 0 deletions
diff --git a/macros/latex/contrib/tqft/README.txt b/macros/latex/contrib/tqft/README.txt
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--- /dev/null
+++ b/macros/latex/contrib/tqft/README.txt
@@ -0,0 +1,9 @@
+----------------------------------------------------------------
+tqft --- a library 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 shapes useful for drawing TQFT diagrams with TikZ/PGF.
+
diff --git a/macros/latex/contrib/tqft/tqft.dtx b/macros/latex/contrib/tqft/tqft.dtx
new file mode 100644
index 0000000000..dc471eed3d
--- /dev/null
+++ b/macros/latex/contrib/tqft/tqft.dtx
@@ -0,0 +1,2146 @@
+% \iffalse meta-comment
+%<*internal>
+\iffalse
+%</internal>
+%<*readme>
+----------------------------------------------------------------
+tqft --- a library 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 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 library for drawing TQFT diagrams with TikZ/PGF
+E-mail: loopspace@mathforge.org
+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 <loopspace@mathforge.org>
+
+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 files tqft.dtx,
+ tqft_doc.tex,
+and the derived files tqft.ins,
+ tqft.pdf,
+ tqft_doc.pdf,
+ tqft.sty, and
+ tikzlibrarytqft.code.tex.
+
+\endpostamble
+\usedir{tex/latex/tqft}
+\generate{
+ \file{\jobname.sty}{\from{\jobname.dtx}{package}}
+}
+\usedir{tex/latex/tqft}
+\generate{
+ \file{tikzlibrary\jobname.code.tex}{\from{\jobname.dtx}{library}}
+}
+%</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}[2017/06/01 v2.1 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{2577}
+%
+% \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}
+% \changes{2.0}{2014/04/07}{Converted nodes to pics}
+% \changes{2.1}{2017/06/01}{Can skip boundary components}
+%
+% \DoNotIndex{\newcommand,\newenvironment}
+%
+% \providecommand*{\url}{\texttt}
+% \GetFileInfo{tqft.dtx}
+% \title{The \textsf{tqft} package: codebase}
+% \author{Andrew Stacey \\ \url{loopspace@mathforge.org}}
+%
+% \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}
+%
+% \subsection{Old Version: Node Shapes}
+%
+% \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}
+% Add a key to switch between the two versions.
+% \begin{macrocode}
+ /tikz/tqft/use nodes/.is choice,
+ /tikz/tqft/use nodes/true/.code={%
+ \tikzset{
+% \end{macrocode}
+% If using nodes, set the defaults
+% \begin{macrocode}
+ tqft/.style={%
+ /tikz/shape=tqft cobordism,
+ /pgf/tqft,
+ /tikz/every tqft/.try
+ },
+% \end{macrocode}
+% Unknowns go to \Verb+/pgf/tqft+
+% \begin{macrocode}
+ tqft/.unknown/.code={%
+ \let\tqft@searchname=\pgfkeyscurrentname%
+ \pgfkeys{%
+ /pgf/tqft/\tqft@searchname={##1}
+ }
+ },
+ }%
+ },
+% \end{macrocode}
+% If not using nodes, set the defaults for the library
+% \begin{macrocode}
+ /tikz/tqft/use nodes/false/.code={%
+ \tikzset{
+ tqft/.style={%
+ pic type=cobordism,
+ tqft/.cd,
+ every tqft/.try,
+ },
+% \end{macrocode}
+% Pass unknown keys on to TikZ.
+% \begin{macrocode}
+ tqft/.unknown/.code={%
+ \let\tqft@searchname=\pgfkeyscurrentname%
+ \pgfkeys{%
+ /tikz/\tqft@searchname={##1}
+ }
+ },
+ }%
+ },
+ /tikz/tqft/use nodes=true,
+% \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}
+% 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
+%
+% \subsection{New Version: Picture Shapes}
+%
+% \iffalse
+%<*library>
+% \fi
+%
+% Issue a warning if the pic syntax is not available.
+%
+% \begin{macrocode}
+\ifcsname pgfk@/handlers/.pic/.@cmd\endcsname
+\else
+\pgfwarning{This library only works with TikZ 3.0 or later; for earlier versions of TikZ use the TQFT package}
+\fi
+% \end{macrocode}
+% For the boundaries, we need elliptical node shapes.
+% \begin{macrocode}
+\usetikzlibrary{shapes.geometric}
+% \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}
+% Split an anchoring coordinate.
+% The \(y\)--value is simply multiplied by the cobordism height (but pointing downwards, so that \(1\) is level with the outgoing boundary).
+% The \(x\)--value is multiplied by the boundary separation, but is shifted so that at the incoming boundary level, or above, then it is in line with the incoming boundaries and similarly at the outgoing boundary level, or below, it is in line with the outgoing boundaries.
+% \begin{macrocode}
+\def\tqft@split(#1,#2){%
+ \pgfmathsetmacro\tqft@y{#2 * (-\tqft@val{cobordism height})}%
+ \pgfmathsetmacro\tqft@x{(#1 - 1 + max(min(#2,1),0)*\tqft@val{offset}) * \tqft@val{boundary separation}}%
+ \def\tqft@shift{(\tqft@x pt, \tqft@y pt)}%
+}%
+% \end{macrocode}
+% Now we set up all the keys that we'll need in the course of this shape
+% \begin{macrocode}
+\tikzset{
+% \end{macrocode}
+% Fix for the fact that the \verb+alias+ key doesn't use the prefix and suffix.
+% \begin{macrocode}
+ pic alias/.code={%
+ \tikz@fig@mustbenamed
+ \expandafter\def\expandafter\tikz@alias\expandafter{\tikz@alias\pgfnodealias{\tikz@pp@name{#1}}{\tikz@fig@name}}%
+ },
+% \end{macrocode}
+% This key is our basic installer key, setting the pic and putting us in the right key family.
+% \begin{macrocode}
+ tqft/.style={%
+ pic type=cobordism,
+ every tqft/.try,
+ tqft/.cd,
+ },
+% \end{macrocode}
+% This deals with unknown keys, passing them on to TikZ.
+% \begin{macrocode}
+ tqft/.unknown/.code={%
+ \let\tqft@searchname=\pgfkeyscurrentname%
+ \pgfkeysalso{%
+ /tikz/\tqft@searchname={#1}
+ }
+ },
+% \end{macrocode}
+% Let's play happy families!
+% \begin{macrocode}
+ tqft/.cd,
+% \end{macrocode}
+% These set our number of boundary components and genus.
+% \begin{macrocode}
+ incoming boundary components/.initial=5,
+ outgoing boundary components/.initial=4,
+ skip incoming boundary components/.initial={},
+ skip outgoing boundary components/.initial={},
+ genus/.initial = 0,
+% \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.
+% \begin{macrocode}
+ circle x radius/.initial=10pt,
+ circle y radius/.initial=5pt,
+% \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}
+% We simulate node placement using the following key.
+% \begin{macrocode}
+ anchor/.initial = none,
+% \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={
+ /tikz/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={
+ /tikz/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={
+ /tikz/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={
+ /tikz/tqft/cylinder to next,
+ },
+ cylinder/.style={
+ /tikz/tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1
+ },
+ /tikz/tqft cylinder/.style={
+ /tikz/tqft/cylinder,
+ },
+ cup/.style={
+ /tikz/tqft,
+ incoming boundary components=1,
+ outgoing boundary components=0
+ },
+ /tikz/tqft cup/.style={
+ /tikz/tqft/cup,
+ },
+ cap/.style={
+ /tikz/tqft,
+ incoming boundary components=0,
+ outgoing boundary components=1
+ },
+ /tikz/tqft cap/.style={
+ /tikz/tqft/cap,
+ },
+}
+% \end{macrocode}
+%
+% This is a little helper macro for getting the values of tqft keys.
+% \begin{macrocode}
+\def\tqft@val#1{\pgfkeysvalueof{/tikz/tqft/#1}}
+% \end{macrocode}
+%
+% Now we define the code for the actual cobordism shape.
+% \begin{macrocode}
+\tikzset{
+ cobordism/.pic={
+% \end{macrocode}
+% Defining the cobordism paths.
+% This holds the full boundary path of the cobordism shape.
+% \begin{macrocode}
+ \gdef\tqft@fullpath{}%
+% \end{macrocode}
+% This is a list of the edge pieces without the boundary circles.
+% \begin{macrocode}
+ \global\let\tqft@blist\pgfutil@gobble%
+% \end{macrocode}
+% This punches the holes (if there are any) in the cobordism shape.
+% \begin{macrocode}
+ \gdef\tqft@gclip{}%
+% \end{macrocode}
+% This is a list of the paths for drawing the holes.
+% \begin{macrocode}
+ \global\let\tqft@glist\pgfutil@gobble%
+% \end{macrocode}
+% This collects any coordinates that are to be defined (it appears to be difficult to define them as we go along).
+% \begin{macrocode}
+ \global\let\tqft@clist\pgfutil@gobble%
+% \end{macrocode}
+% This collects any coordinates that can be used to shift the shape that aren't to be defined using \verb+\tqft@clist+.
+% \begin{macrocode}
+ \global\let\tqft@alist\pgfutil@gobble
+% \end{macrocode}
+% These will be lists of the boundary components, divided into sets as to whether or not they are rendered. For the outgoing ones, we need too lists because they are rendered in the opposite order to how they are labelled.
+% \begin{macrocode}
+ \global\let\tqft@ibdrylist=\pgfutil@gobble
+ \global\let\tqft@cibdrylist=\pgfutil@gobble
+ \global\let\tqft@obdrylist=\pgfutil@gobble
+ \global\let\tqft@cobdrylist=\pgfutil@gobble
+ \global\let\tqft@robdrylist=\pgfutil@gobble
+ \global\let\tqft@rcobdrylist=\pgfutil@gobble
+% \end{macrocode}
+% The first stage is to iterate over the incoming boundary components (if there are any), building up the various paths.
+% \begin{macrocode}
+ \ifnum\tqft@val{incoming boundary components}>0\relax
+% \end{macrocode}
+% We have some so draw the half circle for the first component.
+% Note that we use \verb+\pgf@tqft@upper+ to flip the sign of the start angle depending on the \verb+view from+ setting.
+% \begin{macrocode}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ (-\tqft@val{circle x radius},0) arc[start angle=\pgf@tqft@upper180, end angle=0, x radius=\tqft@val{circle x radius}, y radius=\tqft@val{circle y radius}]
+ }%
+% \end{macrocode}
+% And add the centre to the list for available shifts.
+% \begin{macrocode}
+ \xdef\tqft@alist{%
+ \tqft@alist,-incoming boundary 1/{(0,0)},-incoming boundary/{(0,0)}%
+ }%
+% \end{macrocode}
+% If there are more than one then for each subsequent one we add the curve between them and the corresponding arc of the boundary circle.
+% \begin{macrocode}
+ \ifnum\tqft@val{incoming boundary components}>1\relax
+ \foreach \k in {2,...,\tqft@val{incoming boundary components}} {
+ \edef\tqft@temp{\noexpand\pgfutil@in@{,\k,}{,\tqft@val{skip incoming boundary components},}}
+ \tqft@temp
+ \ifpgfutil@in@
+ \xdef\tqft@cibdrylist{\tqft@cibdrylist,\k}
+ \else
+ \xdef\tqft@ibdrylist{\tqft@ibdrylist,\k}
+ \fi
+ }
+ \ifx\tqft@ibdrylist\pgfutil@gobble
+ \else
+ \foreach \k [
+ remember=\k as \kmo (initially 1),
+ evaluate=\k as \xpos using (\k-1)*\tqft@val{boundary separation} -\tqft@val{circle x radius},
+ ] in \tqft@ibdrylist {
+ \pgfmathsetmacro\xppos{(\kmo - 1)*\tqft@val{boundary separation} + \tqft@val{circle x radius}}
+ \pgfmathsetmacro\cpos{(\xpos + \xppos)/2}
+% \end{macrocode}
+% Add the curve and the arc.
+% \begin{macrocode}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ .. controls +(0,-\tqft@val{cobordism height}/3) and +(0,-\tqft@val{cobordism height}/3) .. (\xpos pt,0) arc[start angle=\pgf@tqft@upper180, end angle=0, x radius=\tqft@val{circle x radius}, y radius=\tqft@val{circle y radius}]
+ }%
+% \end{macrocode}
+% But for the edge path, just add the curve to the list.
+% \begin{macrocode}
+ \xdef\tqft@blist{%
+ \tqft@blist,incoming boundary \k/incoming/{%
+ (\xppos pt,0) .. controls +(0,-\tqft@val{cobordism height}/3) and +(0,-\tqft@val{cobordism height}/3) .. (\xpos pt,0)}%
+ }%
+% \end{macrocode}
+% We add a coordinate at the midpoint of the curve.
+% \begin{macrocode}
+ \xdef\tqft@clist{%
+ \tqft@clist,-between incoming \kmo\space and \k/{(\cpos pt,-\tqft@val{cobordism height}/4)}%
+ }%
+% \end{macrocode}
+% And add the centre to the list for available shifts.
+% \begin{macrocode}
+ \xdef\tqft@alist{%
+ \tqft@alist,-incoming boundary \k/{(\kmo * \tqft@val{boundary separation},0)}%
+ }%
+ }%
+ \fi
+ \fi
+% \end{macrocode}
+% We're at the edge of the last incoming boundary component.
+% What we do now depends on whether or not there are outgoing boundary components.
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>0\relax
+% \end{macrocode}
+% There are, so we add a curve from the end of the last incoming to the last outgoing component to the full path,
+% \begin{macrocode}
+ \pgfmathsetmacro\xppos{(\tqft@val{outgoing boundary components} -1+\tqft@val{offset}) * \tqft@val{boundary separation} +\tqft@val{circle x radius}}%
+ \pgfmathsetmacro\tqft@ht{abs(\tqft@val{incoming boundary components} - \tqft@val{outgoing boundary components} - \tqft@val{offset})}%
+ \pgfmathsetmacro\tqft@ht{1/3 + 2/3*\tqft@ht/(\tqft@ht + 1)}%
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ .. controls +(0,-\tqft@ht*\tqft@val{cobordism height}) and +(0,\tqft@ht*\tqft@val{cobordism height}) .. (\xppos pt, -\tqft@val{cobordism height})
+ }%
+% \end{macrocode}
+% and the edge path.
+% \begin{macrocode}
+ \xdef\tqft@blist{%
+ \tqft@blist,between last incoming and last outgoing/incoming and outgoing/{%
+ (\tqft@val{incoming boundary components} * \tqft@val{boundary separation} + \tqft@val{circle x radius} - \tqft@val{boundary separation},0pt)
+ .. controls +(0,-\tqft@ht*\tqft@val{cobordism height}) and +(0,\tqft@ht*\tqft@val{cobordism height}) .. (\xppos pt, -\tqft@val{cobordism height})}%
+ }%
+% \end{macrocode}
+% In addition, we add a coordinate at the midpoint.
+% \begin{macrocode}
+ \pgfmathsetmacro\xppos{(\xppos + (\tqft@val{incoming boundary components} -1) * \tqft@val{boundary separation} +\tqft@val{circle x radius})/2}%
+ \xdef\tqft@clist{%
+ \tqft@clist,-between last incoming and last outgoing/{(\xppos pt,-\tqft@val{cobordism height}/2)}%
+ }%
+ \else
+% \end{macrocode}
+% There aren't any outgoing boundary components so we loop back to the start.
+% We adjust the height of the control points to take into account the overall width.
+% \begin{macrocode}
+ \pgfmathsetmacro\tqft@ht{1/3 + 2/3*(\tqft@val{incoming boundary components} - 1)/\tqft@val{incoming boundary components}}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ .. controls +(0,-\tqft@ht*\tqft@val{cobordism height}) and +(0,-\tqft@ht*\tqft@val{cobordism height}) .. (-\tqft@val{circle x radius},0)
+ }%
+% \end{macrocode}
+% Same for the edge path.
+% \begin{macrocode}
+ \xdef\tqft@blist{%
+ \tqft@blist,between first incoming and last incoming/incoming and outgoing/{%
+ (\tqft@val{incoming boundary components} * \tqft@val{boundary separation} + \tqft@val{circle x radius} - \tqft@val{boundary separation},0pt)
+ .. controls +(0,-\tqft@ht*\tqft@val{cobordism height}) and +(0,-\tqft@ht*\tqft@val{cobordism height}) .. (-\tqft@val{circle x radius},0)}
+ }%
+% \end{macrocode}
+% Add a coordinate at the midpoint.
+% \begin{macrocode}
+ \pgfmathsetmacro\xppos{(\tqft@val{incoming boundary components} -1) * \tqft@val{boundary separation}/2}%
+ \xdef\tqft@clist{%
+ \tqft@clist,-between first incoming and last incoming/{(\xppos pt,-\tqft@ht*\tqft@val{cobordism height}*3/4)}%
+ }%
+ \fi
+ \else
+% \end{macrocode}
+% There weren't any incoming boundary components, so we test to see if there were any outgoing ones and move to the start of them.
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>0\relax
+ \pgfmathsetmacro\xppos{(\tqft@val{outgoing boundary components} -1+\tqft@val{offset}) * \tqft@val{boundary separation} +\tqft@val{circle x radius}}
+% \end{macrocode}
+% Add a move to the full path,
+% \begin{macrocode}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ (\xppos pt, -\tqft@val{cobordism height})
+ }%
+ \fi
+ \fi
+% \end{macrocode}
+% We're done with the incoming boundary components, now we're set up for the outgoing ones.
+% However we got there, if we have outgoing boundary components then we're now located at the start of them, although we're counting backwards.
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>0\relax
+ \pgfmathsetmacro\xppos{(\tqft@val{outgoing boundary components} -1+\tqft@val{offset}) * \tqft@val{boundary separation} -\tqft@val{circle x radius}}%
+% \end{macrocode}
+% Draw the arc for the first (well, last actually) boundary component.
+% \begin{macrocode}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ arc[end angle=\pgf@tqft@upper180, start angle=0, x radius=\tqft@val{circle x radius}, y radius=\tqft@val{circle y radius}]
+ }%
+% \end{macrocode}
+% And add the centre to the list for available shifts.
+% \begin{macrocode}
+ \xdef\tqft@alist{%
+ \tqft@alist,-outgoing boundary \tqft@val{outgoing boundary components}/{(\xppos pt + \tqft@val{circle x radius},-\tqft@val{cobordism height})},-outgoing boundary/{(\tqft@val{offset}*\tqft@val{boundary separation},-\tqft@val{cobordism height})}%
+ }%
+% \end{macrocode}
+% Do we have more than one boundary component?
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>1\relax
+% \end{macrocode}
+% Yes, so add a curve and arc for each.
+% \begin{macrocode}
+ \foreach \k [evaluate=\k as \ok using int(\tqft@val{outgoing boundary components} - \k + 1)] in {2,...,\tqft@val{outgoing boundary components}} {
+ \edef\tqft@temp{\noexpand\pgfutil@in@{,\ok,}{,\tqft@val{skip outgoing boundary components},}}
+ \tqft@temp
+ \ifpgfutil@in@
+ \xdef\tqft@cobdrylist{\tqft@cobdrylist,\k}
+ \else
+ \xdef\tqft@obdrylist{\tqft@obdrylist,\k}
+ \fi
+ }
+ \ifx\tqft@obdrylist\pgfutil@gobble
+ \else
+ \foreach \k [
+ remember=\k as \kmo (initially 1),
+ evaluate=\k as \xpos using (\tqft@val{outgoing boundary components} - \k + \tqft@val{offset})*\tqft@val{boundary separation} + \tqft@val{circle x radius},
+ ] in \tqft@obdrylist {
+ \pgfmathsetmacro\xppos{(\tqft@val{outgoing boundary components} - \kmo + \tqft@val{offset})*\tqft@val{boundary separation} - \tqft@val{circle x radius}}
+ \pgfmathsetmacro\cpos{(\xpos + \xppos)/2}
+ \pgfmathsetmacro\nk{int(\tqft@val{outgoing boundary components} - \k + 1)}
+ \pgfmathsetmacro\nkpo{int(\tqft@val{outgoing boundary components} - \kmo + 1)}
+% \end{macrocode}
+% Both are added to the full path.
+% \begin{macrocode}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ .. controls +(0,\tqft@val{cobordism height}/3) and +(0,\tqft@val{cobordism height}/3) .. (\xpos pt,-\tqft@val{cobordism height}) arc[end angle=\pgf@tqft@upper180, start angle=0, x radius=\tqft@val{circle x radius}, y radius=\tqft@val{circle y radius}]
+ }%
+% \end{macrocode}
+% Just the arc for the edge paths.
+% \begin{macrocode}
+ \xdef\tqft@blist{%
+ \tqft@blist,between outgoing \nk\space and \nkpo/outgoing/{%
+ (\xppos pt,-\tqft@val{cobordism height})
+ .. controls +(0,\tqft@val{cobordism height}/3) and +(0,\tqft@val{cobordism height}/3) .. (\xpos pt,-\tqft@val{cobordism height}) ++(-2*\tqft@val{circle x radius},0)}%
+ }%
+% \end{macrocode}
+% And a coordinate at the midpoint.
+% \begin{macrocode}
+ \xdef\tqft@clist{%
+ \tqft@clist,-between outgoing \nk\space and \nkpo/{(\cpos pt,-3*\tqft@val{cobordism height}/4)}%
+ }%
+% \end{macrocode}
+% And add the centre to the list for available shifts.
+% \begin{macrocode}
+ \xdef\tqft@alist{%
+ \tqft@alist,-outgoing boundary \nk/{(\xpos pt - \tqft@val{circle x radius},-\tqft@val{cobordism height})}%
+ }%
+ }%
+ \fi
+ \fi
+% \end{macrocode}
+% Now we're at the end of the outgoing boundary components (well, the start actually).
+% What we do now depends on whether or not there are any incoming boundary components.
+% \begin{macrocode}
+ \ifnum\tqft@val{incoming boundary components}>0\relax
+% \end{macrocode}
+% There are, so we draw the path back up.
+% \begin{macrocode}
+ \pgfmathsetmacro\tqft@ht{1/3 + 2/3*abs(\tqft@val{offset})/(abs(\tqft@val{offset}) + 1)}%
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ .. controls +(0,\tqft@ht*\tqft@val{cobordism height}) and +(0,-\tqft@ht*\tqft@val{cobordism height}) .. (-\tqft@val{circle x radius},0)
+ }%
+% \end{macrocode}
+% And the edge path does the same.
+% \begin{macrocode}
+ \xdef\tqft@blist{%
+ \tqft@blist,between first incoming and first outgoing/incoming and outgoing/{%
+ (\tqft@val{offset} * \tqft@val{boundary separation} - \tqft@val{circle x radius},-\tqft@val{cobordism height})
+ .. controls +(0,\tqft@ht*\tqft@val{cobordism height}) and +(0,-\tqft@ht*\tqft@val{cobordism height}) .. (-\tqft@val{circle x radius},0)}%
+ }%
+% \end{macrocode}
+% Add a coordinate at the midpoint.
+% \begin{macrocode}
+ \xdef\tqft@clist{%
+ \tqft@clist,-between first incoming and first outgoing/{(\tqft@val{offset}*\tqft@val{boundary separation}/2-\tqft@val{circle x radius},-\tqft@val{cobordism height}/2)}%
+ }%
+ \else
+% \end{macrocode}
+% No incoming boundary components so loop back to the other end of the outgoing boundary components.
+% \begin{macrocode}
+ \pgfmathsetmacro\xppos{(\tqft@val{outgoing boundary components} -1+\tqft@val{offset}) * \tqft@val{boundary separation} +\tqft@val{circle x radius}}%
+ \pgfmathsetmacro\tqft@ht{1/3 + 2/3*(\tqft@val{outgoing boundary components} - 1)/\tqft@val{outgoing boundary components}}
+% \end{macrocode}
+% Full path.
+% \begin{macrocode}
+ \xdef\tqft@fullpath{%
+ \tqft@fullpath
+ .. controls +(0,\tqft@ht*\tqft@val{cobordism height}) and +(0,\tqft@ht*\tqft@val{cobordism height}) .. (\xppos pt,-\tqft@val{cobordism height})
+ }%
+% \end{macrocode}
+% Edge path.
+% \begin{macrocode}
+ \xdef\tqft@blist{%
+ \tqft@blist,between first and last outgoing/incoming and outgoing/{%
+ (\tqft@val{offset} * \tqft@val{boundary separation} - \tqft@val{circle x radius},-\tqft@val{cobordism height})
+ .. controls +(0,\tqft@ht*\tqft@val{cobordism height}) and +(0,\tqft@ht*\tqft@val{cobordism height}) .. (\xppos pt,-\tqft@val{cobordism height})}%
+ }%
+% \end{macrocode}
+% Add a coordinate at the midpoint.
+% \begin{macrocode}
+ \pgfmathsetmacro\xppos{(\tqft@val{outgoing boundary components}/2 + \tqft@val{offset} -1/2) * \tqft@val{boundary separation}}%
+ \pgfmathsetmacro\tqft@ht{1 -\tqft@ht*3/4}%
+ \xdef\tqft@clist{%
+ \tqft@clist,-between first and last outgoing/{(\xppos pt,-\tqft@ht*\tqft@val{cobordism height})}%
+ }%
+ \fi
+ \fi
+% \end{macrocode}
+% Now we define the clip path for the genus holes.
+% We start with a big rectangle that \emph{ought} to be big enough to contain the whole shape.
+% We start with the top left corner.
+% \begin{macrocode}
+ \pgfmathsetmacro\xpos{%
+ (
+ \tqft@val{outgoing boundary components} > 0 ?
+ (
+ \tqft@val{incoming boundary components} > 0 ?
+ min(0,\tqft@val{offset}) : \tqft@val{offset}
+ ) : 0
+ )
+ *\tqft@val{boundary separation} - 2*\tqft@val{circle x radius}}%
+ \xdef\tqft@gclip{(\xpos pt,2*\tqft@val{circle y radius}) rectangle }%
+% \end{macrocode}
+% Now the bottom right.
+% \begin{macrocode}
+ \pgfmathsetmacro\xpos{%
+ ((
+ \tqft@val{outgoing boundary components} > 0 ?
+ (
+ \tqft@val{incoming boundary components} > 0 ?
+ max(\tqft@val{incoming boundary components},\tqft@val{outgoing boundary components} + \tqft@val{offset}) : \tqft@val{outgoing boundary components} + \tqft@val{offset}
+ ) : \tqft@val{incoming boundary components}
+ )-1)
+ *\tqft@val{boundary separation} + 2*\tqft@val{circle x radius}}%
+% \end{macrocode}
+% Together, these make a rectangle.
+% \begin{macrocode}
+ \xdef\tqft@gclip{\tqft@gclip (\xpos pt,-\tqft@val{cobordism height} - 2*\tqft@val{circle y radius})}%
+% \end{macrocode}
+% Are there any holes?
+% \begin{macrocode}
+ \ifnum\tqft@val{genus}>0\relax
+% \end{macrocode}
+% Yes, so first we need to figure out where to place them.
+% We work out the left-hand edge of the cobordism.
+% \begin{macrocode}
+ \pgfmathsetmacro\xpos{%
+ (
+ \tqft@val{outgoing boundary components} > 0 ?
+ (
+ \tqft@val{incoming boundary components} > 0 ?
+ \tqft@val{offset}/2 : \tqft@val{offset}
+ ) : 0
+ )
+ *\tqft@val{boundary separation} - \tqft@val{circle x radius}}%
+% \end{macrocode}
+% Work out the height that the holes should be punched at.
+% \begin{macrocode}
+ \pgfmathsetmacro\ypos{%
+ (
+ \tqft@val{outgoing boundary components} > 0 ?
+ (
+ \tqft@val{incoming boundary components} > 0 ?
+ -\tqft@val{cobordism height}/2 : -1 + \tqft@val{cobordism height}/3
+ ) : - \tqft@val{cobordism height}/3
+ )}%
+% \end{macrocode}
+% Start our clip path at this point
+% \begin{macrocode}
+ \xdef\tqft@gclip{%
+ \tqft@gclip
+ (\xpos pt,\ypos pt)
+ }%
+% \end{macrocode}
+% Now work out the width of the cobordism, in units of circle half-widths.
+% This may not be very accurate if there aren't any boundary components of a given type.
+% \begin{macrocode}
+ \pgfmathsetmacro\gsize{%
+ ((
+ \tqft@val{outgoing boundary components} > 0 ?
+ (
+ \tqft@val{incoming boundary components} > 0 ?
+ (\tqft@val{incoming boundary components} + \tqft@val{outgoing boundary components})/2 : \tqft@val{outgoing boundary components}
+ ) : \tqft@val{incoming boundary components}
+ )-1)
+ *\tqft@val{boundary separation}/\tqft@val{circle x radius} + 2}%
+% \end{macrocode}
+% Each hole should take up three half-widths, but we want a little extra on the edges so the total number of half-widths we want is \(3g + 1\).
+% Do we need to scale down the holes (we never scale up)?
+% If so, \verb+\gscale+ holds the overall scale factor and \verb+\gxscale+ and \verb+gyscale+ are the resulting horizontal and vertical measurements.
+% The baseline is the size of the boundary circles.
+% \begin{macrocode}
+ \pgfmathsetmacro\gscale{min(1,\gsize/(3*\tqft@val{genus}+1))}%
+ \pgfmathsetmacro\gyscale{\tqft@val{circle y radius}*\gscale*.707}%
+ \pgfmathsetmacro\gxscale{\tqft@val{circle x radius}*\gscale}%
+% \end{macrocode}
+% Each hole should take up 2 half widths, modulo scaling, so the total width used by the holes is \(2 g s\) leaving \(w - 2 g s\) left for the gaps which is divided in to \(g + 1\) lots.
+% \begin{macrocode}
+ \pgfmathsetmacro\gsep{((\gsize - 2*\tqft@val{genus}*\gscale)/(\tqft@val{genus} + 1)*\tqft@val{circle x radius}}%
+% \end{macrocode}
+% We shift in by half of one unit of excess separation.
+% \begin{macrocode}
+ \xdef\tqft@gclip{%
+ \tqft@gclip
+ ++(\gsep/2 pt,0)
+ }%
+% \end{macrocode}
+% Some useful quantities.
+% \begin{macrocode}
+ \pgfmathsetmacro\omrstwo{1 - 1/sqrt(2)}%
+ \pgfmathsetmacro\sqrtwo{sqrt(2)}%
+% \end{macrocode}
+% Now we iterate over the holes.
+% \begin{macrocode}
+ \foreach[
+ evaluate=\k as \kmo using int(2 * \k-1)
+ ] \k in {1,...,\tqft@val{genus}} {
+% \end{macrocode}
+% For the clipping path, we just want the bare hole.
+% \begin{macrocode}
+ \xdef\tqft@gclip{%
+ \tqft@gclip
+% \end{macrocode}
+% Move in by half an excess separation unit and move to the left-hand extent of the hole.
+% \begin{macrocode}
+ ++(\gsep/2 pt + \omrstwo*\gxscale pt,0)
+% \end{macrocode}
+% Now curve up over the hole,
+% \begin{macrocode}
+ .. controls +(\gxscale*\sqrtwo/3 pt,4/3*\gyscale pt) and +(-\gxscale*\sqrtwo/3 pt,4/3*\gyscale pt)
+ .. ++(\sqrtwo*\gxscale pt,0)
+% \end{macrocode}
+% and return on the underside.
+% \begin{macrocode}
+ .. controls +(-\gxscale*\sqrtwo/3 pt,-4/3*\gyscale pt) and +(\gxscale*\sqrtwo/3 pt,-4/3*\gyscale pt)
+ .. ++(-\sqrtwo*\gxscale pt,0)
+% \end{macrocode}
+% Lastly, move to the right-hand edge of the space taken up by this hole.
+% \begin{macrocode}
+ ++(2*\gxscale pt -\omrstwo*\gxscale pt + \gsep/2 pt,0)
+ }
+% \end{macrocode}
+% For the genus \emph{path} we want to add the little ``tails'' which means that the two curves are different, and we need to take into acount the \verb+view from+ direction.
+% \begin{macrocode}
+ \xdef\tqft@glist{%
+ \tqft@glist,%
+ hole \k/lower/{%
+% \end{macrocode}
+% Move to the starting point of the smaller curve and add that.
+% \begin{macrocode}
+ (\xpos pt + \k * \gsep pt + \kmo * \gxscale pt + \gxscale pt -\omrstwo*\gxscale pt,\ypos pt)
+ .. controls +(-\gxscale pt*\sqrtwo/3,\pgf@tqft@upper4/3*\gyscale pt) and +(\gxscale pt*\sqrtwo/3,\pgf@tqft@upper4/3*\gyscale pt)
+ .. ++(-\sqrtwo*\gxscale pt,0)},%
+% Move to the left-hand corner of the path, with the upper or lower chosen by the \verb+view from+ direction.
+ hole \k/upper/{(\xpos pt + \k * \gsep pt + \kmo * \gxscale pt - \gxscale pt,\ypos pt + \pgf@tqft@upper\gyscale pt)%
+% \end{macrocode}
+% Add the larger of the two curves.
+% \begin{macrocode}
+ .. controls +(\gxscale pt*2/3,\pgf@tqft@lower8/3*\gyscale pt) and +(-\gxscale pt*2/3,\pgf@tqft@lower8/3*\gyscale pt)
+ .. ++(2*\gxscale pt,0)}%
+ }%
+% \end{macrocode}
+% Add a coordinate at the centre of the hole.
+% \begin{macrocode}
+ \xdef\tqft@clist{%
+ \tqft@clist,-hole \k/{(\xpos pt + \k * \gsep pt + \kmo * \gxscale pt,\ypos pt)}%
+ }%
+ }%
+ \fi
+% \end{macrocode}
+% Now we start to lay out the cobordism
+% Were we given a shift? If so, shift.
+% \begin{macrocode}
+\gdef\tqft@shift{(0,0)}%
+\edef\tqft@anchor{\tqft@val{anchor}}%
+\expandafter\pgfutil@in@\expandafter{\expandafter,\expandafter}\expandafter{\tqft@anchor}%
+\ifpgfutil@in@
+\expandafter\tqft@split\tqft@anchor\relax
+\else
+\edef\tqft@anchor{-\tqft@val{anchor}}%
+\xdef\tqft@alist{\tqft@clist,\tqft@alist}%
+\foreach \anchor/\coord in \tqft@alist
+{
+ \ifx\anchor\tqft@anchor\relax
+ \global\let\tqft@shift\coord
+ \fi
+}%
+\fi
+\tikz@scan@one@point\pgfutil@firstofone\tqft@shift\relax
+\begin{scope}[shift={(-\pgf@x,-\pgf@y)}]
+% \end{macrocode}
+% At each incoming boundary component we place an elliptical node of the right size.
+% \begin{macrocode}
+\ifnum\tqft@val{incoming boundary components}>0\relax
+\ifx\tqft@ibdrylist\pgfutil@gobble
+\xdef\tqft@ibdrylist{1}
+\else
+\xdef\tqft@ibdrylist{1,\tqft@ibdrylist}
+\fi
+ \foreach[evaluate=\k as \xpos using (\k-1)*\tqft@val{boundary separation}] \k in \tqft@ibdrylist {
+ \node[
+ node contents={},
+ ellipse,
+ inner sep=0pt,
+ outer sep=0pt,
+ minimum width=2*\tqft@val{circle x radius},
+ minimum height=2*\tqft@val{circle y radius},
+ at={(\xpos pt,0)},
+ name=-incoming boundary \k,
+ /tikz/tqft/every boundary component/.try,
+ /tikz/tqft/every incoming boundary component/.try,
+ /tikz/tqft/incoming boundary component \k/.try
+ ];
+ }%
+\ifx\tqft@cibdrylist\pgfutil@gobble
+\else
+ \foreach[evaluate=\k as \xpos using (\k-1)*\tqft@val{boundary separation}] \k in \tqft@cibdrylist {
+ \node[
+ node contents={},
+ ellipse,
+ inner sep=0pt,
+ outer sep=0pt,
+ minimum width=2*\tqft@val{circle x radius},
+ minimum height=2*\tqft@val{circle y radius},
+ at={(\xpos pt,0)},
+ name=-incoming boundary \k,
+ /tikz/tqft/every skipped boundary component/.try,
+ /tikz/tqft/every skipped incoming boundary component/.try,
+ /tikz/tqft/skipped incoming boundary component \k/.try,
+ ];
+}%
+\fi
+% \end{macrocode}
+% Add an alias for the first.
+% \begin{macrocode}
+ \path node also[pic alias=-incoming boundary] (-incoming boundary 1);
+ \fi
+% \end{macrocode}
+% Same for the outgoing boundary components.
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>0\relax
+\ifx\tqft@obdrylist\pgfutil@gobble
+\xdef\tqft@obdrylist{1}
+\else
+\xdef\tqft@obdrylist{1,\tqft@obdrylist}
+\fi
+\foreach \k [evaluate=\k as \ok using int(\tqft@val{outgoing boundary components} - \k + 1)] in \tqft@obdrylist {
+ \xdef\tqft@robdrylist{\tqft@robdrylist,\ok}
+}
+ \foreach[
+ evaluate=\k as \xpos using (\k-1+\tqft@val{offset})*\tqft@val{boundary separation}
+ ] \k in \tqft@robdrylist {
+ \node[
+ node contents={},
+ ellipse,
+ inner sep=0pt,
+ outer sep=0pt,
+ minimum width=2*\tqft@val{circle x radius},
+ minimum height=2*\tqft@val{circle y radius},
+ at={(\xpos pt,-\tqft@val{cobordism height})},
+ name=-outgoing boundary \k,
+ /tikz/tqft/every boundary component/.try,
+ /tikz/tqft/every outgoing boundary component/.try,
+ /tikz/tqft/outgoing boundary component \k/.try
+ ];
+}%
+\ifx\tqft@cobdrylist\pgfutil@gobble
+\else
+\foreach \k [evaluate=\k as \ok using int(\tqft@val{outgoing boundary components} - \k + 1)] in \tqft@cobdrylist {
+ \xdef\tqft@rcobdrylist{\tqft@rcobdrylist,\ok}
+}
+ \foreach[
+ evaluate=\k as \xpos using (\k-1+\tqft@val{offset})*\tqft@val{boundary separation}
+ ] \k in \tqft@rcobdrylist {
+ \node[
+ node contents={},
+ ellipse,
+ inner sep=0pt,
+ outer sep=0pt,
+ minimum width=2*\tqft@val{circle x radius},
+ minimum height=2*\tqft@val{circle y radius},
+ at={(\xpos pt,-\tqft@val{cobordism height})},
+ name=-outgoing boundary \k,
+ /tikz/tqft/every skipped boundary component/.try,
+ /tikz/tqft/every skipped outgoing boundary component/.try,
+ /tikz/tqft/skipped outgoing boundary component \k/.try
+ ];
+ }%
+\fi
+% \end{macrocode}
+% Add an alias for the first.
+% \begin{macrocode}
+ \path node also[pic alias=-outgoing boundary] (-outgoing boundary 1);
+ \fi
+% \end{macrocode}
+% Now we draw the lower paths of the incoming boundary components.
+% \begin{macrocode}
+ \ifnum\tqft@val{incoming boundary components}>0\relax
+ \foreach[evaluate=\k as \xpos using (\k-1)*\tqft@val{boundary separation}] \k in \tqft@ibdrylist {
+ \path[
+ /tikz/tqft/every lower boundary component/.try,
+ /tikz/tqft/every incoming lower boundary component/.try,
+ /tikz/tqft/incoming lower boundary component \k/.try
+ ] (\xpos pt - \tqft@val{circle x radius},0) arc[start angle=\pgf@tqft@lower180,end angle=0, x radius=\tqft@val{circle x radius}, y radius =\tqft@val{circle y radius}];
+ }%
+ \fi
+% \end{macrocode}
+% Same for the outgoing boundary components.
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>0\relax
+ \foreach[
+ evaluate=\k as \xpos using (\k-1+\tqft@val{offset})*\tqft@val{boundary separation}
+ ] \k in \tqft@robdrylist {
+ \path[
+ /tikz/tqft/every lower boundary component/.try,
+ /tikz/tqft/every outgoing lower boundary component/.try,
+ /tikz/tqft/outgoing lower boundary component \k/.try
+ ] (\xpos pt - \tqft@val{circle x radius},-\tqft@val{cobordism height}) arc[start angle=\pgf@tqft@lower180,end angle=0, x radius=\tqft@val{circle x radius}, y radius =\tqft@val{circle y radius}];
+ }%
+ \fi
+% \end{macrocode}
+% Full outer path, clipped against the genus holes in case it is filled.
+% \begin{macrocode}
+ \begin{scope}
+ \path[overlay,clip] \tqft@gclip;
+ \path[
+ /tikz/tqft/cobordism/.try,
+ pic actions,
+ /tikz/tqft/cobordism outer path/.try,
+ ] \tqft@fullpath;
+ \end{scope}
+% \end{macrocode}
+% Now we draw the genus path, outside the clip.
+% We view this as part of the full cobordism path so try to apply the same style as for the full path, but if that is filled then we turn the fill off.
+% It can be turned back on again using the styles \verb+cobordism edge+ or \verb+genus style+.
+% We also apply the \verb+cobordism edge+ style as it could be thought of as part of the non-boundary edge.
+% Finally, it has its own style to enable overrides if the other two get confused.
+% \begin{macrocode}
+\ifx\tqft@glist\pgfutil@gobble
+\else
+\foreach \tqft@gstyle/\tqft@gside/\tqft@gpath in \tqft@glist {
+ \path[
+ /tikz/tqft/cobordism/.try,
+ pic actions,
+ fill=none,
+ shade=none,
+ /tikz/tqft/cobordism edge/.try,
+ /tikz/tqft/genus style/.try,
+ /tikz/tqft/genus \tqft@gside/.try,
+ /tikz/tqft/\tqft@gstyle/.try,
+ /tikz/tqft/\tqft@gstyle\space\tqft@gside/.try,
+ ] \tqft@gpath;
+}
+\fi
+% \end{macrocode}
+% Now we redraw the non-boundary paths.
+% \begin{macrocode}
+\ifx\tqft@blist\pgfutil@gobble
+\else
+\foreach \tqft@bstyle/\tqft@btype/\tqft@bpath in \tqft@blist {
+ \path[
+ /tikz/tqft/cobordism edge/.try,
+ /tikz/tqft/cobordism outer edge/.try,
+ /tikz/tqft/between \tqft@btype/.try,
+ /tikz/tqft/\tqft@bstyle/.try,
+ ] \tqft@bpath;
+}
+\fi
+% \end{macrocode}
+% There were various coordinates that we wanted to define but couldn't.
+% Here, we put those in place.
+% \begin{macrocode}
+ \ifx\tqft@clist\pgfutil@gobble
+ \else
+ \foreach \name/\coord in \tqft@clist {
+ \path \coord node[coordinate,node contents={},name=\name];
+ }
+ \fi
+% \end{macrocode}
+% The last task is to draw the upper paths of the boundary components.
+% First, incoming.
+% \begin{macrocode}
+ \ifnum\tqft@val{incoming boundary components}>0\relax
+ \foreach[evaluate=\k as \xpos using (\k-1)*\tqft@val{boundary separation}] \k in \tqft@ibdrylist {
+ \path[
+ /tikz/tqft/every upper boundary component/.try,
+ /tikz/tqft/every incoming upper boundary component/.try,
+ /tikz/tqft/incoming upper boundary component \k/.try
+ ] (\xpos pt - \tqft@val{circle x radius},0) arc[start angle=\pgf@tqft@upper180,end angle=0, x radius=\tqft@val{circle x radius}, y radius =\tqft@val{circle y radius}];
+ }
+ \fi
+% \end{macrocode}
+% Next, outgoing.
+% \begin{macrocode}
+ \ifnum\tqft@val{outgoing boundary components}>0\relax
+ \foreach[
+ evaluate=\k as \xpos using (\k-1+\tqft@val{offset})*\tqft@val{boundary separation}
+ ] \k in \tqft@robdrylist {
+ \path[
+ /tikz/tqft/every upper boundary component/.try,
+ /tikz/tqft/every outgoing upper boundary component/.try,
+ /tikz/tqft/outgoing upper boundary component \k/.try
+ ] (\xpos pt - \tqft@val{circle x radius},-\tqft@val{cobordism height}) arc[start angle=\pgf@tqft@upper180,end angle=0, x radius=\tqft@val{circle x radius}, y radius =\tqft@val{circle y radius}];
+ }
+ \fi
+\end{scope}
+% \end{macrocode}
+% We're done!
+% Phew.
+% \begin{macrocode}
+ }
+}
+% \end{macrocode}
+%
+% \iffalse
+%</library>
+% \fi
+% \Finale
+
+\endinput
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@@ -0,0 +1,987 @@
+\documentclass{ltxdoc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage{morefloats}
+\usepackage[svgnames]{xcolor}
+\usepackage{tikz}
+\usepackage{tqft}
+\usetikzlibrary{tqft}
+\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}
+
+\newenvironment{example}
+ {\VerbatimEnvironment
+ \begin{VerbatimOut}{example.out}}
+ {\end{VerbatimOut}
+ \begin{center}
+ \setlength{\parindent}{0pt}
+ \fbox{\begin{minipage}{.9\linewidth}
+ \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
+ \lstinputlisting[]{example.out}
+ \end{minipage}}
+
+ \fbox{\begin{minipage}{.9\linewidth}
+ \centering
+ \input{example.out}
+ \end{minipage}}
+\end{center}
+}
+
+\providecommand*{\url}{\texttt}
+\GetFileInfo{tqft.sty}
+
+
+\title{The \textsf{tqft} Ti\emph{k}Z Library: Documentation}
+\author{Andrew Stacey \\ \url{loopspace@mathforge.org}}
+
+\begin{document}
+
+\maketitle
+
+\begin{center}
+\begin{tikzpicture}[
+ scale=.5,
+ every tqft/.style={
+ transform shape
+ },
+ tqft/cobordism/.style={
+ fill=DarkMagenta,
+ draw,
+ ultra thick},
+ ]
+ \pic[
+ name=a,
+ tqft,
+ incoming boundary components=0,
+ outgoing boundary components=3,
+ ];
+ \pic[
+ name=b,
+ at=(a-outgoing boundary 2),
+ tqft cylinder,
+ anchor=incoming boundary 1,
+ ];
+ \pic[
+ at=(a-outgoing boundary 3),
+ name=c,
+ tqft,
+ incoming boundary components=0,
+ outgoing boundary components=2,
+ anchor={(0,1)},
+ ];
+ \pic[
+ at=(c-outgoing boundary 1),
+ name=d,
+ tqft,
+ incoming boundary components=3,
+ outgoing boundary components=1,
+ offset=2.5,
+ anchor=incoming boundary 1,
+ boundary separation=1cm,
+ cobordism height=2.5cm,
+ ];
+ \pic[
+ at=(c-outgoing boundary 2),
+ name=e,
+ tqft,
+ rotate=90,
+ incoming boundary components=0,
+ outgoing boundary components=3,
+ anchor={(2,-.5)}
+ ];
+ \pic[
+ at=(e-outgoing boundary 3),
+ name=f,
+ tqft cylinder,
+ rotate=90,
+ anchor=incoming boundary 1,
+ ];
+ \pic[
+ at=(e-outgoing boundary 2),
+ name=g,
+ tqft cylinder,
+ rotate=90,
+ anchor=incoming boundary 1,
+ ];
+ \pic[
+ at=(g-outgoing boundary 1),
+ name=h,
+ tqft,
+ anchor={(0,1)},
+ incoming boundary components=0,
+ outgoing boundary components=3,
+ ];
+ \pic[
+ at=(h-outgoing boundary 2),
+ name=i,
+ tqft cylinder,
+ anchor=incoming boundary 1,
+ ];
+\end{tikzpicture}
+\end{center}
+
+\section{Introduction}
+This package defines some Ti\emph{k}Z/PGF picture shapes that can be used to construct the diagrams common in Topological Quantum Field Theory (TQFT).
+An example follows:
+
+\begin{example}
+\begin{tikzpicture}[tqft/cobordism/.style={draw}]
+\pic[tqft/pair of pants,name=a];
+\pic[tqft/cylinder to next,anchor=incoming boundary 1,name=c,at=(a-outgoing boundary 1)];
+\pic[tqft/reverse pair of pants, anchor=incoming boundary 1,at=(a-outgoing boundary 2)];
+\end{tikzpicture}
+\end{example}
+
+\tableofcontents
+
+\section{History}
+
+This is the second version of the TQFT package.
+The first version used nodes to draw the shapes.
+However, with the advent of Ti\emph{k}Z3.0 came the ability to define subdrawings called \Verb+pic+s which were a bit like nodes but were geared more towards drawings than containers for text.
+This seems a much more suitable mechanism for drawing these diagrams and so the package has been rewritten to make use of this new facility.
+
+The second version is designed to be similar to the first, but with some improvements.
+The original version was distributed as a \Verb+.sty+ file and so is loaded using \Verb+\usepackage{tqft}+.
+The newer version is a Ti\emph{k}Z library and so is loaded using \Verb+\usetikzlibrary{tqft}+.
+This makes it possible to use both in the same document.
+This is not recommended, but an attempt has been made to make it possible to switch between the two methods.
+This hasn't been extensively tested so use with caution.
+To make the switch use the key \Verb+/tikz/tqft/use nodes=<true|false>+.
+By default, the one loaded last should be in effect at the start of the document.
+
+\section{Keys}
+
+Before giving any details, a word is in order about the keys involved in this package.
+There are many options and keys that can be set via the \Verb+\pgfkeys+ system (which is used for setting options in Ti\emph{k}Z).
+Such keys live in a ``directory'' but often that can be omitted.
+For example, in the Ti\emph{k}Z command \Verb+\draw[red] (0,0) -- (1,0);+ the key \Verb+red+ is actually in the ``directory'' \Verb+/tikz+ but it is not necessary to specify that as it is assumed.
+Defining a ``directory'' helps separate keys and ensure that there is no conflict.
+The keys in this library are (mostly) defined in the directories \Verb+/tikz/tqft+ (the newer version) and \Verb+/pgf/tqft+ (the old version).
+
+Invoking \Verb+/tikz/tqft+ itself sets the ``current directory'' to whichever directory is right for the current version in force and so all subsequent keys do not need prefixing.
+Moreover, any unknown keys are passed on to the \Verb+/tikz+ directory so there is (or should be!) no harm in mixing \Verb+tqft+ specific keys with ordinary Ti\emph{k}Z keys.
+Some examples take advantage of this switch so when copying and modifying examples from this document, it is important to remember that the first \Verb+tqft+ specific key needs an explicit \Verb+tqft/+ prefix.
+
+
+\section{Version 2.0}
+
+\subsection{The Shapes}
+
+There is only one picture shape: \Verb+cobordism+.
+This is a cobordism between a number of incoming circles and a number of outgoing circles, where the numbers of boundary components can be specified as options to the shape.
+There are certain common shapes that are predefined as aliases to the main shape with specified boundaries.
+The list of predefined shapes follows.
+The names are all in the \Verb+tqft+ family, but an alias is made so that \Verb+tqft <shape>+ will work without any further qualification.
+
+\begin{enumerate}
+\item \Verb+pair of pants+
+
+\begin{tikzpicture}
+\pic[draw,tqft/pair of pants];
+\end{tikzpicture}
+
+\item \Verb+reverse pair of pants+
+
+\begin{tikzpicture}
+\pic[draw,tqft/reverse pair of pants];
+\end{tikzpicture}
+
+\item \Verb+cylinder to prior+
+
+This is a cylinder that has been skewed to one side, thus following the same path as the \Verb+pair of pants+ cobordism but with only one outgoing boundary component.
+The name \Verb+to prior+ is because it goes towards the lower-numbered component on the \Verb+pair of pants+.
+
+\begin{tikzpicture}
+\pic[draw,tqft/cylinder to prior];
+\end{tikzpicture}
+
+\item \Verb+cylinder to next+
+
+This is a cylinder that has been skewed to one side, thus following the same path as the \Verb+pair of pants+ cobordism but with only one outgoing boundary component.
+The name \Verb+to next+ is because it goes towards the higher-numbered component on the \Verb+pair of pants+.
+
+\begin{tikzpicture}
+\pic[draw,tqft/cylinder to next];
+\end{tikzpicture}
+
+\item \Verb+cylinder+
+
+This is a straight cylinder.
+
+\begin{tikzpicture}
+\pic[draw,tqft/cylinder];
+\end{tikzpicture}
+
+\item \Verb+cap+
+
+This is a cap.
+
+\begin{tikzpicture}
+\pic[draw,tqft/cap];
+\end{tikzpicture}
+
+\item \Verb+cup+
+
+This is a cup (an upside-down cap).
+
+\begin{tikzpicture}
+\pic[draw,tqft/cup];
+\end{tikzpicture}
+
+\end{enumerate}
+
+The general shape is controlled by the following keys:
+
+\begin{itemize}
+\item \DescribeMacro{view from} To get a simulated 3D effect, the cobordism is drawn as if viewed from a slight angle.
+The value of this key determines whether the cobordism is viewed from the direction of the incoming boundary components or the outgoing ones.
+This key can take the values \Verb+incoming+ and \Verb+outgoing+.
+The default is \Verb+outgoing+.
+\item \DescribeMacro{cobordism height} This is the height of the cobordism (``height'' interpreted in its own internal coordinate system).
+With no offset (q.v.), this would be the distance between the centres of the first incoming and first outgoing boundary components.
+
+\item \DescribeMacro{boundary separation} This is the distance between the centres of the boundary components of the same type.
+
+\item \DescribeMacro{circle x radius} This is the half-width of the boundary circles.
+
+\item \DescribeMacro{circle y radius} This is the half-depth of the boundary circles (``depth'' since, in the internal coordinate system, this corresponds to the \(z\)-axis out of the page).
+
+\item \DescribeMacro{incoming boundary components} The number of incoming boundary components (can be zero).
+
+\item \DescribeMacro{skip incoming boundary components} A list of incoming boundary components to be skipped.
+
+\item \DescribeMacro{outgoing boundary components} The number of outgoing boundary components (can be zero).
+
+\item \DescribeMacro{skip outgoing boundary components} A list of outgoing boundary components to be skipped.
+
+\item \DescribeMacro{offset} This offsets the first outgoing boundary component horizontally relative to the first incoming boundary component.
+It is a dimensionless number (not necessarily an integer) and is interpreted so that a value of \(1\) aligns the first outgoing boundary component with the second incoming boundary component.
+
+\item \DescribeMacro{genus} This defines the number of holes in the shape.
+These are spread out in a horizontal line in the middle of the shape.
+\end{itemize}
+
+\subsection{Styling}
+
+There are various options for styling the diagrams.
+To understand how they work, it is important to know the order in which a cobordism is drawn and how many pieces it decomposes into.
+This is the following list, with the corresponding keys:
+
+\begin{enumerate}
+\item The boundary circles are drawn.
+These are actually elliptical nodes (and thus can be individually styled).
+Applicable styles:
+
+\begin{itemize}
+\item \Verb+every boundary component+,
+\item \Verb+every incoming boundary component+,\\
+or \Verb+every outgoing boundary component+,
+\item \Verb+incoming boundary component <n>+,\\
+or \Verb+outgoing boundary component <n>+
+\end{itemize}
+
+\item The lower edges of the boundary circles are redrawn.
+These are individual arcs.
+
+\begin{itemize}
+\item \Verb+every lower boundary component+,
+\item \Verb+every incoming lower boundary component+,\\or \Verb+every outgoing lower boundary component+,
+\item \Verb+incoming lower boundary component <n>+,\\or \Verb+outgoing lower boundary component <n>+
+\end{itemize}
+
+\item The full edge of the cobordism is drawn.
+This is a closed path so can be sensibly filled.
+It is clipped against a path defined by the genus of the cobordism which results in holes if it is filled (or shaded or anything else that goes in to the interior).
+
+\begin{itemize}
+\item \Verb+cobordism+,
+\item also, any actions specified on the \Verb+pic+ are applied here (specifically, the \Verb+pic actions+ key is invoked; see the Ti\emph{k}Z manual for full details on this),
+\item \Verb+cobordism outer path+.
+\end{itemize}
+
+\item Any holes specified by the genus are now drawn.
+These are styled to give the 3D impression, and this follows the direction specified by the \Verb+view from+ key.
+The paths are split so that each can be individually styled.
+
+\begin{itemize}
+\item \Verb+cobordism+, this style is applied because the curves defined by the genus can be thought of as part of the edge of the cobordism shape.
+\item \Verb+pic actions+, for the same reason as above.
+
+However, following this key then \Verb+fill=none,shade=none+ is issued.
+This is because even if the main shape is filled or shaded, the paths drawing the holes should almost certainly not be.
+\item \Verb+cobordism edge+, the same logic applies to the edge path (q.v.).
+\item \Verb+genus style+,
+\item \Verb+genus upper+ or \Verb+genus lower+,
+\item \Verb+hole <n>+,
+\item \Verb+hole <n> upper+ or \Verb+hole <n> lower+.
+\end{itemize}
+
+\item The non-boundary edge of the cobordism is redrawn.
+This is split in to pieces to allow for individual styling.
+
+\begin{itemize}
+\item \Verb+cobordism edge+,
+\item \Verb+cobordism outer edge+,
+\item \Verb+between incoming+, or \Verb+between outgoing+, or \Verb+between incoming and outgoing+.
+The latter is for the two sides, but note that if the cobordism has no incoming or no outgoing components then it also applies to the ``over the top'' edge.
+\item \Verb+<anchor>+, where the \Verb+<anchor>+ is the name of the anchor that lies on the midpoint of the curve, so it will be one of:
+%
+\begin{itemize}
+\item \Verb=between incoming <n> and <n+1>=,
+\item \Verb=between outgoing <n> and <n+1>=,
+\item \Verb+between first incoming and first outgoing+,
+\item \Verb+between first incoming and first outgoing+,
+\item \Verb+between last incoming and last outgoing+,
+\item \Verb+between first and last incoming+,
+\item \Verb+between first and last outgoing+.
+\end{itemize}
+\end{itemize}
+
+\item The upper edges of the boundary circles are redrawn.
+These are arcs.
+
+\begin{itemize}
+\item \Verb+every upper boundary component+,
+\item \Verb+every incoming upper boundary component+,\\or \Verb+every outgoing upper boundary component+,
+\item \Verb+incoming upper boundary component <n>+,\\or \Verb+outgoing upper boundary component <n>+
+\end{itemize}
+\end{enumerate}
+
+The fact that there are so many is to allow different style to be applied to different pieces and to give as much control as possible, whilst still making it fairly straightforward to draw a simple cobordism.
+The duplication of paths is to allow certain composite pieces to be \emph{filled}.
+Here is a progressively built up cobordism.
+
+\begin{example}
+\begin{tikzpicture}[tqft/view from=incoming]
+\begin{scope}[tqft/every boundary component/.style={fill=green,fill opacity=1}]
+\pic[tqft/cylinder,at={(1,0)}];
+\begin{scope}[tqft/every lower boundary component/.style={draw=purple,thick}]
+\pic[tqft/cylinder,at={(2,0)}];
+\begin{scope}[tqft/cobordism/.style={fill=yellow,fill opacity=.7}]
+\pic[tqft/cylinder,at={(3,0)}];
+\begin{scope}[tqft/cobordism edge/.style={draw,thick,blue}]
+\pic[tqft/cylinder,fill=yellow,fill opacity=.7,at={(4,0)}];
+\begin{scope}[tqft/every upper boundary component/.style={draw,thick,orange}]
+\pic[tqft/cylinder,fill=yellow,fill opacity=.7,at={(5,0)}];
+\end{scope}
+\end{scope}
+\end{scope}
+\end{scope}
+\end{scope}
+\end{tikzpicture}
+\end{example}
+
+Here's an example with lots of styling.
+
+\begin{example}
+\begin{tikzpicture}
+\pic[
+ tqft,
+ incoming boundary components=3,
+ outgoing boundary components=3,
+ offset=1,
+ genus=3,
+ hole 3/.style={ultra thick, purple,solid},
+ genus lower/.style={dashed},
+ fill=red!50,
+ cobordism edge/.style={draw},
+ between incoming and outgoing/.style={dotted},
+ between outgoing 2 and 3/.style={ultra thick},
+];
+\end{tikzpicture}
+\end{example}
+
+\subsection{Anchors}
+
+The cobordism is a \Verb+pic+ so does not have any native anchors.
+Nevertheless, a multitude of coordinates are defined that simulate the anchors associated with nodes.
+There is also support for specifying the shape to be located relative to a particular anchor.
+
+The \Verb+\pic+ should be named via the \Verb+name=<prefix>+ key, whereupon the anchors are prefixed by this value.
+The pseudo-anchors defined have the naming convention \Verb+<prefix>-<anchor name>+ (at the moment, it doesn't check to see if the \Verb+name+ key has been specified so if it isn't then the pseudo-anchors are still defined but with an empty prefix).
+They are:
+%
+\begin{itemize}
+\item \Verb+incoming boundary <n>+, these are in fact elliptical nodes and so also define actual anchors.
+\item \Verb+incoming boundary+ is an alias for \Verb+incoming boundary 1+.
+\item \Verb+outgoing boundary <n>+, same.
+\item \Verb+outgoing boundary+ is an alias for \Verb+outgoing boundary 1+.
+\item \Verb=between incoming <n> and <n+1>=, this lies on the midpoint of the curve between successive boundary components.
+\item \Verb=between outgoing <n> and <n+1>=, this lies on the midpoint of the curve between successive boundary components.
+\item \Verb=between first incoming and first outgoing= is on the edge between the first incoming and first outgoing boundary components; note that this is only defined if there are both incoming and outgoing boundary components.
+\item \Verb=between last incoming and last outgoing= is on the edge between the last incoming and last outgoing boundary components; note that this is only defined if there are both incoming and outgoing boundary components.
+\item \Verb=between first and last incoming=; this is only defined if there are no outgoing components.
+\item \Verb=between first and last outgoing=; this is only defined if there are no incoming components.
+\item \Verb=hole <n>=; if the genus is non-zero, this points to the centre of the \(n\)th hole.
+\end{itemize}
+
+To place the shape relative to an anchor, use the \Verb+tqft/anchor+ key.
+The argument should be just the name of the anchor without the leading \Verb+<prefix>-+.
+The \Verb+anchor+ key can also take another type of argument.
+If its argument is of the form \Verb+(x,y)+ then this is taken as a pseudo-coordinate\footnote{Note that due to the presence of the comma, this type of argument must be protected by braces.}.
+It is interpreted as being \(x\) boundary components across and \(y\) times the cobordism height down.
+However, if an \Verb+offset+ is specified then the resulting \(x\) value is shifted so that if \(y < 0\) then \((1,y)\) is in line with the first incoming boundary component and if \(y > 1\) then \((1,y)\) is in line with the first outgoing boundary component.
+If \(0 < y < 1\) then \((1,y)\) linearly interpolates between the first incoming and first outgoing boundary components.
+Thus \((1,0)\) is the first incoming boundary component, \((1,1)\) the first outgoing boundary component, \((0,0)\) is one unit to the left of the first incoming, and \((1,2)\) one unit below the first outgoing.
+Note that the picture is shifted to put this point at the current coordinate.
+
+\begin{example}
+\begin{tikzpicture}
+\pic[tqft, incoming boundary components=2,outgoing boundary components=4,offset=-1,draw,name=a];
+\foreach \anchor/\placement in
+{
+between first incoming and first outgoing/left,
+between last incoming and last outgoing/right,
+between outgoing 2 and 3/above,
+incoming boundary 1/above left,
+incoming boundary 2/above right,
+outgoing boundary 1/below left,
+outgoing boundary 4/below right}
+\draw[overlay,shift=(a-\anchor)] plot[mark=x] coordinates{(0,0)} node[\placement] {\scriptsize\texttt{(a-\anchor)}};
+\path (a-incoming boundary) +(0,.5) (a-outgoing boundary) +(0,-1);
+\end{tikzpicture}
+\end{example}
+
+\subsection{Notes}
+
+\begin{enumerate}
+\item Like \Verb+node+s, \Verb+pic+s need the \Verb+transform shape+ key to be set to take note of external transformations (other than shifts).
+Also, as the tqft pic uses nodes internally, if you use the \Verb+transform shape+ key on the pic, you might find you need to use \Verb+every node/.style={transform shape}+ as well.
+\item There is an additional \Verb+every tqft+ key which is run when the \Verb+tqft+ key is invoked (which might be via some other key).
+This is better placed than the \Verb+every pic+ key since that applies to a surrounding scope rather than to the \Verb+pic+ itself.
+\item If the \Verb+tqft+ key is invoked, either implicitly or explicitly, then the \Verb+pic type+ is set to \Verb+cobordism+.
+This has the side effect that the invoking syntax has to be completely set by keys; so the \Verb+pic (<name>) at (<coord>) {<type>}+ cannot be used.
+Rather, the \Verb+name+ and \Verb+at+ have to be specified by keys and the \Verb+type+ omitted.
+
+\item If upgrading from the previous version of TQFT, as well as shifting from a \Verb+node+ to a \Verb+pic+, the following changes have been made in the implementation:
+
+\begin{itemize}
+\item The \Verb+flow+ key has not made it across to the new version.
+Use \Verb+transform shape+ and apply your own transformation.
+
+\item The \Verb+circle width+ and \Verb+circle depth+ are now \Verb+circle x radius+ and \Verb+circle y radius+ (the old names weren't correct anyway).
+
+\item The bounding box is a little better, particularly for cobordisms with only one type of boundary component.
+\end{itemize}
+\end{enumerate}
+
+\subsection{More Examples}
+
+\begin{example}
+\begin{tikzpicture}[tqft/cobordism height=1.5cm,tqft/boundary separation=1.5cm]
+\foreach \coord/\style in {
+{(0,0)}/{tqft/view from=outgoing,fill},
+{(5,0)}/{tqft/view from=incoming,draw},
+{(0,-8)}/{fill=orange,fill opacity=.5,tqft/every lower boundary component/.style={draw,blue,ultra thin,dashed},tqft/every upper boundary component/.style={draw,green},tqft/cobordism edge/.style={draw,purple},tqft/every boundary component/.style={fill=yellow}},
+{(5,-8)}/{fill=orange,fill opacity=.5,tqft/cobordism edge/.style={draw,purple},tqft/every boundary component/.style={fill=yellow,draw=green}}
+} {
+\begin{scope}
+\edef\styleit{\noexpand\tikzset{every tqft/.style={\style}}}
+\styleit
+\pic[tqft/cap,name=h,at=\coord];
+\pic[tqft/pair of pants,anchor=incoming boundary 1,name=a,at=(h-outgoing boundary 1)];
+\pic[tqft/cylinder to next,anchor={(0,1)},name=d,at=(a-outgoing boundary 2)];
+\pic[tqft/reverse pair of pants,anchor=incoming boundary 1,name=b,at=(a-outgoing boundary 2)];
+\pic[tqft/cylinder to prior,anchor=incoming boundary 1,name=c,at=(b-outgoing boundary 1)];
+\pic[tqft/cylinder,anchor=incoming boundary 1,name=e,at=(a-outgoing boundary 1)];
+\pic[tqft/cylinder,anchor=incoming boundary 1,name=f,at=(e-outgoing boundary 1)];
+\pic[tqft/reverse pair of pants,anchor=incoming boundary 1,name=g,at=(f-outgoing boundary 1)];
+\pic[tqft/cup,anchor=incoming boundary 1,name=i,at=(g-outgoing boundary 1)];
+\end{scope}
+}
+\end{tikzpicture}
+\end{example}
+
+\begin{example}
+\begin{tikzpicture}[every tqft/.append style={transform shape}]
+\foreach \ang in {0,90,180,270} {
+\begin{scope}[rotate=\ang]
+\pic[draw,tqft/pair of pants,name=a,at={(3,3)}];
+\pic[draw,tqft/cap,anchor=outgoing boundary 1,at=(a-incoming boundary 1)];
+\pic[fill,tqft/cup,anchor=incoming boundary 1,at=(a-outgoing boundary 1)];
+\pic[draw,tqft/cup,anchor=incoming boundary 1,at=(a-outgoing boundary 2)];
+\end{scope}
+}
+\end{tikzpicture}
+\end{example}
+
+\begin{example}
+\begin{tikzpicture}[
+ tqft,
+ every outgoing boundary component/.style={fill=blue!50},
+ outgoing boundary component 3/.style={fill=none,draw=red},
+ every incoming boundary component/.style={fill=green!50},
+ every lower boundary component/.style={draw,ultra thick, dashed},
+ every upper boundary component/.style={draw,purple},
+ cobordism/.style={fill=red!50},
+ cobordism edge/.style={draw},
+ genus=3,
+ hole 2/.style={ultra thick, blue},
+ view from=incoming,
+ anchor=between incoming 1 and 2
+]
+\pic[rotate=90,every node/.style={transform shape},name=a,tqft,incoming boundary components=5,skip incoming boundary components={2,4},outgoing boundary components=7,skip outgoing boundary components={2,3,5},offset=-.5];
+
+\begin{scope}[every pin edge/.style={<-}]
+\foreach \anchor/\ang in {
+ hole 1/-90,
+ hole 2/90,
+ hole 3/-90,
+ incoming boundary 3/90,
+ outgoing boundary 4/-90,
+ between last incoming and last outgoing/180,
+ between first incoming and first outgoing/180,
+ between incoming 1 and 3/90,
+ between outgoing 1 and 4/-90,
+ between outgoing 4 and 6/-90
+} {
+ \node[pin=\ang:\anchor,at=(a-\anchor),inner sep=0pt] {};
+}
+\draw[<-] (0,0) -- ++(0,3);
+\end{scope}
+\end{tikzpicture}
+\end{example}
+
+%\begin{example}
+\begin{tikzpicture}
+\pic[
+ tqft,
+ incoming boundary components=2,
+ outgoing boundary components=2,
+ genus=2,
+ draw,
+ name=a
+];
+\pic[
+ tqft,
+ incoming boundary components=2,
+ outgoing boundary components=1,
+ draw,
+ at=(a-outgoing boundary 1),
+ offset=.5,
+ cobordism height=1cm,
+ name=b
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=3,
+ draw,
+ at=(b-outgoing boundary 1),
+ offset=-1,
+ name=c
+];
+\pic[tqft,
+ incoming boundary components=2,
+ outgoing boundary components=1,
+ draw,
+ at=(c-outgoing boundary 1),
+ anchor=incoming boundary 2,
+ name=d,
+ boundary separation=1.6cm,
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(c-outgoing boundary 3),
+ offset=.5,
+ name=e,
+ every outgoing lower boundary component/.style={draw}
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(c-outgoing boundary 2),
+ name=f
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=2,
+ draw,
+ at=(f-outgoing boundary),
+ name=g,
+ offset=-.5,
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(g-outgoing boundary 1),
+ name=h,
+ offset=-.25,
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(g-outgoing boundary 2),
+ name=i,
+ offset=.25,
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(h-outgoing boundary),
+ name=j,
+ every outgoing lower boundary component/.style={draw}
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(i-outgoing boundary),
+ name=k,
+ every outgoing lower boundary component/.style={draw}
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(d-outgoing boundary),
+ name=l
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=0,
+ draw,
+ at=(l-outgoing boundary),
+ name=m
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(d-incoming boundary),
+ anchor=outgoing boundary,
+ name=n
+];
+\pic[tqft,
+ incoming boundary components=1,
+ outgoing boundary components=1,
+ draw,
+ at=(n-incoming boundary),
+ anchor=outgoing boundary,
+ name=o
+];
+\pic[tqft,
+ incoming boundary components=3,
+ outgoing boundary components=3,
+ draw,
+ at=(o-incoming boundary),
+ anchor={(2,1)},
+ name=p,
+ boundary separation=1.25cm,
+ outgoing lower boundary component 1/.style={draw},
+ outgoing lower boundary component 3/.style={draw}
+];
+\pic[tqft,
+ incoming boundary components=5,
+ outgoing boundary components=5,
+ genus=3,
+ at=(k-outgoing boundary),
+ anchor={(4,-1)},
+ draw,
+ name=q,
+ every outgoing lower boundary component/.style={draw}
+];
+\path (q-incoming boundary 3) ++(0,1) node {\Huge \(=\)};
+\end{tikzpicture}
+%\end{example}
+
+\section{Version 1.0}
+
+\tikzset{tqft/use nodes=true}
+
+\subsection{The Node Shapes}
+
+There are only two shapes, \Verb+tqft cobordism+ and \Verb+tqft boundary circle+.
+The first, which is the main shape, is a cobordism between a number of incoming circles and a number of outgoing circles, where the numbers of boundary components can be specified as options to the shape.
+The second is just the boundary circle.
+It is used as a sub-node of the first to add extra anchors, but can be used by itself.
+There are certain common shapes that are predefined as aliases to the main shape with specified boundaries.
+The list of predefined shapes follows.
+The names are all in the \Verb+tqft+ family, but an alias is made so that \Verb+tqft nodeshape+ will work without any further qualification.
+
+\begin{enumerate}
+\item \Verb+pair of pants+
+
+\begin{tikzpicture}
+\node[draw,tqft/pair of pants] (a) {};
+\end{tikzpicture}
+
+\item \Verb+reverse pair of pants+
+
+\begin{tikzpicture}
+\node[draw,tqft/reverse pair of pants] (a) {};
+\end{tikzpicture}
+
+\item \Verb+cylinder to prior+
+
+This is a cylinder that has been skewed to one side, thus following the same path as the \Verb+pair of pants+ cobordism but with only one outgoing boundary component.
+The name \Verb+to prior+ is because it goes towards the lower-numbered component on the \Verb+pair of pants+.
+
+\begin{tikzpicture}
+\node[draw,tqft/cylinder to prior] (a) {};
+\end{tikzpicture}
+
+\item \Verb+cylinder to next+
+
+This is a cylinder that has been skewed to one side, thus following the same path as the \Verb+pair of pants+ cobordism but with only one outgoing boundary component.
+The name \Verb+to next+ is because it goes towards the higher-numbered component on the \Verb+pair of pants+.
+
+\begin{tikzpicture}
+\node[draw,tqft/cylinder to next] (a) {};
+\end{tikzpicture}
+
+\item \Verb+cylinder+
+
+This is a straight cylinder.
+
+\begin{tikzpicture}
+\node[draw,tqft/cylinder] (a) {};
+\end{tikzpicture}
+
+\item \Verb+cap+
+
+This is a cap.
+
+\begin{tikzpicture}
+\node[draw,tqft/cap] (a) {};
+\end{tikzpicture}
+
+\item \Verb+cup+
+
+This is a cup (an upside-down cap).
+
+\begin{tikzpicture}
+\node[draw,tqft/cup] (a) {};
+\end{tikzpicture}
+
+\end{enumerate}
+
+The general shape is controlled by the following keys:
+
+\begin{itemize}
+\item \DescribeMacro{flow} A cobordism ``flows'' from its incoming to its outgoing boundaries.
+This key controls the direction of that flow.
+The shape is transformed so that the incoming-outgoing axis aligns with the argument.
+However, the transformation may be more than just a rotation as the shape is set up so that the numbering of the boundary components is always left-to-right or top-to-bottom (as appropriate).
+Currently, this key can take the values \Verb+north+, \Verb+south+ (default), \Verb+east+, and \Verb+west+.
+
+\item \DescribeMacro{view from} To get a simulated 3D effect, the cobordism is drawn as if viewed from a slight angle.
+The value of this key determines whether the cobordism is viewed from the direction of the incoming boundary components or the outgoing ones.
+This key can take the values \Verb+incoming+ and \Verb+outgoing+.
+The default is \Verb+outgoing+.
+\item \DescribeMacro{cobordism height} This is the height of the cobordism (``height'' interpreted in its own internal coordinate system).
+With no offset (q.v.), this would be the distance between the centres of the first incoming and first outgoing boundary components.
+
+\item \DescribeMacro{boundary separation} This is the distance between the centres of the boundary components of the same type.
+
+\item \DescribeMacro{circle width} This is the half-width of the boundary circles.
+
+\item \DescribeMacro{circle depth} This is the half-depth of the boundary circles (``depth'' since, in the internal coordinate system, this corresponds to the \(z\)-axis out of the page).
+
+\item \DescribeMacro{incoming boundary components} The number of incoming boundary components (can be zero).
+
+\item \DescribeMacro{outgoing boundary components} The number of outgoing boundary components (can be zero).
+
+\item \DescribeMacro{offset} This offsets the first outgoing boundary component horizontally relative to the first incoming boundary component.
+It is a dimensionless number (not necessarily an integer) and is interpreted so that a value of \(1\) aligns the first outgoing boundary component with the second incoming boundary component.
+\end{itemize}
+
+\subsection{Styling}
+
+There are various options for styling the diagrams.
+To understand how they work, it is important to know the order in which a cobordism is drawn and how many pieces it decomposes into.
+This is the following list, with the corresponding key:
+
+\begin{enumerate}
+\item The boundary circles are drawn.
+\Verb+boundary style+
+\item The lower edges of the boundary circles are redrawn.
+\Verb+boundary lower style+
+\item The cobordism itself is drawn.
+\item The non-boundary edge of the cobordism is redrawn.
+\Verb+cobordism style+
+\item The upper edges of the boundary circles are redrawn.
+\Verb+boundary upper style+
+\end{enumerate}
+
+The fact that there are so many is to allow different style to be applied to different pieces.
+The duplication is to allow certain composite pieces to be \emph{filled}.
+All of these items can be styled separately.
+The style given to the node itself is passed on to the third item in that list, the cobordism itself.
+The styles of the others are controlled by a series of keys, each of should be a list of styles to be applied to that component.
+Not all options make sense, in particular only the first and third can be filled.
+(That is, the \Verb+fill+ style is ignored on the other components.)
+Here is a progressively built up cobordism.
+
+\begin{example}
+\begin{tikzpicture}
+\begin{scope}[tqft/boundary style={fill=purple,fill opacity=1}]
+\node[tqft/cylinder] at (1,0) {};
+\begin{scope}[tqft/boundary lower style={draw,dashed,green,thick}]
+\node[tqft/cylinder] at (2,0) {};
+\begin{scope}
+\node[tqft/cylinder,fill=yellow,fill opacity=.7] at (3,0) {};
+\begin{scope}[tqft/cobordism style={draw,thick,blue}]
+\node[tqft/cylinder,fill=yellow,fill opacity=.7] at (4,0) {};
+\begin{scope}[tqft/boundary upper style={draw,thick,orange}]
+\node[tqft/cylinder,fill=yellow,fill opacity=.7] at (5,0) {};
+\end{scope}
+\end{scope}
+\end{scope}
+\end{scope}
+\end{scope}
+\end{tikzpicture}
+\end{example}
+
+\subsection{Anchors}
+
+As with all PGF node shapes, there are certain anchors defined by the \Verb+tqft+ shape.
+These are the \Verb+center+ (and \Verb+centre+) anchors and the \Verb+incoming boundary n+, \Verb+outgoing boundary n+ anchors.
+The positioning of the \Verb+center+ anchor is slightly unusual in that if there are no, say, incoming boundary components then the centre anchor is still at the same height above the outgoing boundary components as if there were incoming boundary components.
+The reason for this is two-fold: computing the \emph{actual} centre of the shape in such circumstances would be tricky, and when aligning these shapes it is more useful to have the anchors consistent across shapes of varying boundary components.
+
+There are also the directional anchors \Verb+north+, \Verb+south+, \Verb+east+, \Verb+west+, \Verb+north east+, \Verb+north west+, \Verb+south east+, \Verb+south west+.
+The \Verb+east+ and \Verb+west+ anchors are placed at the midpoints of the sides.
+The \Verb+north+ and \Verb+south+ anchors are placed in a vertical line with the \Verb+center+ anchor and vertically aligned with the centres of the corresponding boundary circles.
+The other four directional anchors are placed at the corners of the cobordism (the placement of these anchors in the case that there are no boundary circles in the corresponding direction may change in future versions).
+
+The \Verb+incoming boundary n+ and \Verb+outgoing boundary n+ are placed at the centres of the corresponding boundary components, with the numbering starting at the left or the top as appropriate to the flow of the cobordism.
+A hack borrowed from the \Verb+regular polygon+ shape ensures that there are always enough anchors for the boundary components.
+
+There are also anchors placed at the midpoint of the cobordism edge between the boundary circles.
+The names of these are \Verb+after incoming boundary n+ and \Verb+after outgoing boundary n+.
+
+The above anchors can all be ``floated'' off the cobordism using the keys \Verb+outer sep+, \Verb+outer xsep+, and \Verb+outer ysep+.
+The last two are the ones actually used, the first is a shortcut for setting both simultaneously.
+
+There are also ``sub-nodes''.
+Provding the main node is named, each boundary circle is covered by a \Verb+tqft boundary circle+ node.
+This means that the anchors of the \Verb+tqft boundary circle+ can be used.
+These cannot be used for placing the main shape, but can be used afterwards.
+These are not affected by the \Verb+outer (x/y)sep+ keys.
+The names of these sub-nodes are of the form \Verb+name incoming n+ and \Verb+name outgoing n+ where \Verb+name+ is the name of the main node.
+The \Verb+tqft boundary circle+ shape is based on an ellipse and defines a boundary so the syntax \Verb+(name.angle)+ works as expected.
+It also defines anchors \Verb+next+, \Verb+prior+, \Verb+above+, and \Verb+below+.
+These correspond to where the boundary circle in the prescribed direction should be placed.
+
+\begin{example}
+\begin{tikzpicture}
+\node[tqft, incoming boundary components=2,outgoing boundary components=4,offset=-1,draw] (a) {};
+\foreach \anchor/\placement in
+{
+north/above,
+south/below,
+east/right,
+west/left,
+north west/left,
+south west/left,
+north east/right,
+south east/right,
+incoming boundary 1/above left,
+incoming boundary 2/above right,
+outgoing boundary 1/below left,
+outgoing boundary 4/below right,
+after outgoing boundary 1/below}
+\draw[shift=(a.\anchor)] plot[mark=x] coordinates{(0,0)} node[\placement] {\scriptsize\texttt{(a.\anchor)}};
+\end{tikzpicture}
+\end{example}
+
+\begin{example}
+\begin{tikzpicture}
+\node[tqft,cylinder, circle width=2cm, circle depth=1cm, cobordism height=4cm,boundary separation=3cm,draw] (b) {};
+\foreach \anchor/\placement in
+{
+prior/left,
+next/right,
+above/above,
+below/below,
+0/right,
+60/right,
+200/left}
+\draw[shift=(b incoming 1.\anchor)] plot[mark=x] coordinates{(0,0)} node[\placement] {\scriptsize\texttt{(b incoming 1.\anchor)}};
+\end{tikzpicture}
+\end{example}
+
+\subsection{Improvements}
+
+Here are some ideas for extending this, and some minor ``bugs''.
+
+\begin{enumerate}
+\item Make \Verb+incoming boundary+ an alias of \Verb+incoming boundary 1+ so that if there is only one incoming boundary component then we don't need to specify the number (ditto outgoing).
+\item No thought has been given as to where the text gets placed if it is specified.
+\item Add the ability to hide certain boundary components.
+This is useful if the shapes are not specified in their natural order so certain boundary components should be hidden behind earlier drawn shapes.
+\item Some style options on the main node get passed to the other pieces (\Verb+fill opacity+ being one).
+This shouldn't happen, or should happen by design not by accident.
+\item The bounding box isn't as good as it could be.
+\item Add a way to specify more directions for the flow.
+\item Add the ability to apply different styles to the incoming and outgoing components.
+\end{enumerate}
+
+\subsection{More Examples}
+
+\begin{example}
+\begin{tikzpicture}[tqft/cobordism height=1.5cm,tqft/boundary separation=1.5cm]
+\foreach \coord/\style in {
+{(0,0)}/{tqft/view from=outgoing,fill},
+{(5,0)}/{tqft/view from=incoming,draw},
+{(0,-8)}/{fill=orange,fill opacity=.5,tqft/boundary lower style={draw,blue,ultra thin,dashed},tqft/boundary upper style={draw,green},tqft/cobordism style={draw,purple},tqft/boundary style={fill=yellow}},
+{(5,-8)}/{fill=orange,fill opacity=.5,tqft/cobordism style={draw,purple},tqft/boundary style={fill=yellow,draw=green}}
+} {
+\begin{scope}
+\edef\styleit{\noexpand\tikzset{every node/.style={\style}}}
+\styleit
+\node[tqft/cap] (h) at \coord {};
+\node[tqft/pair of pants,anchor=incoming boundary 1] (a) at (h.outgoing boundary 1) {};
+\node[tqft/cylinder to next,anchor=incoming boundary 1] (d) at (a.incoming boundary 2) {};
+\node[tqft/reverse pair of pants,anchor=incoming boundary 1] (b) at (a.outgoing boundary 2) {};
+\node[tqft/cylinder to prior,anchor=incoming boundary 1] (c) at (b.outgoing boundary 1) {};
+\node[tqft/cylinder,anchor=incoming boundary 1] (e) at (a.outgoing boundary 1) {};
+\node[tqft/cylinder,anchor=incoming boundary 1] (f) at (e.outgoing boundary 1) {};
+\node[tqft/reverse pair of pants,anchor=incoming boundary 1] (g) at (f.outgoing boundary 1) {};
+\node[tqft/cup,anchor=incoming boundary 1] (i) at (g.outgoing boundary 1) {};
+\end{scope}
+}
+\end{tikzpicture}
+\end{example}
+
+\begin{example}
+\begin{tikzpicture}
+\node[draw,tqft/pair of pants] (a) {};
+\node[draw,tqft/cap,anchor=outgoing boundary 1] at (a.incoming boundary 1) {};
+\node[fill,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 1) {};
+\node[draw,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 2) {};
+\begin{scope}[tqft/flow=east]
+\node[draw,tqft/pair of pants] (a) at (4,0) {};
+\node[draw,tqft/cap,anchor=outgoing boundary 1] at (a.incoming boundary 1) {};
+\node[fill,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 1) {};
+\node[draw,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 2) {};
+\end{scope}
+\begin{scope}[tqft/flow=north]
+\node[draw,tqft/pair of pants] (a) at (0,-4) {};
+\node[draw,tqft/cap,anchor=outgoing boundary 1] at (a.incoming boundary 1) {};
+\node[fill,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 1) {};
+\node[draw,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 2) {};
+\end{scope}
+\begin{scope}[tqft/flow=west]
+\node[draw,tqft/pair of pants] (a) at (4,-4) {};
+\node[draw,tqft/cap,anchor=outgoing boundary 1] at (a.incoming boundary 1) {};
+\node[fill,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 1) {};
+\node[draw,tqft/cup,anchor=incoming boundary 1] at (a.outgoing boundary 2) {};
+\end{scope}
+\end{tikzpicture}
+\end{example}
+
+\end{document}