texlive[51048] Master/texmf-dist: braids (8may19)
commits+karl at tug.org
commits+karl at tug.org
Wed May 8 23:15:00 CEST 2019
Revision: 51048
http://tug.org/svn/texlive?view=revision&revision=51048
Author: karl
Date: 2019-05-08 23:15:00 +0200 (Wed, 08 May 2019)
Log Message:
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braids (8may19)
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trunk/Master/texmf-dist/tex/latex/braids/braids.sty
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trunk/Master/texmf-dist/doc/latex/braids/README.txt
trunk/Master/texmf-dist/doc/latex/braids/braids.pdf
trunk/Master/texmf-dist/doc/latex/braids/braids.tex
trunk/Master/texmf-dist/doc/latex/braids/braids_code.pdf
trunk/Master/texmf-dist/source/latex/braids/braids_code.dtx
trunk/Master/texmf-dist/source/latex/braids/braids_code.ins
trunk/Master/texmf-dist/tex/latex/braids/tikzlibrarybraids.code.tex
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trunk/Master/texmf-dist/doc/latex/braids/README
trunk/Master/texmf-dist/doc/latex/braids/braids_doc.pdf
trunk/Master/texmf-dist/doc/latex/braids/braids_doc.tex
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-----------------------------------------------------------------
-braids --- a style file for drawing braid diagrams with TikZ/PGF
-E-mail: stacey at 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 commands for drawing braid diagrams with TikZ/PGF.
-It was designed and tested with PGF2.10.
-The initial idea of this package came from a question and answer on the site http://tex.stackexchange.com.
-
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+----------------------------------------------------------------
+braids --- a style file for drawing braid diagrams with TikZ/PGF
+E-mail: loopspace at mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+This package defines some commands for drawing braid diagrams with TikZ/PGF.
+The initial idea of this package came from a question and answer on the site http://tex.stackexchange.com.
+
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+\documentclass{ltxdoc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage{morefloats}
+\usepackage{tikz}
+\usepackage{braids}
+\usetikzlibrary{braids}
+\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}
+ \input{example.out}
+ \end{minipage}}
+\end{center}
+}
+
+\providecommand*{\url}{\texttt}
+\GetFileInfo{tikzlibrarybraids.code.tex}
+
+\title{The \textsf{braids} Package: Documentation}
+\author{Andrew Stacey \\ \texttt{loopspace at mathforge.org}}
+\date{\fileversion~from \filedate}
+
+\begin{document}
+
+\maketitle
+
+\begin{center}
+ \begin{tikzpicture}
+ \pic[
+ line width=1.5pt,
+ red,
+ line cap=round,
+ braid/.cd,
+ width=.75cm,
+ height=.5cm,
+ strand 3/.style={gray,line width=1pt},
+ strand 6/.style={gray,line width=1pt},
+ strand 7/.style={gray,line width=1pt},
+ strand 10/.style={gray,line width=1pt},
+ strand 14/.style={gray,line width=1pt},
+ strand 15/.style={gray,line width=1pt},
+ strand 16/.style={gray,line width=1pt},
+ strand 18/.style={gray,line width=1pt},
+ ] {braid={s_1-s_4-s_8-s_{12}-s_{16} s_2-s_5-s_7-s_9-s_{13}-s_{15} s_2-s_5-s_7-s_9-s_{15} s_1-s_4-s_8-s_{16} s_1-s_4-s_7-s_9-s_{17} s_2-s_5-s_{17} s_2-s_{13}-s_{16} s_1-s_{12}-s_{15}}};
+\end{tikzpicture}
+\end{center}
+
+\section{Introduction}
+
+This is a package for drawing braid diagrams using PGF/TikZ.
+An example follows.
+
+\begin{example}
+\begin{center}
+\begin{tikzpicture}
+\pic[
+ rotate=90,
+ braid/.cd,
+ every strand/.style={ultra thick},
+ strand 1/.style={red},
+ strand 2/.style={green},
+ strand 3/.style={blue},
+] {braid={s_1 s_2^{-1} s_1 s_2^{-1} s_1 s_2^{-1}}};
+\end{tikzpicture}
+\end{center}
+\end{example}
+
+\section{TikZ Library Usage}
+
+Version 2.0 changed the implementation to use the TikZ \Verb+pic+ syntax.
+It also converted it to a TikZ library, so to use it put the following in the preamble.
+
+\begin{verbatim}
+\usetikzlibrary{braids}
+\end{verbatim}
+
+(Or add it to the copious list of TikZ libraries that you are already using.)
+
+\bigskip
+
+\DescribeMacro{braid}
+A braid is specified by the pic name \Verb+braid+.
+The usual syntax for this is as follows:
+
+\Verb+\pic[options] at (coordinate) {braid={braid-word}};+
+
+\DescribeMacro{braid-word}
+The \Verb+braid-word+ is an expression in the braid group, such as \Verb+s_1 s_2^{-1} s_{3,5}+.
+The generator labels are not significant.
+If the subscript is a single number, as in \Verb+s_2+, the crossing goes from that number over the next.
+If the subscript is two numbers, as in \Verb+s_{2,4}+, the crossing goes from the first over the second, with both the crossing strands passing over all of the intervening strands.
+The exponent can be \Verb+1+, \Verb+{-1}+, or missing (in which case it defaults to \Verb+1+, note also that the exponent is read as a \TeX-token so \Verb+{1}+ is also legal).
+If the exponent is \(-1\) then the over and under strands swap.
+
+\begin{itemize}
+\item \Verb+s_1+ is strand \(1\) over strand \(2\).
+\item \Verb+s_1^{-1}+ is strand \(2\) over strand \(1\).
+\item \Verb+s_{1,3}+ is strand \(1\) over strand \(3\), and both are over strand \(2\).
+\end{itemize}
+
+Certain other symbols are allowed in the \Verb+braid-word+ which control the rendering of the braid.
+These extras are as follows.
+
+\begin{enumerate}
+\item To get crossings to render at the same height, separate them with a hyphen (note: no check is made to ensure that the crossings can legally be put at the same height; \emph{caveat emptor}).
+For example, \Verb+s_1-s_3+.
+
+\item To draw a \emph{floor} -- which is a rectangle behind the braid occupying some number of levels (the default being one level) -- precede the braid element by a vertical line, as in \Verb+s_1 | s_2+.
+The floor is itself a pic which, by default, consists of a rectangle and two horizontal lines.
+The rectangle picks up any \Verb+fill+ options and the lines any \Verb+draw+ options that are set in the \Verb+braid/every floor+ and \Verb+braid/floor <n>+ styles.
+The \Verb+n+ is the level number, starting at \(1\).
+
+More general floors can be drawn using the key \Verb+braid/add floor+.
+This takes one argument which is a comma separated list of parameters that specifies the position and size floor:
+%
+\begin{verbatim}
+braid/add floor={x,y,width,height,name}
+\end{verbatim}
+%
+The units used are the ``natural'' units of the braid: strand separation and level height.
+The \Verb+name+ is optional and if given can be used to style the floor in that the style \Verb+braid/floor <name>+ is applied to that floor.
+
+Replacing the floor pic will change how it is drawn.
+The coordinate system is set up for the floor pic so that the floor is a unit square with lower left corner at the origin.
+
+\item The identity element can occur in the braid-word.
+It is represented by \Verb+1+.
+This inserts the identity which corresponds to no crossing.
+However, it takes the same amount of space as if there were a crossing.
+
+\end{enumerate}
+
+\subsection{Style Options}
+\label{sec:picstyleopts}
+
+There are various keys that change the behaviour or rendering of the braid.
+All of these are in the \Verb+/tikz/braid/+ namespace.
+
+\DescribeMacro{number of strands} The key \Verb+number of strands+ sets the minimum number of strands for the braid.
+The number of strands will grow according to the terms in the braid word so this merely sets a lower bound.
+If not set, the number of strands will be determined by the terms in the braid word.
+
+\DescribeMacro{height}
+The key \Verb+height+ sets the height of the piece of the braid corresponding to an element in the group.
+This can be negative.
+
+\DescribeMacro{width}
+The key \Verb+width+ sets the separation of the strands in the braid.
+This can be negative.
+
+\DescribeMacro{border height}
+The key \Verb+border height+ adds a little extra length to the strands at the start and end of the braid.
+
+\DescribeMacro{gap}
+The key \Verb+gap+ is used to determine how much of a gap to leave in the under strand at a crossing.
+This should be a number strictly between 0 and .5.
+The curve is drawn using a cubic bezier and the gap is in terms of the time parameter, so the gap will not increase exactly proportionally to the value given by this key, though that is a reasonable approximation.
+
+\DescribeMacro{control factor}
+As just said, the parts of the strands involved in a crossing are drawn using a cubic bezier curve.
+The control points are vertically above or below their respective end point.
+This key determines that vertical separation.
+It is multiplied by the \Verb+height+ so that it scales properly.
+It can be set to 0 whereupon the strands in the crossing are straight lines.
+The default is 0.5.
+
+\DescribeMacro{nudge factor}
+The crossings are not quite placed one after another.
+There is a small ``nudge'' between the end of one crossing and the start of another.
+Due to the way that the strands are lengthened, if there is no ``nudge'' then some PDF renderers produce slightly strange results at certain magnifications.
+This key controls how much that ``nudge'' is, as a factor of the \Verb+height+.
+For the aforementioned reason, it should not be set to 0 (the default is 0.05).
+Note that this does not change the height of a crossing.
+Rather, it nudges the height at which the strands start to cross over.
+
+\DescribeMacro{every strand, strand <n>}
+The style of the strands are controlled by two types of option.
+Style options that are set on the \Verb+pic+ are passed to every strand.
+It is also possible to add style options to individual strands using the keys \Verb+every strand+ and \Verb+strand <n>+.
+The strands are numbered by their starting position.
+
+\DescribeMacro{every floor, floor <n>}
+When a floor is requested behind a crossing, it is rendered as a pic.
+These keys control how the floor is styled.
+
+\subsection{Coordinates and Anchors}
+
+The braid is littered with coordinates.
+Each strand gets a coordinate at each end, and at every level between crossings.
+These are labelled and numbered by the initial strand position and the crossing level.
+They are also labelled and numbered by the final strand position with the prefix \Verb+rev+.
+With a \Verb+name prefix+, the coordinate names look like the following:
+%
+\begin{verbatim}
+<name prefix>-<strand number>-<crossing number>
+<name prefix>-rev-<strand number>-<crossing number>
+\end{verbatim}
+%
+The crossing number can also be either \Verb+s+ or \Verb+e+ for the start and end of the strand.
+Note that \Verb+-1-0+ and \Verb+-1-s+ are slightly different in that \Verb+s+ includes the border height.
+
+\DescribeMacro{anchor}
+The key \Verb+anchor+ (in the \Verb+braid+ name space) can be used to shift the braid so that a different part of it is at the specified location.
+It uses the same syntax as the coordinates, except without the \Verb+<name prefix>-+.
+In the following example, the braid is shifted so that where the third strand starts the second level is at the position \Verb+(1,1)+
+
+\begin{example}
+\begin{center}
+\begin{tikzpicture}
+\fill[purple] (1,1) circle[radius=3mm];
+\pic[braid/anchor=3-2,rotate=90] at (1,1) {braid={s_2 s_1 s_2 s_1}};
+\end{tikzpicture}
+\end{center}
+\end{example}
+
+
+\section{Examples}
+
+Here are more detailed examples.
+
+\begin{example}
+\begin{center}
+\begin{tikzpicture}
+\pic[
+ braid/every floor/.style={fill=yellow},
+ braid/floor 1/.style={draw=black,dashed,fill=yellow!50!green},
+ line width=2pt,
+ braid/strand 1/.style={red},
+ braid/strand 2/.style={blue},
+ braid/strand 3/.style={green},
+ braid/add floor={2,4,3,2,a},
+ braid/floor a/.style={fill=pink},
+ name prefix=braid,
+] at (2,0) {braid={| s_1-s_3-s_5 | s_2^{-1}-s_4| s_1-s_4 s_2^{-1} s_1-s_3 s_2^{-1}-s_4^{-1}}};
+\fill[yellow] (2,0) circle (4pt);
+\node[at=(braid-3-s),pin=north west:strand 3 start] {};
+\node[at=(braid-3-e),pin=south west:strand 3 end] {};
+\node[at=(braid-rev-3-s),pin=north east:strand 3 (from bottom) start] {};
+\node[at=(braid-rev-3-e),pin=south east:strand 3 (from bottom) end] {};
+\end{tikzpicture}
+\end{center}
+\end{example}
+
+\begin{example}
+\begin{center}
+\begin{tikzpicture}
+\pic[
+ braid/.cd,
+ number of strands=3,
+ line width=8pt,
+ strand 1/.style={red},
+ strand 2/.style={green},
+ strand 3/.style={blue},
+ gap=0.1,
+ control factor=0,
+ nudge factor=0,
+ name prefix=braid,
+] {braid={a_2 a_1 a_2^{-1} a_1}};
+\node[circle,draw,fill=white,inner sep=0pt] at (braid-2-1) {\(+\)};
+\node[circle,draw,fill=white,inner sep=0pt] at (braid-3-1) {\(-\)};
+\node[circle,draw,fill=white,inner sep=0pt] at (braid-2-3) {\(+\)};
+\end{tikzpicture}
+\end{center}
+
+\end{example}
+
+\newpage
+
+\section{Original Package Usage (Depreciated)}
+
+The original version was as a separate package.
+This is still included for backwards compatibility.
+To use this package, you need to put the following in the preamble.
+
+\begin{verbatim}
+\usepackage{braids}
+\end{verbatim}
+
+\DescribeMacro{\braid}
+A braid is specified by the command \Verb+\braid+.
+The syntax for this command is as follows:
+
+\Verb+\braid[style options] (name) at (coordinate) braid-word;+
+
+\DescribeMacro{braid-word}
+The \Verb+braid-word+ is an expression in the braid group, such as \Verb+s_1 s_2^{-1}+.
+The generator labels are not significant.
+The exponent can be \Verb+1+, \Verb+{-1}+, or missing (in which case it defaults to \Verb+1+, note also that the exponent is read as a \TeX-token so \Verb+{1}+ is also legal).
+Certain other symbols are allowed in the \Verb+braid-word+ which control the rendering of the braid.
+These extras are as follows.
+
+\begin{enumerate}
+\item To get crossings to render at the same height, separate them with a hyphen (note: no check is made to ensure that the crossings can legally be put at the same height; \emph{caveat emptor}).
+
+\item To draw a \emph{floor}, precede the braid element by a vertical line.
+What happens then is that when the braid is rendered, the coordinates of the rectangle behind that crossing (wide enough to encompass all the strands) is passed to a command.
+The intention is that this command draw something behind the braid.
+The command is configurable by a key (see \ref{sec:styleopts}).
+
+\item The identity element can occur in the braid-word.
+It is represented by \Verb+1+.
+This inserts the identity which corresponds to no crossing.
+However, it takes the same amount of space as if there were a crossing.
+
+\item Strands can be labelled between crossings.
+To do this, the commands \Verb+\label+, \Verb+\olabel+, and \Verb+\clabel+ are provided.
+These take three arguments, the first is optional.
+The result of this command is to place a node on top of a particular strand between the crossings where the command is given.
+The first (optional) argument can be used to pass style options to this node.
+The second argument is the strand number.
+The third argument is the label text.
+
+The three commands differ as to how they interpret the strand number.
+For \Verb+\olabel+, the strand number is taken to mean the strand that starts at that position.
+For \Verb+\clabel+, the strand number is taken to mean the strand that is currently at that position.
+The behaviour of \Verb+\label+ is to choose one or other of these depending on whether the key \Verb+strand label by origin+ is true or false.
+This key only has an effect at the start of the braid-word; it cannot be reset in the middle.
+
+\item Style options can be given in the middle of a braid-word by enclosing them in square brackets.
+There are not many style options that it makes sense to change in the middle of the braid-word, since the strands are rendered all in one go at the end.
+
+\item Scoping is handled by using braces.
+Thus to change a style only briefly, enclose the desired scope in braces.
+\end{enumerate}
+
+\DescribeMacro{name}
+The (optional) \Verb+name+ acts a little like the \Verb+name+ of a TikZ node.
+When it is specified, the routine that renders the braid also saves certain coordinates as if they were node anchors.
+Specifically, \Verb+coordinate+ nodes are placed at the centre of the braid diagram and at the ends of each strand.
+The centre has the label \Verb+name+, the strands are labelled \Verb+name-number-end+ and \Verb+name-rev-number-end+, where \Verb+name+ is the name given to the braid, \Verb+number+ is the number of the strand counting from the left, and \Verb+end+ is either \Verb+s+ for the start or \Verb+e+ for the end.
+If the version with \Verb+rev+ is used then the numbers correspond to the \emph{final} positions of the braids.
+The name can also be specified with the \Verb+name+ key.
+
+\DescribeMacro{at}
+The (optional) \Verb+at (coordinate)+ syntax positions the braid at the \Verb+coordinate+ in the current picture.
+Due to the implementation, the coordinate has to be known at the start, but the width and height of the braid are only known at the end.
+Therefore, the braid is positioned so that the start of the first strand is at \Verb+(coordinate)+.
+This can also be specified using the \Verb+at+ key.
+
+\DescribeMacro{style options}
+The \Verb+style options+ set the style for the braid strands.
+They can be grouped into three types: options that set up the main parameters for the braid, options that set the default style for the strands, and options that set up styles for individual strands.
+The options are as follows.
+
+\subsection{Style Options}
+\label{sec:styleopts}
+
+\DescribeMacro{number of strands} The key \Verb+number of strands+ sets the minimum number of strands for the braid.
+The number of strands will grow according to the terms in the braid word so this merely sets a lower bound.
+If not set, the number of strands will be determined by the terms in the braid word.
+
+\DescribeMacro{height}
+The key \Verb+height+ sets the height of the piece of the braid corresponding to an element in the group.
+
+\DescribeMacro{width}
+The key \Verb+width+ sets the separation of the strands in the braid.
+
+\DescribeMacro{border height}
+The key \Verb+border height+ adds a little extra length to the strands at the start and end of the braid.
+
+\DescribeMacro{gap}
+The key \Verb+gap+ is used to determine how much of a gap to leave in the under strand at a crossing.
+This should be a number strictly between 0 and .5.
+The curve is drawn using a cubic bezier and the gap is in terms of the time parameter, so the gap will not increase exactly proportionally to the value given by this key, though that is a reasonable approximation.
+
+\DescribeMacro{control factor}
+As just said, the parts of the strands involved in a crossing are drawn using a cubic bezier curve.
+The control points are vertically above or below their respective end point.
+This key determines that vertical separation.
+It is multiplied by the \Verb+height+ so that it scales properly.
+It can be set to 0 whereupon the strands in the crossing are straight lines.
+The default is 0.5.
+
+\DescribeMacro{nudge factor}
+The crossings are not quite placed one after another.
+There is a small ``nudge'' between the end of one crossing and the start of another.
+Due to the way that the strands are lengthened, if there is no ``nudge'' then some PDF renderers produce slightly strange results at certain magnifications.
+This key controls how much that ``nudge'' is, as a factor of the \Verb+height+.
+For the aforementioned reason, it should not be set to 0 (the default is 0.05).
+Note that this does not change the height of a crossing.
+Rather, it nudges the height at which the strands start to cross over.
+
+\DescribeMacro{style strands}
+The style of the strands are controlled by two types of option.
+Style options that are set on the \Verb+\braid+ command are passed to every strand.
+It is also possible to add style options to individual strands using the key \Verb+style strands+.
+This takes two options, a comma-delimited list of strand numbers (which could be just a single number) and a list of options to be applied to that strand.
+Thus, the syntax is \Verb+style strands={n,m,...}{options}+.
+The strands are numbered by their starting position.
+Not all of the standard TikZ style options are possible due to the way that the strands are constructed.
+Basically, the options that are allowed are those that do not require changing the path or drawing it more than once.
+
+\DescribeMacro{floor command}
+When a floor is requested behind a crossing, the actual way to render it is determined by a command.
+This key allows the user to define that command.
+The argument to this key should be the code that should be executed for each floor.
+To avoid the hassle of getting the number of hashes right, the command should take no arguments.
+Rather, the coordinates of the rectangle are saved in to macros \Verb+\floorsx+, \Verb+\floorsy+, \Verb+\floorex+, \Verb+\floorey+ (these macros will expand to something like \Verb+10pt+) and the command should use these to position the drawing.
+The default is to draw a line at the top and at the bottom of the rectangle.
+
+\DescribeMacro{style floors}
+\DescribeMacro{style all floors}
+In the spirit of separating \emph{style} and \emph{content}, the style options for the floors can be specified separately to the command (of course, they could be built in to the command).
+One advantage of this over building them in to the command is to allow them to be overridden for individual floors.
+The \Verb+style all floors+ sets up options to be used for \emph{all} floors, whilst the \Verb+style floors={n,m,...}{options}+ sets up options to be used only for the listed floor.
+Anything specified in the \Verb+floor command+ will take precedence over both of these.
+
+Any other style options are passed to the underlying TikZ/PGF system and so may influence how the braid is drawn (but note that not all keys make sense due to the implementation).
+
+
+\section{Examples}
+
+Here are more detailed examples.
+
+\begin{example}
+\begin{center}
+\begin{tikzpicture}
+\braid[
+ style all floors={fill=yellow},
+ style floors={1}{dashed,fill=yellow!50!green},
+ floor command={%
+ \fill (\floorsx,\floorsy) rectangle (\floorex,\floorey);
+ \draw (\floorsx,\floorsy) -- (\floorex,\floorsy);
+ },
+ line width=2pt,
+ style strands={1}{red},
+ style strands={2}{blue},
+ style strands={3}{green}
+] (braid) at (2,0) | s_1-s_3-s_5 | s_2^{-1}-s_4| s_1-s_4 s_2^{-1} s_1-s_3 s_2^{-1}-s_4^{-1};
+\fill[yellow] (2,0) circle (4pt);
+\fill[purple] (braid) circle (4pt);
+\node[at=(braid-3-s),pin=north west:strand 3] {};
+\node[at=(braid-3-e),pin=south west:strand 3] {};
+\node[at=(braid-rev-3-s),pin=north east:strand 3 (from bottom)] {};
+\node[at=(braid-rev-3-e),pin=south east:strand 3 (from bottom)] {};
+\end{tikzpicture}
+\end{center}
+\end{example}
+
+\begin{example}
+\begin{center}
+\begin{tikzpicture}
+\braid[
+ number of strands=3,
+ line width=8pt,
+ style strands={1}{red},
+ style strands={2}{green},
+ style strands={3}{blue},
+ gap=0.1,
+ control factor=0,
+ nudge factor=0,
+ strand label by origin=true,
+ strand label/.style={circle,draw,fill=white,inner sep=0pt},
+ yscale=1] (braid_1) a_2 \label{2}{\(+\)} \clabel{2}{\(-\)} a_1 a_2^{-1} \olabel{2}{\(+\)} a_1;
+\end{tikzpicture}
+\end{center}
+
+\end{example}
+
+\end{document}
+% Local Variables:
+% tex-output-type: "pdf18"
+% End:
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___________________________________________________________________
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--- trunk/Master/texmf-dist/doc/latex/braids/braids_code.pdf 2019-05-08 21:09:31 UTC (rev 51047)
+++ trunk/Master/texmf-dist/doc/latex/braids/braids_code.pdf 2019-05-08 21:15:00 UTC (rev 51048)
Property changes on: trunk/Master/texmf-dist/doc/latex/braids/braids_code.pdf
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===================================================================
--- trunk/Master/texmf-dist/doc/latex/braids/braids_doc.tex 2019-05-08 21:09:31 UTC (rev 51047)
+++ trunk/Master/texmf-dist/doc/latex/braids/braids_doc.tex 2019-05-08 21:15:00 UTC (rev 51048)
@@ -1,178 +0,0 @@
-\documentclass{ltxdoc}
-\usepackage[T1]{fontenc}
-\usepackage{lmodern}
-\usepackage{morefloats}
-\usepackage{tikz}
-\usepackage{braids}
-\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}
- \input{example.out}
- \end{minipage}}
-\end{center}
-}
-
-\providecommand*{\url}{\texttt}
-\GetFileInfo{braids.sty}
-
-\title{The \textsf{braids} Package: Documentation}
-\author{Andrew Stacey \\ \url{stacey at math.ntnu.no}}
-\date{\fileversion~from \filedate}
-
-\begin{document}
-
-\maketitle
-
-\begin{center}
-\begin{tikzpicture}
-\braid[width=.75cm,height=.5cm,line width=1.5pt,red,line cap=round,style strands={3,6,7,10,14,15,16,18}{gray,line width=1pt}] s_1-s_4-s_8-s_{12}-s_{16} s_2-s_5-s_7-s_9-s_{13}-s_{15} s_2-s_5-s_7-s_9-s_{15} s_1-s_4-s_8-s_{16} s_1-s_4-s_7-s_9-s_{17} s_2-s_5-s_{17} s_2-s_{13}-s_{16} s_1-s_{12}-s_{15};
-\end{tikzpicture}
-\end{center}
-
-\section{Introduction}
-
-This is a package for drawing braid diagrams using PGF/TikZ.
-An example follows.
-
-\begin{example}
-\begin{center}
-\begin{tikzpicture}
-\braid[rotate=90,style strands={1}{red},style strands={2}{blue},style strands={3}{green}] s_1 s_2^{-1} s_1 s_2^{-1} s_1 s_2^{-1};
-\end{tikzpicture}
-\end{center}
-\end{example}
-
-\section{Usage}
-
-\DescribeMacro{\braid}
-A braid is specified by the command \Verb+\braid+.
-The syntax for this command is as follows:
-
-\Verb+\braid[style options] (name) at (coordinate) braid-word;+
-
-\DescribeMacro{braid-word}
-The \Verb+braid-word+ is an expression in the braid group, such as \Verb+s_1 s_2^{-1}+.
-The generator labels are not significant.
-The exponent can be \Verb+1+, \Verb+{-1}+, or missing (in which case it defaults to \Verb+1+, note also that the exponent is read as a \TeX-token so \Verb+{1}+ is also legal).
-Certain other symbols are allowed in the \Verb+braid-word+ which control the rendering of the braid.
-To get crossings to render at the same height, separate them with a hyphen (note: no check is made to ensure that the crossings can legally be put at the same height; \emph{caveat emptor}).
-To draw a \emph{floor}, precede the braid element by a vertical line.
-What happens then is that when the braid is rendered, the coordinates of the rectangle behind that crossing (wide enough to encompass all the strands) is passed to a command.
-The intention is that this command draw something behind the braid.
-The command is configurable by a key (see \ref{sec:styleopts}).
-
-\DescribeMacro{name}
-The (optional) \Verb+name+ acts a little like the \Verb+name+ of a TikZ node.
-When it is specified, the routine that renders the braid also saves certain coordinates as if they were node anchors.
-Specifically, \Verb+coordinate+ nodes are placed at the centre of the braid diagram and at the ends of each strand.
-The centre has the label \Verb+name+, the strands are labelled \Verb+name-number-end+ and \Verb+name-rev-number-end+, where \Verb+name+ is the name given to the braid, \Verb+number+ is the number of the strand counting from the left, and \Verb+end+ is either \Verb+s+ for the start or \Verb+e+ for the end.
-If the version with \Verb+rev+ is used then the numbers correspond to the \emph{final} positions of the braids.
-The name can also be specified with the \Verb+name+ key.
-
-\DescribeMacro{at}
-The (optional) \Verb+at (coordinate)+ syntax positions the braid at the \Verb+coordinate+ in the current picture.
-Due to the implementation, the coordinate has to be known at the start, but the width and height of the braid are only known at the end.
-Therefore, the braid is positioned so that the start of the first strand is at \Verb+(coordinate)+.
-This can also be specified using the \Verb+at+ key.
-
-\DescribeMacro{style options}
-The \Verb+style options+ set the style for the braid strands.
-They can be grouped into three types: options that set up the main parameters for the braid, options that set the default style for the strands, and options that set up styles for individual strands.
-The options are as follows.
-
-\subsection{Style Options}
-\label{sec:styleopts}
-
-\DescribeMacro{number of strands} The key \Verb+number of strands+ sets the minimum number of strands for the braid.
-The number of strands will grow according to the terms in the braid word so this merely sets a lower bound.
-If not set, the number of strands will be determined by the terms in the braid word.
-
-\DescribeMacro{height}
-The key \Verb+height+ sets the height of the piece of the braid corresponding to an element in the group.
-
-\DescribeMacro{width}
-The key \Verb+width+ sets the separation of the strands in the braid.
-
-\DescribeMacro{border height}
-The key \Verb+border height+ adds a little extra length to the strands at the start and end of the braid.
-
-\DescribeMacro{style strands}
-The style of the strands are controlled by two types of option.
-Style options that are set on the \Verb+\braid+ command are passed to every strand.
-It is also possible to add style options to individual strands using the key \Verb+style strands+.
-This takes two options, a comma-delimited list of strand numbers (which could be just a single number) and a list of options to be applied to that strand.
-Thus, the syntax is \Verb+style strands={n,m,...}{options}+.
-The strands are numbered by their starting position.
-Not all of the standard TikZ style options are possible due to the way that the strands are constructed.
-Basically, the options that are allowed are those that do not require changing the path or drawing it more than once.
-
-\DescribeMacro{floor command}
-When a floor is requested behind a crossing, the actual way to render it is determined by a command.
-This key allows the user to define that command.
-The argument to this key should be the code that should be executed for each floor.
-To avoid the hassle of getting the number of hashes right, the command should take no arguments.
-Rather, the coordinates of the rectangle are saved in to macros \Verb+\floorsx+, \Verb+\floorsy+, \Verb+\floorex+, \Verb+\floorey+ (these macros will expand to something like \Verb+10pt+) and the command should use these to position the drawing.
-The default is to draw a line at the top and at the bottom of the rectangle.
-
-\DescribeMacro{style floors}
-\DescribeMacro{style all floors}
-In the spirit of separating \emph{style} and \emph{content}, the style options for the floors can be specified separately to the command (of course, they could be built in to the command).
-One advantage of this over building them in to the command is to allow them to be overridden for individual floors.
-The \Verb+style all floors+ sets up options to be used for \emph{all} floors, whilst the \Verb+style floors={n,m,...}{options}+ sets up options to be used only for the listed floor.
-Anything specified in the \Verb+floor command+ will take precedence over both of these.
-
-Any other style options are passed to the underlying TikZ/PGF system and so may influence how the braid is drawn (but note that not all keys make sense due to the implementation).
-
-
-\section{Example}
-
-Here is a more detailed example.
-
-
-\begin{example}
-\begin{center}
-\begin{tikzpicture}
-\braid[
- style all floors={fill=yellow},
- style floors={1}{dashed,fill=yellow!50!green},
- floor command={%
- \fill (\floorsx,\floorsy) rectangle (\floorex,\floorey);
- \draw (\floorsx,\floorsy) -- (\floorex,\floorsy);
- },
- line width=2pt,
- style strands={1}{red},
- style strands={2}{blue},
- style strands={3}{green}
-] (braid) at (2,0) | s_1-s_3-s_5 | s_2^{-1}-s_4| s_1-s_4 s_2^{-1} s_1-s_3 s_2^{-1}-s_4^{-1};
-\fill[yellow] (2,0) circle (4pt);
-\fill[purple] (braid) circle (4pt);
-\node[at=(braid-3-s),pin=north west:strand 3] {};
-\node[at=(braid-3-e),pin=south west:strand 3] {};
-\node[at=(braid-rev-3-s),pin=north east:strand 3 (from bottom)] {};
-\node[at=(braid-rev-3-e),pin=south east:strand 3 (from bottom)] {};
-\end{tikzpicture}
-\end{center}
-\end{example}
-\end{document}
-
-% Local Variables:
-% tex-output-type: "pdf18"
-% End:
Deleted: trunk/Master/texmf-dist/source/latex/braids/braids.dtx
===================================================================
--- trunk/Master/texmf-dist/source/latex/braids/braids.dtx 2019-05-08 21:09:31 UTC (rev 51047)
+++ trunk/Master/texmf-dist/source/latex/braids/braids.dtx 2019-05-08 21:15:00 UTC (rev 51048)
@@ -1,946 +0,0 @@
-% \iffalse meta-comment
-%<*internal>
-\iffalse
-%</internal>
-%<*readme>
-----------------------------------------------------------------
-braids --- a style file for drawing braid diagrams with TikZ/PGF
-E-mail: stacey at 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 commands for drawing braid diagrams with TikZ/PGF.
-It was designed and tested with PGF2.10.
-The initial idea of this package came from a question and answer on the site http://tex.stackexchange.com.
-%</readme>
-%<*internal>
-\fi
-\def\nameofplainTeX{plain}
-\ifx\fmtname\nameofplainTeX\else
- \expandafter\begingroup
-\fi
-%</internal>
-%<*install>
-\input docstrip.tex
-\keepsilent
-\askforoverwritefalse
-\preamble
-----------------------------------------------------------------
-braids --- a style file for drawing braid diagrams with TikZ/PGF
-E-mail: stacey at math.ntnu.no
-Released under the LaTeX Project Public License v1.3c or later
-See http://www.latex-project.org/lppl.txt
-----------------------------------------------------------------
-
-\endpreamble
-\postamble
-
-Copyright (C) 2011 by Andrew Stacey <stacey at math.ntnu.no>
-
-This work may be distributed and/or modified under the
-conditions of the LaTeX Project Public License (LPPL), either
-version 1.3c of this license or (at your option) any later
-version. The latest version of this license is in the file:
-
-http://www.latex-project.org/lppl.txt
-
-This work is "maintained" (as per LPPL maintenance status) by
-Andrew Stacey.
-
-This work consists of the files braids.dtx
- braids_doc.tex
-and the derived files README.txt,
- braids.ins,
- braids.pdf,
- braids.sty,
- braids_doc.pdf.
-
-\endpostamble
-\usedir{tex/latex/braids}
-\generate{
- \file{\jobname.sty}{\from{\jobname.dtx}{package}}
-}
-%</install>
-%<install>\endbatchfile
-%<*internal>
-\usedir{source/latex/braids}
-\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{braids}[2011/05/07 v1.0 Tikz/PGF commands for drawing braid 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{815}
-%
-% \CharacterTable
-% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
-% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
-% Digits \0\1\2\3\4\5\6\7\8\9
-% Exclamation \! Double quote \" Hash (number) \#
-% Dollar \$ Percent \% Ampersand \&
-% Acute accent \' Left paren \( Right paren \)
-% Asterisk \* Plus \+ Comma \,
-% Minus \- Point \. Solidus \/
-% Colon \: Semicolon \; Less than \<
-% Equals \= Greater than \> Question mark \?
-% Commercial at \@ Left bracket \[ Backslash \\
-% Right bracket \] Circumflex \^ Underscore \_
-% Grave accent \` Left brace \{ Vertical bar \|
-% Right brace \} Tilde \~}
-%
-%
-% \changes{1.0}{2011/05/03}{Converted to DTX file}
-%
-% \DoNotIndex{\newcommand,\newenvironment}
-%
-% \providecommand*{\url}{\texttt}
-% \GetFileInfo{braids.sty}
-% \title{The \textsf{braids} package: codebase}
-% \author{Andrew Stacey \\ \url{stacey at math.ntnu.no}}
-% \date{\fileversion~from \filedate}
-%
-% \maketitle
-%
-% \begin{center}
-% \begin{tikzpicture}
-% \braid[line width=3pt,line cap=round,style strands={1}{blue},number of strands=7] s_1 s_2 s_5^{-1};
-% \end{tikzpicture}
-% \end{center}
-%
-% \section{Introduction}
-%
-% This is a package for drawing braid diagrams using PGF/TikZ.
-% Its inspiration was a question and answer on the website \url{http://tex.stackexchange.com}.
-%
-% \StopEventually{}
-%
-% \section{Implementation}
-%
-% \iffalse
-%<*package>
-% \fi
-%
-% Test the version of PGF to see if it's what we expect.
-% If not, issue a warning (but continue anyway; after all, it \emph{might just work}).
-% \begin{macrocode}
-\def\braid at pgfversion{2.10}%
-\ifx\pgfversion\braid at pgfversion
-\else
-\PackageWarning{braids}{This package was designed using PGF2.10; you are using \pgfversion.}%
-\fi
-% \end{macrocode}
-% \begin{macro}{\ge at addto@macro}
-% This is an expanded version of \Verb+\g at addto@macro+.
-% Namely, it adds the \emph{expansion} of the second argument to the first.
-% \begin{macrocode}
-\long\def\ge at addto@macro#1#2{%
- \begingroup
- \toks@\expandafter\expandafter\expandafter{\expandafter#1#2}%
- \xdef#1{\the\toks@}%
- \endgroup}
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}{\braid}
-% This is the user command.
-% We start a group to ensure that all our assignments are local, and then call our initialisation code.
-% The optional argument is for any keys to be set.
-% \begin{macrocode}
-\newcommand{\braid}[1][]{%
- \begingroup
- \braid at start{#1}}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at process}
-% This is the token swallower.
-% This takes the next token on the braid specification and passes it to the handler command (in the macro \Verb+\braid at token+) which decides what to do next.
-% (Incidentally, the code here is heavily influenced by TikZ.
-% That's probably not very surprising.)
-% \begin{macrocode}
-\def\braid at process{%
- \afterassignment\braid at handle\let\braid at token=%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at process@start}
-% This is a variant of \Verb+\braid at process+ which is used at the start where we might have a few extra bits and pieces before the braid itself starts.
-% Specifically, we test for the \Verb+at+ and \Verb+(name)+ possibilities.
-% \begin{macrocode}
-\def\braid at process@start{%
- \afterassignment\braid at handle@start\let\braid at token=%
-}
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}{\braid at handle@start}
-% This is the handler in use at the start.
-% It looks for the tokens \Verb+a+ or \Verb+(+ which (might) signal the start of an \Verb+at (coordinate)+ or \Verb+(name)+.
-% If we get anything else (modulo spaces) we decide that we've reached the end of the initialisation stuff and it is time to get started on the braid itself.
-% \begin{macrocode}
-\def\braid at handle@start{%
- \let\braid at next=\braid at handle
- \ifx\braid at token a
-% \end{macrocode}
-% We got an \Verb+a+ so we might have an \Verb+at (coordinate)+
-% \begin{macrocode}
- \let\braid at next=\braid at maybe@locate
- \else
- \ifx\braid at token(%)
-% \end{macrocode}
-% We got an \Verb+(+ so we have a name
-% \begin{macrocode}
- \iffalse)\fi %Indentation hack!
- \let\braid at next=\braid at assign@name
- \else
- \ifx\braid at token\@sptoken
-% \end{macrocode}
-% Space; boring, redo from start
-% \begin{macrocode}
- \let\braid at next=\braid at process@start
- \fi
- \fi
- \fi
- \braid at next%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at handle}
-% This is the main handler for parsing the braid word.
-% It decides what action to take depending on what the token is.
-% We have to be a bit careful with catcodes, some packages set
-% \Verb+;+ and \Verb+|+ to be active.
-% We should probably also be careful with \Verb+^+ and \Verb+_+.
-% \begin{macrocode}
-\let\braid at semicolon=;
-\let\braid at bar=|
-\def\braid at handle{%
- \let\braid at next=\braid at process
-% \end{macrocode}
-% Start by checking our catcodes to see what we should check against
-% \begin{macrocode}
- \ifnum\the\catcode`\;=\active
- \expandafter\let\expandafter\braid at semicolon\tikz at activesemicolon
- \fi
- \ifnum\the\catcode`\|=\active
- \expandafter\let\expandafter\braid at bar\tikz at activebar
- \fi
- \ifx\braid at token\braid at semicolon
-% \end{macrocode}
-% Semicolon, means that we're done reading our braid.
-% It's time to render it.
-% \begin{macrocode}
- \let\braid at next=\braid at render
- \else
- \ifx\braid at token^
-% \end{macrocode}
-% Superscript character, the next token tells us whether it's an over-crossing or an under-crossing.
-% \begin{macrocode}
- \let\braid at next=\braid at sup
- \else
- \ifx\braid at token_
-% \end{macrocode}
-% Subscript character, the next token tells us which strands cross.
-% \begin{macrocode}
- \let\braid at next=\braid at sub
- \else
- \ifx\braid at token-
-% \end{macrocode}
-% Hyphen, this is so that we can have more than one crossing on the same level.
-% \begin{macrocode}
- \braid at increase@levelfalse
- \else
- \ifx\braid at token[
-% \end{macrocode}
-% Open bracket, this means we have some more options to process.
-% \begin{macrocode}
- \let\braid at next=\braid at process@options
- \else
- \ifx\braid at token\braid at bar
-% \end{macrocode}
-% Bar, this tells us that we want a ``floor'' at this point.
-% \begin{macrocode}
- \edef\braid at tmp{,\expandafter\the\value{braid at level}}%
- \ge at addto@macro\braid at floors\braid at tmp%
- \else
- \ifx\braid at token\bgroup
-% \end{macrocode}
-% Begin group, which we reinterpret as begining a scope.
-% \begin{macrocode}
- \braid at beginscope
- \else
- \ifx\braid at token\egroup
-% \end{macrocode}
-% End group, which ends the scope
-% \begin{macrocode}
- \braid at endscope
- \else
-% \end{macrocode}
-% Otherwise, we add the token to the braid label.
-% \begin{macrocode}
- \ge at addto@macro\braid at label{\braid at token}%
- \fi
- \fi
- \fi
- \fi
- \fi
- \fi
- \fi
- \fi
- \braid at next%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at maybe@locate}
-% If we got an \Verb+a+ token in the \Verb+\braid at handle@start+ then it \emph{might} mean we're looking at \Verb+at (coordinate)+ or it might mean that the user has decided to use \Verb+a+ as the braid parameter.
-% So we examine the next token for a \Verb+t+.
-% \begin{macrocode}
-\def\braid at maybe@locate{%
- \afterassignment\braid@@maybe at locate\let\braid at token=%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid@@maybe at locate}
-% This is where we test for \Verb+t+ and act appropriately.
-% \begin{macrocode}
-\def\braid@@maybe at locate{%
- \let\braid at next=\braid at handle
- \ifx\braid at token t
- \let\braid at next=\braid at find@location
- \fi
- \braid at next%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at find@location}
-% This macro starts us looking for a coordinate.
-% \begin{macrocode}
-\def\braid at find@location{%
- \afterassignment\braid@@find at location\let\braid at token=%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid@@find at location}
-% This is the test for the start of a coordinate.
-% If we get a \Verb+(+ that means we've reached the coordinate.
-% A space means ``carry on''.
-% Anything else is a (non-fatal) error.
-% \begin{macrocode}
-\def\braid@@find at location{%
- \let\braid at next=\braid at location@error
- \ifx\braid at token(%)
- \let\braid at next=\braid at locate
- \else
- \ifx\braid at token\@sptoken
- \let\braid at next=\braid at find@location
- \fi
- \fi
- \braid at next%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at location@error}
-% This is our error message for not getting a location.
-% \begin{macrocode}
-\def\braid at location@error{%
- \PackageWarning{braids}{Could not figure out location for braid}%
- \braid at process@start%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at locate}
-% If we reached a \Verb+(+ when looking for a coordinate, everything up to the next \Verb+)+ is that coordinate.
-% Then we parse the coordinate and call the relocation macro.
-% \begin{macrocode}
-\def\braid at locate#1){%
- \tikz at scan@one at point\braid at relocate(#1)%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at relocate}
-% This is the macro that actually does the relocation.
-% \begin{macrocode}
-\def\braid at relocate#1{%
- #1\relax
- \advance\pgf at x by -\braid at width
- \pgftransformshift{\pgfqpoint{\pgf at x}{\pgf at y}}
- \braid at process@start%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at assign@name}
-% This macro saves our name.
-% \begin{macrocode}
-\def\braid at assign@name#1){%
- \def\braid at name{#1}%
- \braid at process@start%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at process@options}
-% The intention of this macro is to allow setting of style options mid-braid.
-% (At present, this wouldn't make a lot of sense.)
-% \begin{macrocode}
-\def\braid at process@options#1]{%
- \tikzset{#1}%
- \braid at process%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% The next macros handle the actual braid elements.
-% Everything has to have a subscript, but the superscript is optional and can come before or after the subscript.
-%
-% \begin{macro}{\braid at sup}
-% This handles braid elements of the form \Verb+a^{-1}_2+.
-% \begin{macrocode}
-\def\braid at sup#1_#2{\g at addto@macro\braid at label{_{#2}^{#1}}\braid at add@crossing{#2}{#1}}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at sub}
-% \begin{macrocode}
-% This handles braid elements of the form \Verb+a_1+ or \Verb+a_1^{-1}+.
-\def\braid at sub#1{\@ifnextchar^{\braid@@sub{#1}}{\g at addto@macro\braid at label{_{#1}}\braid at add@crossing{#1}{1}}}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid@@sub}
-% Helper macro for \Verb+\braid at sub+.
-% \begin{macrocode}
-\def\braid@@sub#1^#2{\g at addto@macro\braid at label{_{#1}^{#2}}\braid at add@crossing{#1}{#2}}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at ne}
-% Remember what \Verb+1+ looks like for testing against.
-% \begin{macrocode}
-\def\braid at ne{1}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at add@crossing}
-% This is the macro which adds the crossing to the current list of strands.
-% The strands are stored as \emph{soft paths} (see the TikZ/PGF documentation).
-% So this selects the right strands and then extends them according to the crossing type.
-% \begin{macrocode}
-\def\braid at add@crossing#1#2{%
-% \end{macrocode}
-% Our crossing type, which is \Verb+#2+, is one of \Verb+1+ or \Verb+-1+.
-% Our strands are \Verb+#1+ and \Verb-#1+1-.
-% \begin{macrocode}
- \edef\braid at crossing@type{#2}%
- \edef\braid at this@strand{#1}%
- \pgfmathtruncatemacro{\braid at next@strand}{#1+1}
-% \end{macrocode}
-% Increment the level counter, if requested.
-% The controls whether the crossing is on the same level as the previous one or is one level further on.
-% \begin{macrocode}
- \ifbraid at increase@level
- \stepcounter{braid at level}
- \fi
-% \end{macrocode}
-% Default is to request increment so we set it for next time.
-% \begin{macrocode}
- \braid at increase@leveltrue
-% \end{macrocode}
-% Now we figure out the coordinates of the crossing.
-% \Verb+(\braid at tx,\braid at ty)+ is the top-left corner (assuming the braid flows down the page).
-% \Verb+(\braid at nx,\braid at ny)+ is the bottom-right corner (assuming the braid flows down the page).
-% We start by setting \Verb+(\braid at tx,\braid at ty)+ according to the level and strand number, then shift \Verb+\braid at ty+ by \Verb+\braid at eh+ which is the ``edge height'' (the little extra at the start and end of each strand).
-% Then from these values, we set \Verb+(\braid at nx,\braid at ny)+ by adding on the appropriate amount.
-% The heights \Verb+\braid at cy+ and \Verb+\braid at dy+ are for the control points for the strands as they cross.
-% They're actually the same height, but using two gives us the possibility of changing them independently in a later version of this package.
-% Lastly, we bring \Verb+\braid at ty+ and \Verb+\braid at ny+ towards each other just a little so that there is ``clear water'' between subsequent crossings (makes it look a bit better if the same strand is used in subsequent crossings).
-% \begin{macrocode}
- \braid at tx=\braid at this@strand\braid at width
- \braid at ty=\value{braid at level}\braid at height
- \advance\braid at ty by \braid at eh
- \braid at nx=\braid at tx
- \braid at ny=\braid at ty
- \advance\braid at nx by \braid at width
- \advance\braid at ny by \braid at height
- \braid at cy=\braid at ty
- \braid at dy=\braid at ny
- \advance\braid at cy by .5\braid at height
- \advance\braid at dy by -.5\braid at height
- \advance\braid at ty by .05\braid at height
- \advance\braid at ny by -.05\braid at height
-% \end{macrocode}
-% Now we try to find a starting point for the strand ending here.
-% We might not have used this strand before, so it might not exist.
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at this@path at origin\csname braid at strand@\braid at this@strand @origin\endcsname
-% \end{macrocode}
-% If we haven't seen this strand before, that one will be \Verb+\relax+.
-% \begin{macrocode}
-\ifx\braid at this@path at origin\relax
-% \end{macrocode}
-% Haven't seen this strand before, so initialise it.
-% Record the initial position of the strand.
-% \begin{macrocode}
- \let\braid at this@path at origin\braid at this@strand
-% \end{macrocode}
-% Start a new soft path.
-% \begin{macrocode}
- \pgfsyssoftpath at setcurrentpath{\@empty}
- \pgfpathmoveto{\pgfpoint{\braid at tx}{0pt}}
-% \end{macrocode}
-% Save the path as \Verb+\braid at this@path+.
-% \begin{macrocode}
- \pgfsyssoftpath at getcurrentpath{\braid at this@path}
- \else
-% \end{macrocode}
-% We have seen this before, so we simply copy the associated path in to \Verb+\braid at this@path+.
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at this@path\csname braid at strand@\braid at this@path at origin\endcsname
- \fi
-% \end{macrocode}
-% Now we do the same again with the other strand in the crossing.
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at next@path at origin\csname braid at strand@\braid at next@strand @origin\endcsname
- \ifx\braid at next@path at origin\relax
- \let\braid at next@path at origin\braid at next@strand
- \pgfsyssoftpath at setcurrentpath{\@empty}
- \pgfpathmoveto{\pgfpoint{\braid at nx}{0pt}}
- \pgfsyssoftpath at getcurrentpath{\braid at next@path}
- \else
- \expandafter\let\expandafter\braid at next@path\csname braid at strand@\braid at next@path at origin\endcsname
- \fi
-% \end{macrocode}
-% Now that we have the paths for our two strands, we extend them to the next level.
-% We start by selecting the first path.
-% \begin{macrocode}
- \pgfsyssoftpath at setcurrentpath{\braid at this@path}
-% \end{macrocode}
-% Draw a line down to the current level, note that this line is always non-trivial since we shifted the corners of the crossing in a little.
-% \begin{macrocode}
- \pgfpathlineto{\pgfqpoint{\braid at tx}{\braid at ty}}
-% \end{macrocode}
-% Curve across to the next position.
-% Depending on the crossing type, we either have a single curve or we have to break it in two.
-% \begin{macrocode}
-\ifx\braid at crossing@type\braid at over@cross
-% \end{macrocode}
-% We're on the overpass, so just one curve needed.
-% \begin{macrocode}
-\pgfpathcurveto{\pgfqpoint{\braid at tx}{\braid at cy}}{\pgfqpoint{\braid at nx}{\braid at dy}}{\pgfqpoint{\braid at nx}{\braid at ny}}
-\else
-% \end{macrocode}
-% We're on the underpass, so we need to interrupt our path to allow the other curve to go past.
-% The choice of \Verb+.4+ and \Verb+.6+ should probably be configurable.
-% \begin{macrocode}
-\pgfpathcurvebetweentimecontinue{0}{.4}{\pgfqpoint{\braid at tx}{\braid at ty}}{\pgfqpoint{\braid at tx}{\braid at cy}}{\pgfqpoint{\braid at nx}{\braid at dy}}{\pgfqpoint{\braid at nx}{\braid at ny}}
-\pgfpathcurvebetweentime{.6}{1}{\pgfqpoint{\braid at tx}{\braid at ty}}{\pgfqpoint{\braid at tx}{\braid at cy}}{\pgfqpoint{\braid at nx}{\braid at dy}}{\pgfqpoint{\braid at nx}{\braid at ny}}
-\fi
-% \end{macrocode}
-% We're done with this path, so now we save it.
-% \begin{macrocode}
- \pgfsyssoftpath at getcurrentpath{\braid at this@path}
-% \end{macrocode}
-% Now do the same with the second path.
-% \begin{macrocode}
- \pgfsyssoftpath at setcurrentpath{\braid at next@path}
- \pgfpathlineto{\pgfqpoint{\braid at nx}{\braid at ty}}
-\ifx\braid at crossing@type\braid at over@cross
-\pgfpathcurvebetweentimecontinue{0}{.4}{\pgfqpoint{\braid at nx}{\braid at ty}}{\pgfqpoint{\braid at nx}{\braid at cy}}{\pgfqpoint{\braid at tx}{\braid at dy}}{\pgfqpoint{\braid at tx}{\braid at ny}}
-\pgfpathcurvebetweentime{.6}{1}{\pgfqpoint{\braid at nx}{\braid at ty}}{\pgfqpoint{\braid at nx}{\braid at cy}}{\pgfqpoint{\braid at tx}{\braid at dy}}{\pgfqpoint{\braid at tx}{\braid at ny}}
-\else
- \pgfpathcurveto{\pgfqpoint{\braid at nx}{\braid at cy}}{\pgfqpoint{\braid at tx}{\braid at dy}}{\pgfqpoint{\braid at tx}{\braid at ny}}
-\fi
- \pgfsyssoftpath at getcurrentpath{\braid at next@path}
-% \end{macrocode}
-% Now save the paths to their proper macros again.
-% \begin{macrocode}
- \expandafter\let\csname braid at strand@\braid at this@path at origin \endcsname\braid at this@path
- \expandafter\let\csname braid at strand@\braid at next@path at origin \endcsname\braid at next@path
-% \end{macrocode}
-% Now update the origins
-% \begin{macrocode}
- \expandafter\let\csname braid at strand@\braid at this@strand @origin\endcsname\braid at next@path at origin
- \expandafter\let\csname braid at strand@\braid at next@strand @origin\endcsname\braid at this@path at origin
-% \end{macrocode}
-% increment the strand counter, if necessary
-% \begin{macrocode}
- \pgfmathparse{\value{braid at strands} < \braid at next@strand ? "\noexpand\setcounter{braid at strands}{\braid at next@strand}" : ""}
- \pgfmathresult
-% \end{macrocode}
-% And merrily go on our way with the next bit of the braid specification.
-% \begin{macrocode}
- \braid at process%
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at floors@trim}
-% The list of floors, if given, will start with a superfluous comma.
-% This removes it.
-% \begin{macrocode}
-\def\braid at floors@trim,{}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at render@floor}
-% This is the default rendering for floors: it draws a rectangle.
-% \begin{macrocode}
-\def\braid at render@floor{%
- \draw (\floorsx,\floorsy) rectangle (\floorex,\floorey);
-}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at render}
-% This is called at the end of the braid and it renders the braids and floors according to whatever has been built up up to now.
-% \begin{macrocode}
-\def\braid at render{
-% \end{macrocode}
-% Check for floors since we do them first.
-% \begin{macrocode}
- \ifx\braid at floors\@empty
- \else
-% \end{macrocode}
-% Have some floors, start a scope and prepare to render them.
-% \begin{macrocode}
- \pgfsys at beginscope
-% \end{macrocode}
-% Clear the path (just to be sure).
-% \begin{macrocode}
- \pgfsyssoftpath at setcurrentpath{\empty}
-% \end{macrocode}
-% Trim the initial comma off the list of floors.
-% \begin{macrocode}
- \edef\braid at floors{\expandafter\braid at floors@trim\braid at floors}
-% \end{macrocode}
-% Initialise our horizontal coordinates.
-% \begin{macrocode}
- \braid at tx=\braid at width
- \advance\braid at tx by \braid at eh
- \braid at nx=\value{braid at strands}\braid at width
- \advance\braid at nx by -\braid at eh
-% \end{macrocode}
-% Loop over the list of floors.
-% \begin{macrocode}
- \foreach \braid at f in \braid at floors {
- \pgfsys at beginscope
-% \end{macrocode}
-% Figure out the vertical coordinates for the current floor.
-% \begin{macrocode}
- \braid at ty=\braid at f\braid at height
- \advance\braid at ty by \braid at eh
- \advance\braid at ty by \braid at height
- \braid at ny=\braid at ty
- \advance\braid at ny by \braid at height
-% \end{macrocode}
-% Save the coordinates for use in the floor rendering macro.
-% \begin{macrocode}
- \edef\floorsx{\the\braid at tx}
- \edef\floorsy{\the\braid at ty}
- \edef\floorex{\the\braid at nx}
- \edef\floorey{\the\braid at ny}
- \let\tikz at options=\pgfutil at empty
-% \end{macrocode}
-% Load general floor style options.
-% \begin{macrocode}
- \expandafter\tikzset\expandafter{\braid at floors@style}
-% \end{macrocode}
-% Load any style options specific to this floor.
-% We're actually offset by 2 from what the user thinks the floor level is.
-% \begin{macrocode}
- \pgfmathtruncatemacro{\braid at ff}{\braid at f+2}
-% \end{macrocode}
-% Load the relevant floor style, if it exists.
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at floor@style\csname braid at options@floor@\braid at ff\endcsname
- \ifx\braid at floor@style\relax
- \else
-% \end{macrocode}
-% There is a floor style for this level, so process it.
-% \begin{macrocode}
- \expandafter\tikzset\expandafter{\braid at floor@style}%
- \fi
-% \end{macrocode}
-% The \Verb+\tikzset+ just parses the options, we need to call \Verb+\tikz at options+ to actually set them.
-% \begin{macrocode}
-\tikz at options
-% \end{macrocode}
-% Now we call the rendering code.
-% \begin{macrocode}
-\braid at render@floor
-% \end{macrocode}
-% Done!
-% End the scope for \emph{this} floor and go again.
-% \begin{macrocode}
-\pgfsys at endscope
- }
-% \end{macrocode}
-% Done rendering floors, end the scope.
-% \begin{macrocode}
- \pgfsys at endscope
- \fi
-% \end{macrocode}
-% Finished with floors (if we had them), now get on with the strands.
-% \begin{macrocode}
- \stepcounter{braid at level}
- \foreach \braid at k in {1,...,\value{braid at strands}} {
-% \end{macrocode}
-% Start a local scope to ensure we don't mess with other braids
-% \begin{macrocode}
- \pgfsys at beginscope
-% \end{macrocode}
-% Default is to draw each braid
-% \begin{macrocode}
- \tikz at mode@drawtrue%
- \let\tikz at mode=\pgfutil at empty
- \let\tikz at options=\pgfutil at empty
-% \end{macrocode}
-% (x,y) coordinates of bottom of strand
-% \begin{macrocode}
- \braid at tx=\braid at k\braid at width
- \braid at ty=\value{braid at level}\braid at height
- \advance\braid at ty by 2\braid at eh
-% \end{macrocode}
-% Try to find the starting point of this strand
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at path@origin\csname braid at strand@\braid at k @origin\endcsname
- \ifx\braid at path@origin\relax
-% \end{macrocode}
-% If that doesn't exist, we'll just draw a straight line
-% so we move to the top of the current position
-% \begin{macrocode}
- \pgfsyssoftpath at setcurrentpath{\@empty}
- \pgfpathmoveto{\pgfqpoint{\braid at tx}{0pt}}
- \let\braid at path@origin\braid at k
- \else
-% \end{macrocode}
-% If the path does exist, we load it
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at path\csname braid at strand@\braid at path@origin\endcsname
- \pgfsyssoftpath at setcurrentpath{\braid at path}
- \fi
-% \end{macrocode}
-% Extend the path to the bottom
-% \begin{macrocode}
- \pgflineto{\pgfqpoint{\braid at tx}{\braid at ty}}
-% \end{macrocode}
-% Load common style options
-% \begin{macrocode}
- \expandafter\tikzset\expandafter{\braid at style}
-% \end{macrocode}
-% Load any style options specific to this strand
-% \begin{macrocode}
- \expandafter\let\expandafter\braid at style\csname braid at options@strand@\braid at path@origin\endcsname
- \ifx\braid at style\relax
- \else
- \expandafter\tikzset\expandafter{\braid at style}
- \fi
-\braid at options
- \tikz at mode
- \tikz at options
-% \end{macrocode}
-% This is the command that actually draws the strand.
-% \begin{macrocode}
- \edef\tikz at temp{\noexpand\pgfusepath{%
- \iftikz at mode@draw draw\fi%
- }}%
- \tikz at temp
-% \end{macrocode}
-% If our braid has a name, we label the ends of the strand.
-% \begin{macrocode}
-\ifx\braid at name\pgfutil at empty
-\else
-% \end{macrocode}
-% Label the ends of the strand.
-% \begin{macrocode}
-\coordinate (\braid at name-\braid at path@origin-e) at (\braid at tx,\braid at ty);
-\coordinate (\braid at name-rev-\braid at k-e) at (\braid at tx,\braid at ty);
-\braid at nx=\braid at path@origin\braid at width
-\coordinate (\braid at name-\braid at path@origin-s) at (\braid at nx,0pt);
-\coordinate (\braid at name-rev-\braid at k-s) at (\braid at nx,0pt);
-\fi
-% \end{macrocode}
-% Done with this strand, close the scope and do the next one.
-% \begin{macrocode}
- \pgfsys at endscope
- }
-% \end{macrocode}
-% If our braid has a name, we also want to label the centre.
-% \begin{macrocode}
- \ifx\braid at name\pgfutil at empty
- \else
- \braid at tx=\value{braid at strands}\braid at width
- \braid at ty=\value{braid at level}\braid at height
- \advance\braid at ty by 2\braid at eh
- \advance\braid at tx by \braid at width
- \braid at tx=.5\braid at tx
- \braid at ty=.5\braid at ty
- \coordinate (\braid at name) at (\braid at tx,\braid at ty);
- \fi
-% \end{macrocode}
-% All done now, close the scope and end the group (which was opened right at the start).
-% \begin{macrocode}
- \pgfsys at endscope
- \endgroup}
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\braid at start}
-% This starts off the braid, initialising a load of stuff.
-% We start a PGF scope, set the level to \(-1\), the label, floors, and name to empty, process any options we're given, and save certain lengths for later use..
-% \begin{macrocode}
-\def\braid at start#1{%
- \pgfsys at beginscope
- \setcounter{braid at level}{-1}%
- \let\braid at label\@empty
- \let\braid at floors\@empty
- \let\braid at name\empty
- \pgfkeys{/pgf/braid/.cd,#1}
- \let\braid at options\tikz at options
- \tikz at transform
- \setcounter{braid at strands}{\pgfkeysvalueof{/pgf/braid/number of strands}}%
- \braid at width=\pgfkeysvalueof{/pgf/braid/width}
- \braid at height=\pgfkeysvalueof{/pgf/braid/height}
- \braid at eh=\pgfkeysvalueof{/pgf/braid/border height}
- \braid at height=-\braid at height
- \braid at eh=-\braid at eh
- \braid at increase@leveltrue
- \braid at process@start
-}
-% \end{macrocode}
-% \end{macro}
-%
-% These are the lengths we'll use as we construct the braid
-% \begin{macrocode}
-\newdimen\braid at width
-\newdimen\braid at height
-\newdimen\braid at tx
-\newdimen\braid at ty
-\newdimen\braid at nx
-\newdimen\braid at ny
-\newdimen\braid at cy
-\newdimen\braid at dy
-\newdimen\braid at eh
-% \end{macrocode}
-%
-% An if to decide whether or not to step to the next level or not
-% \begin{macrocode}
-\newif\ifbraid at increase@level
-% \end{macrocode}
-%
-% Some initial values
-% \begin{macrocode}
-\let\braid at style\pgfutil at empty
-\let\braid at floors@style\pgfutil at empty
-\def\braid at over@cross{1}
-% \end{macrocode}
-%
-% Counters to track the strands and the levels.
-% \begin{macrocode}
-\newcounter{braid at level}
-\newcounter{braid at strands}
-% \end{macrocode}
-%
-% All the keys we'll use.
-% \begin{macrocode}
-\pgfkeys{
-% \end{macrocode}
-% Handle unknown keys by passing them to \Verb+pgf+ and \Verb+tikz+.
-% \begin{macrocode}
- /tikz/braid/.search also={/pgf},
- /pgf/braid/.search also={/pgf,/tikz},
-% \end{macrocode}
-% Our ``namespace'' is \Verb+/pgf/braid+.
-% \begin{macrocode}
- /pgf/braid/.cd,
- number of strands/.initial=0,
- height/.initial=1cm,
- width/.initial=1cm,
- border height/.initial=.25cm,
- name/.code={%
- \def\braid at name{#1}%
- },
- at/.code={%
- \braid at relocate{#1}%
- },
- floor command/.code={%
- \def\braid at render@floor{#1}%
- },
- style strands/.code 2 args={%
- \def\braid at temp{#2}%
- \braidset{style each strand/.list={#1}}%
- },
- style each strand/.code={%
- \expandafter\edef\csname braid at options@strand@#1\endcsname{\braid at temp}%
- },
- style floors/.code 2 args={%
- \def\braid at temp{#2}%
- \braidset{style each floor/.list={#1}}%
- },
- style each floor/.code={%
- \expandafter\edef\csname braid at options@floor@#1\endcsname{\braid at temp}%
- },
- style all floors/.code={%
- \def\braid at floors@style{#1}
- }
-}
-% \end{macrocode}
-% \begin{macro}{\braidset}
-% Shorthand for setting braid-specific keys.
-% \begin{macrocode}
-\def\braidset#1{%
- \pgfkeys{/pgf/braid/.cd,#1}}
-% \end{macrocode}
-% \end{macro}
-% \iffalse
-%</package>
-% \fi
-%
-% \Finale
-
-\endinput
Added: trunk/Master/texmf-dist/source/latex/braids/braids_code.dtx
===================================================================
--- trunk/Master/texmf-dist/source/latex/braids/braids_code.dtx (rev 0)
+++ trunk/Master/texmf-dist/source/latex/braids/braids_code.dtx 2019-05-08 21:15:00 UTC (rev 51048)
@@ -0,0 +1,2321 @@
+% \iffalse meta-comment
+%<*internal>
+\iffalse
+%</internal>
+%<*readme>
+----------------------------------------------------------------
+braids --- a style file for drawing braid diagrams with TikZ/PGF
+E-mail: loopspace at mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+This package defines some commands for drawing braid diagrams with TikZ/PGF.
+The initial idea of this package came from a question and answer on the site http://tex.stackexchange.com.
+%</readme>
+%<*internal>
+\fi
+\def\nameofplainTeX{plain}
+\ifx\fmtname\nameofplainTeX\else
+ \expandafter\begingroup
+\fi
+%</internal>
+%<*install>
+\input l3docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\preamble
+----------------------------------------------------------------
+braids --- a style file for drawing braid diagrams with TikZ/PGF
+E-mail: loopspace at 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) 2011-2019 by Andrew Stacey <loopspace at 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 braids.dtx
+ braids_doc.tex
+and the derived files README.txt,
+ braids.ins,
+ braids.pdf,
+ braids.sty,
+ tikzlibrarybraids.code.tex,
+ braids_doc.pdf.
+
+\endpostamble
+\usedir{tex/latex/braids}
+\generate{
+ \file{braids.sty}{\from{\jobname.dtx}{package}}
+}
+\generate{
+ \file{tikzlibrarybraids.code.tex}{\from{\jobname.dtx}{library}}
+}
+%</install>
+%<install>\endbatchfile
+%<*internal>
+\usedir{source/latex/braids}
+\generate{
+ \file{\jobname.ins}{\from{\jobname.dtx}{install}}
+}
+\nopreamble\nopostamble
+\usedir{doc/latex/braids}
+\generate{
+ \file{README.txt}{\from{\jobname.dtx}{readme}}
+}
+\ifx\fmtname\nameofplainTeX
+ \expandafter\endbatchfile
+\else
+ \expandafter\endgroup
+\fi
+%</internal>
+%<*package>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{braids}[2011/10/18 v1.1 Tikz/PGF commands for drawing braid diagrams]
+%</package>
+%<*driver>
+\documentclass{l3doc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage{tikz}
+\usepackage{braids}
+\usetikzlibrary{braids}
+
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
+\begin{document}
+ \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{1949}
+%
+% \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{1.1}{2011/05/03}{Extended syntax}
+% \changes{2.0}{2019/03/20}{Converted TikZ library}
+%
+% \DoNotIndex{\newcommand,\newenvironment}
+%
+% \GetFileInfo{tikzlibrarybraids.code.tex}
+% \title{The \textsf{braids} package: codebase}
+% \author{Andrew Stacey \\ \texttt{loopspace at mathforge.org}}
+% \date{\fileversion~from \filedate}
+%
+% \maketitle
+%
+% \section{Introduction}
+%
+% This is a package for drawing braid diagrams using PGF/TikZ.
+% Its inspiration was a question and answer on the website \texttt{http://tex.stackexchange.com}.
+%
+% \section{History}
+%
+% \begin{itemize}
+% \item v1.0 First public release.
+%
+% \item v1.1 Added ability to configure the gap size, the control points, and the ``nudge''.
+% Added ability to add labels to strands between crossings.
+%
+% \item v2 Reimplemented as TikZ library rather than a standalone package.
+% \end{itemize}
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+% \iffalse
+%<*package>
+% \fi
+%
+% Issue a notice that this is a depreciated version of the braids package.
+% \begin{macrocode}
+\PackageWarning{braids}{%
+ This package has been reimplemented as a TikZ library; if starting with a fresh document, please consider using that instead.%
+}%
+% \end{macrocode}
+%
+% \begin{macro}[internal]{\ge at addto@macro}
+% This is an expanded version of \Verb+\g at addto@macro+.
+% Namely, it adds the \emph{expansion} of the second argument to the first.
+% \begin{macrocode}
+\long\def\ge at addto@macro#1#2{%
+ \begingroup
+ \toks@\expandafter\expandafter\expandafter{\expandafter#1#2}%
+ \xdef#1{\the\toks@}%
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\braid}
+% This is the user command.
+% We start a group to ensure that all our assignments are local, and then call our initialisation code.
+% The optional argument is for any keys to be set.
+% \begin{macrocode}
+\newcommand{\braid}[1][]{%
+ \begingroup
+ \braid at start{#1}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at process}
+% This is the token swallower.
+% This takes the next token on the braid specification and passes it to the handler command (in the macro \Verb+\braid at token+) which decides what to do next.
+% (Incidentally, the code here is heavily influenced by TikZ.
+% That's probably not very surprising.)
+% \begin{macrocode}
+\def\braid at process{%
+ \afterassignment\braid at handle\let\braid at token=%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at process@start}
+% This is a variant of \Verb+\braid at process+ which is used at the start where we might have a few extra bits and pieces before the braid itself starts.
+% Specifically, we test for the \Verb+at+ and \Verb+(name)+ possibilities.
+% \begin{macrocode}
+\def\braid at process@start{%
+ \afterassignment\braid at handle@start\let\braid at token=%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at handle@start}
+% This is the handler in use at the start.
+% It looks for the tokens \Verb+a+ or \Verb+(+ which (might) signal the start of an \Verb+at (coordinate)+ or \Verb+(name)+.
+% If we get anything else (modulo spaces) we decide that we've reached the end of the initialisation stuff and it is time to get started on the braid itself.
+% \begin{macrocode}
+\def\braid at handle@start{%
+ \let\braid at next=\braid at handle
+ \ifx\braid at token a
+% \end{macrocode}
+% We got an \Verb+a+ so we might have an \Verb+at (coordinate)+
+% \begin{macrocode}
+ \let\braid at next=\braid at maybe@locate
+ \else
+ \ifx\braid at token(%)
+% \end{macrocode}
+% We got an \Verb+(+ so we have a name
+% \begin{macrocode}
+ \iffalse)\fi %Indentation hack!
+ \let\braid at next=\braid at assign@name
+ \else
+ \ifx\braid at token\@sptoken
+% \end{macrocode}
+% Space; boring, redo from start
+% \begin{macrocode}
+ \let\braid at next=\braid at process@start
+ \fi
+ \fi
+ \fi
+ \braid at next%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at handle}
+% This is the main handler for parsing the braid word.
+% It decides what action to take depending on what the token is.
+% We have to be a bit careful with catcodes, some packages set
+% \Verb+;+ and \Verb+|+ to be active.
+% We should probably also be careful with \Verb+^+ and \Verb+_+.
+% \begin{macrocode}
+\let\braid at semicolon=;
+\let\braid at bar=|
+\def\braid at handle{%
+ \let\braid at next=\braid at process
+% \end{macrocode}
+% Start by checking our catcodes to see what we should check against
+% \begin{macrocode}
+ \ifnum\the\catcode`\;=\active
+ \expandafter\let\expandafter\braid at semicolon\tikz at activesemicolon
+ \fi
+ \ifnum\the\catcode`\|=\active
+ \expandafter\let\expandafter\braid at bar\tikz at activebar
+ \fi
+ \ifx\braid at token\braid at semicolon
+% \end{macrocode}
+% Semicolon, means that we're done reading our braid.
+% It's time to render it.
+% \begin{macrocode}
+ \let\braid at next=\braid at render
+ \else
+ \ifx\braid at token^
+% \end{macrocode}
+% Superscript character, the next token tells us whether it's an over-crossing or an under-crossing.
+% \begin{macrocode}
+ \let\braid at next=\braid at sup
+ \else
+ \ifx\braid at token_
+% \end{macrocode}
+% Subscript character, the next token tells us which strands cross.
+% \begin{macrocode}
+ \let\braid at next=\braid at sub
+ \else
+ \ifx\braid at token-
+% \end{macrocode}
+% Hyphen, this is so that we can have more than one crossing on the same level.
+% \begin{macrocode}
+ \braid at increase@levelfalse
+ \else
+ \ifx\braid at token1%
+% \end{macrocode}
+% 1: this means the ``identity'' crossing, so no crossing here.
+% Increase the level, unless overriden, and add to the label.
+% \begin{macrocode}
+ \ifbraid at increase@level
+ \stepcounter{braid at level}
+ \fi
+ \braid at increase@leveltrue
+ \ge at addto@macro\braid at label{\braid at token}%
+ \else
+ \ifx\braid at token[%
+% \end{macrocode}
+% Open bracket, this means we have some more options to process.
+% \begin{macrocode}
+ \let\braid at next=\braid at process@options
+ \else
+ \ifx\braid at token\braid at bar
+% \end{macrocode}
+% Bar, this tells us that we want a ``floor'' at this point.
+% \begin{macrocode}
+ \edef\braid at tmp{,\expandafter\the\value{braid at level}}%
+ \ge at addto@macro\braid at floors\braid at tmp%
+ \else
+ \ifx\braid at token\bgroup
+% \end{macrocode}
+% Begin group, which we reinterpret as begining a scope.
+% \begin{macrocode}
+ \braid at beginscope
+ \else
+ \ifx\braid at token\egroup
+% \end{macrocode}
+% End group, which ends the scope
+% \begin{macrocode}
+ \braid at endscope
+ \else
+ \ifx\braid at token\braid at olabel@strand
+ \let\braid at next=\braid at olabel@strand
+ \else
+ \ifx\braid at token\braid at clabel@strand
+ \let\braid at next=\braid at clabel@strand
+ \else
+% \end{macrocode}
+% Otherwise, we add the token to the braid label.
+% \begin{macrocode}
+ \ge at addto@macro\braid at label{\braid at token}%
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \braid at next%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at maybe@locate}
+% If we got an \Verb+a+ token in the \Verb+\braid at handle@start+ then it \emph{might} mean we're looking at \Verb+at (coordinate)+ or it might mean that the user has decided to use \Verb+a+ as the braid parameter.
+% So we examine the next token for a \Verb+t+.
+% \begin{macrocode}
+\def\braid at maybe@locate{%
+ \afterassignment\braid@@maybe at locate\let\braid at token=%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid@@maybe at locate}
+% This is where we test for \Verb+t+ and act appropriately.
+% \begin{macrocode}
+\def\braid@@maybe at locate{%
+ \let\braid at next=\braid at handle
+ \ifx\braid at token t
+ \let\braid at next=\braid at find@location
+ \fi
+ \braid at next%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at find@location}
+% This macro starts us looking for a coordinate.
+% \begin{macrocode}
+\def\braid at find@location{%
+ \afterassignment\braid@@find at location\let\braid at token=%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid@@find at location}
+% This is the test for the start of a coordinate.
+% If we get a \Verb+(+ that means we've reached the coordinate.
+% A space means ``carry on''.
+% Anything else is a (non-fatal) error.
+% \begin{macrocode}
+\def\braid@@find at location{%
+ \let\braid at next=\braid at location@error
+ \ifx\braid at token(%)
+ \let\braid at next=\braid at locate
+ \else
+ \ifx\braid at token\@sptoken
+ \let\braid at next=\braid at find@location
+ \fi
+ \fi
+ \braid at next%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at location@error}
+% This is our error message for not getting a location.
+% \begin{macrocode}
+\def\braid at location@error{%
+ \PackageWarning{braids}{Could not figure out location for braid}%
+ \braid at process@start%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at locate}
+% If we reached a \Verb+(+ when looking for a coordinate, everything up to the next \Verb+)+ is that coordinate.
+% Then we parse the coordinate and call the relocation macro.
+% \begin{macrocode}
+\def\braid at locate#1){%
+ \tikz at scan@one at point\braid at relocate(#1)%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at relocate}
+% This is the macro that actually does the relocation.
+% \begin{macrocode}
+\def\braid at relocate#1{%
+ #1\relax
+ \advance\pgf at x by -\braid at width
+ \pgftransformshift{\pgfqpoint{\pgf at x}{\pgf at y}}
+ \braid at process@start%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at assign@name}
+% This macro saves our name.
+% \begin{macrocode}
+\def\braid at assign@name#1){%
+ \def\braid at name{#1}%
+ \braid at process@start%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at process@options}
+% The intention of this macro is to allow setting of style options mid-braid.
+% (At present, this wouldn't make a lot of sense.)
+% \begin{macrocode}
+\def\braid at process@options#1]{%
+ \tikzset{#1}%
+ \braid at process%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% The next macros handle the actual braid elements.
+% Everything has to have a subscript, but the superscript is optional and can come before or after the subscript.
+%
+% \begin{macro}[internal]{\braid at sup}
+% This handles braid elements of the form \Verb+a^{-1}_2+.
+% \begin{macrocode}
+\def\braid at sup#1_#2{%
+ \g at addto@macro\braid at label{_{#2}^{#1}}%
+ \braid at add@crossing{#2}{#1}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at sub}
+% \begin{macrocode}
+% This handles braid elements of the form \Verb+a_1+ or \Verb+a_1^{-1}+.
+\def\braid at sub#1{%
+ \@ifnextchar^{\braid@@sub{#1}}%
+ {\g at addto@macro\braid at label{_{#1}}\braid at add@crossing{#1}{1}}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid@@sub}
+% Helper macro for \Verb+\braid at sub+.
+% \begin{macrocode}
+\def\braid@@sub#1^#2{%
+ \g at addto@macro\braid at label{_{#1}^{#2}}%
+ \braid at add@crossing{#1}{#2}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at ne}
+% Remember what \Verb+1+ looks like for testing against.
+% \begin{macrocode}
+\def\braid at ne{1}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at add@crossing}
+% This is the macro which adds the crossing to the current list of strands.
+% The strands are stored as \emph{soft paths} (see the TikZ/PGF documentation).
+% So this selects the right strands and then extends them according to the crossing type.
+% \begin{macrocode}
+\def\braid at add@crossing#1#2{%
+% \end{macrocode}
+% Our crossing type, which is \Verb+#2+, is one of \Verb+1+ or \Verb+-1+.
+% Our strands are \Verb+#1+ and \Verb-#1+1-.
+% \begin{macrocode}
+ \edef\braid at crossing@type{#2}%
+ \edef\braid at this@strand{#1}%
+ \pgfmathtruncatemacro{\braid at next@strand}{#1+1}
+% \end{macrocode}
+% Increment the level counter, if requested.
+% The controls whether the crossing is on the same level as the previous one or is one level further on.
+% \begin{macrocode}
+ \ifbraid at increase@level
+ \stepcounter{braid at level}
+ \fi
+% \end{macrocode}
+% Default is to request increment so we set it for next time.
+% \begin{macrocode}
+ \braid at increase@leveltrue
+% \end{macrocode}
+% Now we figure out the coordinates of the crossing.
+% \Verb+(\braid at tx,\braid at ty)+ is the top-left corner (assuming the braid flows down the page).
+% \Verb+(\braid at nx,\braid at ny)+ is the bottom-right corner (assuming the braid flows down the page).
+% We start by setting \Verb+(\braid at tx,\braid at ty)+ according to the level and strand number, then shift \Verb+\braid at ty+ by \Verb+\braid at eh+ which is the ``edge height'' (the little extra at the start and end of each strand).
+% Then from these values, we set \Verb+(\braid at nx,\braid at ny)+ by adding on the appropriate amount.
+% The heights \Verb+\braid at cy+ and \Verb+\braid at dy+ are for the control points for the strands as they cross.
+% They're actually the same height, but using two gives us the possibility of changing them independently in a later version of this package.
+% Lastly, we bring \Verb+\braid at ty+ and \Verb+\braid at ny+ towards each other just a little so that there is ``clear water'' between subsequent crossings (makes it look a bit better if the same strand is used in subsequent crossings).
+% \begin{macrocode}
+ \braid at tx=\braid at this@strand\braid at width
+ \braid at ty=\value{braid at level}\braid at height
+ \advance\braid at ty by \braid at eh
+ \braid at nx=\braid at tx
+ \braid at ny=\braid at ty
+ \advance\braid at nx by \braid at width
+ \advance\braid at ny by \braid at height
+ \advance\braid at ty by \braid at nf\braid at height
+ \advance\braid at ny by -\braid at nf\braid at height
+ \braid at cy=\braid at ty
+ \braid at dy=\braid at ny
+ \advance\braid at cy by \braid at cf\braid at height
+ \advance\braid at dy by -\braid at cf\braid at height
+% \end{macrocode}
+% Now we try to find a starting point for the strand ending here.
+% We might not have used this strand before, so it might not exist.
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at this@path at origin%
+ \csname braid at strand@\braid at this@strand @origin\endcsname
+% \end{macrocode}
+% If we haven't seen this strand before, that one will be \Verb+\relax+.
+% \begin{macrocode}
+\ifx\braid at this@path at origin\relax
+% \end{macrocode}
+% Haven't seen this strand before, so initialise it.
+% Record the initial position of the strand.
+% \begin{macrocode}
+ \let\braid at this@path at origin\braid at this@strand
+% \end{macrocode}
+% Start a new soft path.
+% \begin{macrocode}
+ \pgfsyssoftpath at setcurrentpath{\@empty}
+ \pgfpathmoveto{\pgfpoint{\braid at tx}{0pt}}
+% \end{macrocode}
+% Save the path as \Verb+\braid at this@path+.
+% \begin{macrocode}
+ \pgfsyssoftpath at getcurrentpath{\braid at this@path}
+ \else
+% \end{macrocode}
+% We have seen this before, so we simply copy the associated path in to \Verb+\braid at this@path+.
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at this@path%
+ \csname braid at strand@\braid at this@path at origin\endcsname
+ \fi
+% \end{macrocode}
+% Now we do the same again with the other strand in the crossing.
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at next@path at origin%
+ \csname braid at strand@\braid at next@strand @origin\endcsname
+ \ifx\braid at next@path at origin\relax
+ \let\braid at next@path at origin\braid at next@strand
+ \pgfsyssoftpath at setcurrentpath{\@empty}
+ \pgfpathmoveto{\pgfpoint{\braid at nx}{0pt}}
+ \pgfsyssoftpath at getcurrentpath{\braid at next@path}
+ \else
+ \expandafter\let\expandafter\braid at next@path%
+ \csname braid at strand@\braid at next@path at origin\endcsname
+ \fi
+% \end{macrocode}
+% Now that we have the paths for our two strands, we extend them to the next level.
+% We start by selecting the first path.
+% \begin{macrocode}
+ \pgfsyssoftpath at setcurrentpath{\braid at this@path}
+% \end{macrocode}
+% Draw a line down to the current level, note that this line is always non-trivial since we shifted the corners of the crossing in a little.
+% \begin{macrocode}
+ \pgfpathlineto{\pgfqpoint{\braid at tx}{\braid at ty}}
+% \end{macrocode}
+% Curve across to the next position.
+% Depending on the crossing type, we either have a single curve or we have to break it in two.
+% Our gap is to interrupt at times determined by the gap key.
+% \begin{macrocode}
+\pgfmathsetmacro{\braid at gst}{0.5 - \pgfkeysvalueof{/pgf/braid/gap}}%
+\pgfmathsetmacro{\braid at gend}{0.5 + \pgfkeysvalueof{/pgf/braid/gap}}%
+\ifx\braid at crossing@type\braid at over@cross
+% \end{macrocode}
+% We're on the overpass, so just one curve needed.
+% \begin{macrocode}
+ \pgfpathcurveto{\pgfqpoint{\braid at tx}{\braid at cy}}%
+ {\pgfqpoint{\braid at nx}{\braid at dy}}%
+ {\pgfqpoint{\braid at nx}{\braid at ny}}
+\else
+% \end{macrocode}
+% We're on the underpass, so we need to interrupt our path to allow the other curve to go past.
+% \begin{macrocode}
+ \pgfpathcurvebetweentimecontinue{0}{\braid at gst}%
+ {\pgfqpoint{\braid at tx}{\braid at ty}}%
+ {\pgfqpoint{\braid at tx}{\braid at cy}}%
+ {\pgfqpoint{\braid at nx}{\braid at dy}}%
+ {\pgfqpoint{\braid at nx}{\braid at ny}}%
+ \pgfpathcurvebetweentime{\braid at gend}{1}%
+ {\pgfqpoint{\braid at tx}{\braid at ty}}%
+ {\pgfqpoint{\braid at tx}{\braid at cy}}%
+ {\pgfqpoint{\braid at nx}{\braid at dy}}%
+ {\pgfqpoint{\braid at nx}{\braid at ny}}
+\fi
+% \end{macrocode}
+% We're done with this path, so now we save it.
+% \begin{macrocode}
+ \pgfsyssoftpath at getcurrentpath{\braid at this@path}
+% \end{macrocode}
+% Now do the same with the second path.
+% \begin{macrocode}
+ \pgfsyssoftpath at setcurrentpath{\braid at next@path}
+ \pgfpathlineto{\pgfqpoint{\braid at nx}{\braid at ty}}
+\ifx\braid at crossing@type\braid at over@cross
+ \pgfpathcurvebetweentimecontinue{0}{\braid at gst}%
+ {\pgfqpoint{\braid at nx}{\braid at ty}}%
+ {\pgfqpoint{\braid at nx}{\braid at cy}}%
+ {\pgfqpoint{\braid at tx}{\braid at dy}}%
+ {\pgfqpoint{\braid at tx}{\braid at ny}}
+ \pgfpathcurvebetweentime{\braid at gend}{1}%
+ {\pgfqpoint{\braid at nx}{\braid at ty}}%
+ {\pgfqpoint{\braid at nx}{\braid at cy}}%
+ {\pgfqpoint{\braid at tx}{\braid at dy}}%
+ {\pgfqpoint{\braid at tx}{\braid at ny}}
+\else
+ \pgfpathcurveto{\pgfqpoint{\braid at nx}{\braid at cy}}%
+ {\pgfqpoint{\braid at tx}{\braid at dy}}%
+ {\pgfqpoint{\braid at tx}{\braid at ny}}
+\fi
+ \pgfsyssoftpath at getcurrentpath{\braid at next@path}
+% \end{macrocode}
+% Now save the paths to their proper macros again.
+% \begin{macrocode}
+ \expandafter\let%
+ \csname braid at strand@\braid at this@path at origin \endcsname%
+ \braid at this@path
+ \expandafter\let%
+ \csname braid at strand@\braid at next@path at origin \endcsname%
+ \braid at next@path
+% \end{macrocode}
+% Now update the origins
+% \begin{macrocode}
+ \expandafter\let%
+ \csname braid at strand@\braid at this@strand @origin\endcsname%
+ \braid at next@path at origin
+ \expandafter\let%
+ \csname braid at strand@\braid at next@strand @origin\endcsname%
+ \braid at this@path at origin
+% \end{macrocode}
+% increment the strand counter, if necessary
+% \begin{macrocode}
+ \pgfmathparse{\value{braid at strands} < \braid at next@strand ?
+ "\noexpand\setcounter{braid at strands}{\braid at next@strand}" : ""}
+ \pgfmathresult
+% \end{macrocode}
+% And merrily go on our way with the next bit of the braid specification.
+% \begin{macrocode}
+ \braid at process%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at olabel@strand}
+% This macro allows us to label a strand just before a crossing.
+% The first argument is the strand number at that particular crossing and the second is the label.
+% We also save the current height.
+% This version takes the strand number as meaning the \emph{original} ordering.
+% \begin{macrocode}
+\newcommand{\braid at olabel@strand}[3][]{%
+ \edef\braid at tmp{{\the\value{braid at level}}}%
+ \expandafter\ifx\csname braid at strand@#2 at origin\endcsname\relax
+ \g at addto@macro\braid at tmp{{#2}}%
+ \else
+ \edef\braid at tmpa{{\csname braid at strand@#2 at origin\endcsname}}%
+ \ge at addto@macro\braid at tmp{\braid at tmpa}%
+ \fi
+ \g at addto@macro\braid at tmp{{#3}{#1}}%
+ \ge at addto@macro{\braid at strand@labels}{\braid at tmp}%
+ \braid at process%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at clabel@strand}
+% This macro allows us to label a strand just before a crossing.
+% The first argument is the strand number at that particular crossing and the second is the label.
+% We also save the current height.
+% This version takes the strand number as meaning the \emph{current} ordering.
+% \begin{macrocode}
+\newcommand{\braid at clabel@strand}[3][]{%
+ \edef\braid at tmp{{\the\value{braid at level}}}%
+ \g at addto@macro\braid at tmp{{#2}{#3}{#1}}%
+ \ge at addto@macro{\braid at strand@labels}{\braid at tmp}%
+ \braid at process%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at floors@trim}
+% The list of floors, if given, will start with a superfluous comma.
+% This removes it.
+% \begin{macrocode}
+\def\braid at floors@trim,{}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at render@floor}
+% This is the default rendering for floors: it draws a rectangle.
+% \begin{macrocode}
+\def\braid at render@floor{%
+ \draw (\floorsx,\floorsy) rectangle (\floorex,\floorey);
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at render@strand at labels}
+% This starts rendering the labels on the strands at the crossings.
+% \begin{macrocode}
+\def\braid at render@strand at labels#1{%
+ \def\braid at tmp{#1}%
+ \ifx\braid at tmp\pgfutil at empty
+ \let\braid at next=\pgfutil at gobble
+ \else
+ \let\braid at next=\braid@@render at strand@labels
+ \fi
+ \braid at next{#1}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid@@render at strand@labels}
+% This is the actual renderer.
+% \begin{macrocode}
+\def\braid@@render at strand@labels#1#2#3#4{%
+ \begingroup
+ \pgfscope
+ \let\tikz at options=\pgfutil at empty
+ \let\tikz at mode=\pgfutil at empty
+ \let\tik at transform=\pgfutil at empty
+ \let\tikz at fig@name=\pgfutil at empty
+ \tikzset{/pgf/braid/strand label,#4}%
+ \braid at nx=#2\braid at width
+ \braid at ny=#1\braid at height
+ \advance\braid at ny by \braid at eh
+ \advance\braid at ny by \braid at height
+ \pgftransformshift{\pgfqpoint{\braid at nx}{\braid at ny}}%
+ \tikz at options
+ \setbox\pgfnodeparttextbox=\hbox%
+ \bgroup%
+ \tikzset{every text node part/.try}%
+ \ifx\tikz at textopacity\pgfutil at empty%
+ \else%
+ \pgfsetfillopacity{\tikz at textopacity}%
+ \pgfsetstrokeopacity{\tikz at textopacity}%
+ \fi%
+ \pgfinterruptpicture%
+ \tikz at textfont%
+ \ifx\tikz at text@width\pgfutil at empty%
+ \else%
+ \begingroup%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@width}%
+ \pgfutil at minipage[t]{\pgf at x}\leavevmode\hbox{}%
+ \tikz at text@action%
+ \fi%
+ \tikz at atbegin@node%
+ \bgroup%
+ \aftergroup\unskip%
+ \ifx\tikz at textcolor\pgfutil at empty%
+ \else%
+ \pgfutil at colorlet{.}{\tikz at textcolor}%
+ \fi%
+ \pgfsetcolor{.}%
+ \setbox\tikz at figbox=\box\pgfutil at voidb@x%
+ \tikz at uninstallcommands%
+ \tikz at halign@check%
+ \ignorespaces%
+ #3
+ \egroup
+ \tikz at atend@node%
+ \ifx\tikz at text@width\pgfutil at empty%
+ \else%
+ \pgfutil at endminipage%
+ \endgroup%
+ \fi%
+ \endpgfinterruptpicture%
+ \egroup%
+ \ifx\tikz at text@width\pgfutil at empty%
+ \else%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@width}%
+ \wd\pgfnodeparttextbox=\pgf at x%
+ \fi%
+ \ifx\tikz at text@height\pgfutil at empty%
+ \else%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@height}%
+ \ht\pgfnodeparttextbox=\pgf at x%
+ \fi%
+ \ifx\tikz at text@depth\pgfutil at empty%
+ \else%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@depth}%
+ \dp\pgfnodeparttextbox=\pgf at x%
+ \fi%
+ \pgfmultipartnode{\tikz at shape}{\tikz at anchor}{\tikz at fig@name}{%
+ {\begingroup\tikz at finish}%
+ }%
+ \endpgfscope
+ \endgroup
+ \braid at render@strand at labels%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at render}
+% This is called at the end of the braid and it renders the braids and floors according to whatever has been built up up to now.
+% \begin{macrocode}
+\def\braid at render{
+% \end{macrocode}
+% Check for floors since we do them first.
+% \begin{macrocode}
+ \ifx\braid at floors\@empty
+ \else
+% \end{macrocode}
+% Have some floors, start a scope and prepare to render them.
+% \begin{macrocode}
+ \pgfsys at beginscope
+% \end{macrocode}
+% Clear the path (just to be sure).
+% \begin{macrocode}
+ \pgfsyssoftpath at setcurrentpath{\empty}
+% \end{macrocode}
+% Trim the initial comma off the list of floors.
+% \begin{macrocode}
+ \edef\braid at floors{\expandafter\braid at floors@trim\braid at floors}
+% \end{macrocode}
+% Initialise our horizontal coordinates.
+% \begin{macrocode}
+ \braid at tx=\braid at width
+ \advance\braid at tx by \braid at eh
+ \braid at nx=\value{braid at strands}\braid at width
+ \advance\braid at nx by -\braid at eh
+% \end{macrocode}
+% Loop over the list of floors.
+% \begin{macrocode}
+ \foreach \braid at f in \braid at floors {
+ \pgfsys at beginscope
+% \end{macrocode}
+% Figure out the vertical coordinates for the current floor.
+% \begin{macrocode}
+ \braid at ty=\braid at f\braid at height
+ \advance\braid at ty by \braid at eh
+ \advance\braid at ty by \braid at height
+ \braid at ny=\braid at ty
+ \advance\braid at ny by \braid at height
+% \end{macrocode}
+% Save the coordinates for use in the floor rendering macro.
+% \begin{macrocode}
+ \edef\floorsx{\the\braid at tx}
+ \edef\floorsy{\the\braid at ty}
+ \edef\floorex{\the\braid at nx}
+ \edef\floorey{\the\braid at ny}
+ \let\tikz at options=\pgfutil at empty
+% \end{macrocode}
+% Load general floor style options.
+% \begin{macrocode}
+ \expandafter\tikzset\expandafter{\braid at floors@style}
+% \end{macrocode}
+% Load any style options specific to this floor.
+% We're actually offset by 2 from what the user thinks the floor level is.
+% \begin{macrocode}
+ \pgfmathtruncatemacro{\braid at ff}{\braid at f+2}
+% \end{macrocode}
+% Load the relevant floor style, if it exists.
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at floor@style%
+ \csname braid at options@floor@\braid at ff\endcsname
+ \ifx\braid at floor@style\relax
+ \else
+% \end{macrocode}
+% There is a floor style for this level, so process it.
+% \begin{macrocode}
+ \expandafter\tikzset\expandafter{\braid at floor@style}%
+ \fi
+% \end{macrocode}
+% The \Verb+\tikzset+ just parses the options, we need to call \Verb+\tikz at options+ to actually set them.
+% \begin{macrocode}
+\tikz at options
+% \end{macrocode}
+% Now we call the rendering code.
+% \begin{macrocode}
+\braid at render@floor
+% \end{macrocode}
+% Done!
+% End the scope for \emph{this} floor and go again.
+% \begin{macrocode}
+\pgfsys at endscope
+ }
+% \end{macrocode}
+% Done rendering floors, end the scope.
+% \begin{macrocode}
+ \pgfsys at endscope
+ \fi
+% \end{macrocode}
+% Finished with floors (if we had them), now get on with the strands.
+% \begin{macrocode}
+ \stepcounter{braid at level}
+ \foreach \braid at k in {1,...,\value{braid at strands}} {
+% \end{macrocode}
+% Start a local scope to ensure we don't mess with other braids
+% \begin{macrocode}
+ \pgfsys at beginscope
+% \end{macrocode}
+% Default is to draw each braid
+% \begin{macrocode}
+ \tikz at mode@drawtrue%
+ \let\tikz at mode=\pgfutil at empty
+ \let\tikz at options=\pgfutil at empty
+% \end{macrocode}
+% (x,y) coordinates of bottom of strand
+% \begin{macrocode}
+ \braid at tx=\braid at k\braid at width
+ \braid at ty=\value{braid at level}\braid at height
+ \advance\braid at ty by 2\braid at eh
+% \end{macrocode}
+% Try to find the starting point of this strand
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at path@origin%
+ \csname braid at strand@\braid at k @origin\endcsname
+ \ifx\braid at path@origin\relax
+% \end{macrocode}
+% If that doesn't exist, we'll just draw a straight line
+% so we move to the top of the current position
+% \begin{macrocode}
+ \pgfsyssoftpath at setcurrentpath{\@empty}
+ \pgfpathmoveto{\pgfqpoint{\braid at tx}{0pt}}
+ \let\braid at path@origin\braid at k
+ \else
+% \end{macrocode}
+% If the path does exist, we load it
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at path%
+ \csname braid at strand@\braid at path@origin\endcsname
+ \pgfsyssoftpath at setcurrentpath{\braid at path}
+ \fi
+% \end{macrocode}
+% Extend the path to the bottom
+% \begin{macrocode}
+ \pgflineto{\pgfqpoint{\braid at tx}{\braid at ty}}
+% \end{macrocode}
+% Load common style options
+% \begin{macrocode}
+ \expandafter\tikzset\expandafter{\braid at style}
+% \end{macrocode}
+% Load any style options specific to this strand
+% \begin{macrocode}
+ \expandafter\let\expandafter\braid at style%
+ \csname braid at options@strand@\braid at path@origin\endcsname
+ \ifx\braid at style\relax
+ \else
+ \expandafter\tikzset\expandafter{\braid at style}
+ \fi
+\braid at options
+ \tikz at mode
+ \tikz at options
+% \end{macrocode}
+% This is the command that actually draws the strand.
+% \begin{macrocode}
+ \edef\tikz at temp{\noexpand\pgfusepath{%
+ \iftikz at mode@draw draw\fi%
+ }}%
+ \tikz at temp
+% \end{macrocode}
+% If our braid has a name, we label the ends of the strand.
+% \begin{macrocode}
+\ifx\braid at name\pgfutil at empty
+\else
+% \end{macrocode}
+% Label the ends of the strand.
+% \begin{macrocode}
+\coordinate (\braid at name-\braid at path@origin-e) at (\braid at tx,\braid at ty);
+\coordinate (\braid at name-rev-\braid at k-e) at (\braid at tx,\braid at ty);
+\braid at nx=\braid at path@origin\braid at width
+\coordinate (\braid at name-\braid at path@origin-s) at (\braid at nx,0pt);
+\coordinate (\braid at name-rev-\braid at k-s) at (\braid at nx,0pt);
+\fi
+% \end{macrocode}
+% Done with this strand, close the scope and do the next one.
+% \begin{macrocode}
+ \pgfsys at endscope
+ }
+% \end{macrocode}
+% If our braid has a name, we also want to label the centre.
+% \begin{macrocode}
+ \ifx\braid at name\pgfutil at empty
+ \else
+ \braid at tx=\value{braid at strands}\braid at width
+ \braid at ty=\value{braid at level}\braid at height
+ \advance\braid at ty by 2\braid at eh
+ \advance\braid at tx by \braid at width
+ \braid at tx=.5\braid at tx
+ \braid at ty=.5\braid at ty
+ \coordinate (\braid at name) at (\braid at tx,\braid at ty);
+ \fi
+% \end{macrocode}
+% Now we label the strands if needed.
+% \begin{macrocode}
+ \ifx\braid at strand@labels\pgfutil at empty
+ \else
+ \expandafter\braid at render@strand at labels\braid at strand@labels{}%
+ \fi
+% \end{macrocode}
+% All done now, close the scope and end the group (which was opened right at the start).
+% \begin{macrocode}
+ \pgfsys at endscope
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\braid at start}
+% This starts off the braid, initialising a load of stuff.
+% We start a PGF scope, set the level to \(-1\), the label, floors, and name to empty, process any options we're given, and save certain lengths for later use..
+% \begin{macrocode}
+\def\braid at start#1{%
+ \pgfsys at beginscope
+ \setcounter{braid at level}{-1}%
+ \let\braid at label\@empty
+ \let\braid at strand@labels\@empty
+ \let\braid at floors\@empty
+ \let\braid at name\empty
+ \let\clabel=\braid at clabel@strand
+ \let\olabel=\braid at olabel@strand
+ \pgfkeys{/pgf/braid/.cd,#1}%
+ \ifbraid at strand@labels at origin
+ \let\label=\braid at olabel@strand
+ \else
+ \let\label=\braid at clabel@strand
+ \fi
+ \let\braid at options\tikz at options
+ \tikz at transform
+ \setcounter{braid at strands}{%
+ \pgfkeysvalueof{/pgf/braid/number of strands}}%
+ \braid at width=\pgfkeysvalueof{/pgf/braid/width}%
+ \braid at height=\pgfkeysvalueof{/pgf/braid/height}%
+ \braid at eh=\pgfkeysvalueof{/pgf/braid/border height}%
+ \pgfkeysgetvalue{/pgf/braid/control factor}{\braid at cf}%
+ \pgfkeysgetvalue{/pgf/braid/nudge factor}{\braid at nf}%
+ \braid at height=-\braid at height
+ \braid at eh=-\braid at eh
+ \braid at increase@leveltrue
+ \braid at process@start
+}
+% \end{macrocode}
+% \end{macro}
+%
+% These are the lengths we'll use as we construct the braid
+% \begin{macrocode}
+\newdimen\braid at width
+\newdimen\braid at height
+\newdimen\braid at tx
+\newdimen\braid at ty
+\newdimen\braid at nx
+\newdimen\braid at ny
+\newdimen\braid at cy
+\newdimen\braid at dy
+\newdimen\braid at eh
+% \end{macrocode}
+%
+% An if to decide whether or not to step to the next level or not
+% \begin{macrocode}
+\newif\ifbraid at increase@level
+% \end{macrocode}
+% An if to decide whether label indices should be absolute or not
+% \begin{macrocode}
+\newif\ifbraid at strand@labels at origin
+% \end{macrocode}
+%
+%
+% Some initial values
+% \begin{macrocode}
+\let\braid at style\pgfutil at empty
+\let\braid at floors@style\pgfutil at empty
+\def\braid at over@cross{1}
+% \end{macrocode}
+%
+% Counters to track the strands and the levels.
+% \begin{macrocode}
+\newcounter{braid at level}
+\newcounter{braid at strands}
+% \end{macrocode}
+%
+% All the keys we'll use.
+% \begin{macrocode}
+\pgfkeys{
+% \end{macrocode}
+% Handle unknown keys by passing them to \Verb+pgf+ and \Verb+tikz+.
+% \begin{macrocode}
+ /tikz/braid/.search also={/pgf},
+ /pgf/braid/.search also={/pgf,/tikz},
+% \end{macrocode}
+% Our ``namespace'' is \Verb+/pgf/braid+.
+% \begin{macrocode}
+ /pgf/braid/.cd,
+ number of strands/.initial=0,
+ height/.initial=1cm,
+ width/.initial=1cm,
+ gap/.initial=.1,
+ border height/.initial=.25cm,
+ control factor/.initial=.5,
+ nudge factor/.initial=.05,
+ name/.code={%
+ \def\braid at name{#1}%
+ },
+ at/.code={%
+ \braid at relocate{#1}%
+ },
+ floor command/.code={%
+ \def\braid at render@floor{#1}%
+ },
+ style strands/.code 2 args={%
+ \def\braid at temp{#2}%
+ \braidset{style each strand/.list={#1}}%
+ },
+ style each strand/.code={%
+ \expandafter\edef%
+ \csname braid at options@strand@#1\endcsname{\braid at temp}%
+ },
+ style floors/.code 2 args={%
+ \def\braid at temp{#2}%
+ \braidset{style each floor/.list={#1}}%
+ },
+ style each floor/.code={%
+ \expandafter\edef%
+ \csname braid at options@floor@#1\endcsname{\braid at temp}%
+ },
+ style all floors/.code={%
+ \def\braid at floors@style{#1}
+ },
+ strand label/.style={},
+ strand label by origin/.is if=braid at strand@labels at origin,
+}
+% \end{macrocode}
+% \begin{macro}{\braidset}
+% Shorthand for setting braid-specific keys.
+% \begin{macrocode}
+\def\braidset#1{%
+ \pgfkeys{/pgf/braid/.cd,#1}}
+% \end{macrocode}
+% \end{macro}
+%
+% \iffalse
+%</package>
+% \fi
+% \begin{macrocode}
+%<*library>
+%<@@=braid>
+% \end{macrocode}
+%
+% \section{Reimplementation as a TikZ Library}
+%
+% Life is so much easier with \LaTeX3.
+% \begin{macrocode}
+\ProvidesFile{tikzlibrarybraids.code.tex}[%
+ 2019/03/20 v2.0 Tikz/PGF library for drawing braid diagrams%
+]
+\RequirePackage{expl3}
+\ExplSyntaxOn
+% \end{macrocode}
+% Define all the variables we'll be using.
+% \begin{macrocode}
+\tl_new:N \l_@@_tmpa_tl
+\tl_new:N \l_@@_tmpb_tl
+\tl_new:N \l_@@_tmpc_tl
+\tl_new:N \l_@@_tmpd_tl
+\tl_new:N \l_@@_anchor_strand_tl
+\tl_new:N \l_@@_anchor_level_tl
+\fp_new:N \l_@@_height_fp
+\fp_new:N \l_@@_width_fp
+\fp_new:N \l_@@_nudge_fp
+\fp_new:N \l_@@_control_fp
+\fp_new:N \l_@@_ctrlax_fp
+\fp_new:N \l_@@_ctrlay_fp
+\fp_new:N \l_@@_ctrlbx_fp
+\fp_new:N \l_@@_ctrlby_fp
+\fp_new:N \l_@@_endx_fp
+\fp_new:N \l_@@_endy_fp
+\fp_new:N \l_@@_anchor_x_fp
+\fp_new:N \l_@@_anchor_y_fp
+\int_new:N \l_@@_tmpa_int
+\int_new:N \l_@@_length_int
+\int_new:N \l_@@_strands_int
+\int_new:N \l_@@_crossing_int
+\int_new:N \l_@@_anchor_level_int
+\int_new:N \l_@@_floor_int
+\seq_new:N \l_@@_word_seq
+\seq_new:N \l_@@_crossing_seq
+\seq_new:N \l_@@_anchor_seq
+\seq_new:N \l_@@_floors_seq
+\str_new:N \l_@@_tmpa_str
+\str_new:N \l_@@_sup_str
+\str_set:Nn \l_@@_sup_str {^}
+\str_new:N \l_@@_sub_str
+\str_set:Nn \l_@@_sub_str {_}
+\str_new:N \l_@@_hyphen_str
+\str_set:Nn \l_@@_hyphen_str {-}
+\str_new:N \l_@@_bar_str
+\str_set:Nn \l_@@_bar_str {|}
+\str_new:N \l_@@_one_str
+\str_set:Nn \l_@@_one_str {1}
+\bool_new:N \l_@@_step_level_bool
+\bool_new:N \l_@@_swap_crossing_bool
+\bool_new:N \l_@@_floor_bool
+\prop_new:N \l_@@_strands_prop
+\prop_new:N \l_@@_permutation_prop
+\prop_new:N \l_@@_crossing_permutation_prop
+\prop_new:N \l_@@_inverse_prop
+\prop_new:N \l_@@_anchor_prop
+% \end{macrocode}
+% Our interface is through a TikZ pic.
+% \begin{macrocode}
+\tikzset{
+ braid/.pic={
+ code={
+ \@@_parse_word:n {#1}
+ \@@_count:
+ \@@_render:
+ }
+ },
+ floor/.pic={
+ code={
+ \path[pic~ actions, draw=none] (0,0) rectangle (1,1);
+ \path[pic~ actions, fill=none] (0,0) -- (1,0) (0,1) -- (1,1);
+ }
+ },
+ /tikz/braid/.search~ also={/tikz},
+ braid/.cd,
+% \end{macrocode}
+% The various TikZ parameters for the braid.
+%
+% The anchor determines which part of the braid is located at the position specified by the pic.
+% It can be of the form \Verb+n-m+ where \Verb+n+ is a strand number and +m+ is a crossing level.
+% The strand number can be either a number or \Verb+rev-n+ to use the ending numbering of the strands.
+% The crossing level can also be \Verb+s+ or \Verb+e+ which means the actual start or end of the strand (including the border).
+%
+% \begin{macrocode}
+ anchor/.initial=1-s,
+% \end{macrocode}
+% \Verb+number of strands+ sets a minimum for the number of strands in the braid (otherwise, it is set by the strands used in the specified crossings).
+% \begin{macrocode}
+ number~ of~ strands/.initial=0,
+% \end{macrocode}
+% \Verb+height+ is the distance between crossings (can be negative).
+% \begin{macrocode}
+ height/.initial=-1cm,
+% \end{macrocode}
+% \Verb+width+ is the distance between strands (can be negative).
+% \begin{macrocode}
+ width/.initial=1cm,
+% \end{macrocode}
+% \Verb+gap+ is for determining the gap in the under-strand of a crossing.
+% \begin{macrocode}
+ gap/.initial=.05,
+% \end{macrocode}
+% \Verb+border height+ is a length added at the start and end of each strand.
+% \begin{macrocode}
+ border~ height/.initial=.25cm,
+% \end{macrocode}
+% \Verb+floor border+ is added to the width of any floors
+% \begin{macrocode}
+ floor~ border/.initial=.25cm,
+% \end{macrocode}
+% \Verb+floors+ is a list of floors to draw, specified as a cslist of coordinates as (x,y,w,h,a) in which the units are numbers of strands and crossing levels.
+% The parameters are: coordinates of lower left corner, width, height, (optional) name for styling.
+% \begin{macrocode}
+ add~ floor/.code={
+ \seq_push:Nn \l_@@_floors_seq {#1}
+ },
+% \end{macrocode}
+% \Verb+control factor+ determines the proportion of the \Verb+height+ used for the control points.
+% \begin{macrocode}
+ control~ factor/.initial=.5,
+% \end{macrocode}
+% \Verb+nudge factor+ is used to compress each crossing slightly within its rectangle.
+% \begin{macrocode}
+ nudge~ factor/.initial=.05
+}
+% \end{macrocode}
+%
+% \begin{macro}[internal]{\@@_parse_word:Nn}
+% Parse the braid word as a token list and convert it into a sequence.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_parse_word:n #1
+{
+ \seq_clear:N \l_@@_word_seq
+ \tl_clear:N \l_@@_tmpa_tl
+ \tl_set:Nn \l_@@_tmpb_tl {#1}
+
+ \bool_until_do:nn { \tl_if_empty_p:N \l_@@_tmpb_tl }
+ {
+% \end{macrocode}
+% We step through the braid specification, looking for special characters.
+% To avoid catcode issues, the comparison is as strings.
+% Some actions may involve consuming more tokens from the list so we can't do a simple \Verb+map_inline+ but have to keep stripping off the head token.
+%
+% The idea is to store information about the current crossing in a token list (noting that it may be specified in a variety of orders) and then when we're sure we have all the information we add it to our sequence of crossings.
+% \begin{macrocode}
+ \str_set:Nx \l_@@_tmpa_str {\tl_head:N \l_@@_tmpb_tl}
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+% \end{macrocode}
+%
+% \begin{macrocode}
+ \str_case_e:nnTF {\l_@@_tmpa_str}
+ {
+% \end{macrocode}
+% Underscore introduces the crossing numbers
+% \begin{macrocode}
+ {_}
+ {
+ \tl_put_right:Nx \l_@@_tmpa_tl
+ {
+ \exp_not:N \@@_parse_index:n {\tl_head:N \l_@@_tmpb_tl}
+ }
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+ }
+% \end{macrocode}
+% Power is used to indicate inverse.
+% \begin{macrocode}
+ {^}
+ {
+ \tl_put_left:Nx \l_@@_tmpa_tl
+ {
+ \exp_not:N \@@_parse_exponent:n {\tl_head:N \l_@@_tmpb_tl}
+ }
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+ }
+% \end{macrocode}
+% Bar is for floors.
+% \begin{macrocode}
+ {|}
+ {
+ \tl_if_empty:NF \l_@@_tmpa_tl
+ {
+ \seq_put_right:NV \l_@@_word_seq \l_@@_tmpa_tl
+ \tl_clear:N \l_@@_tmpa_tl
+ }
+
+ \tl_set:Nn \l_@@_tmpa_tl {
+ \bool_set_false:N \l_@@_step_level_bool
+ \bool_set_true:N \l_@@_floor_bool
+ }
+ \seq_put_right:NV \l_@@_word_seq \l_@@_tmpa_tl
+ \tl_clear:N \l_@@_tmpa_tl
+ }
+% \end{macrocode}
+% Hyphen says the next crossing is on the same level as the current one.
+% \begin{macrocode}
+ {-}
+ {
+ \tl_put_right:Nn \l_@@_tmpa_tl
+ {
+ \bool_set_false:N \l_@@_step_level_bool
+ }
+ }
+% \end{macrocode}
+% \(1\) is for the identity (i.e., no crossing but still have a level).
+% We put a nop token on the list so that it is no longer empty.
+% \begin{macrocode}
+ {1}
+ {
+ \tl_if_empty:NF \l_@@_tmpa_tl
+ {
+ \seq_put_right:NV \l_@@_word_seq \l_@@_tmpa_tl
+ \tl_clear:N \l_@@_tmpa_tl
+ }
+ \tl_put_right:Nn \l_@@_tmpa_tl {\@@_do_identity:}
+ }
+% \end{macrocode}
+% Ignore spaces.
+% \begin{macrocode}
+ {~}
+ {
+ }
+ }
+ {
+ }
+ {
+% \end{macrocode}
+% If we get an unrecognised token, it's our trigger to start accumulating information for the next crossing.
+% \begin{macrocode}
+ \tl_if_empty:NF \l_@@_tmpa_tl
+ {
+ \seq_put_right:NV \l_@@_word_seq \l_@@_tmpa_tl
+ \tl_clear:N \l_@@_tmpa_tl
+ }
+ }
+ }
+% \end{macrocode}
+% At the end, we also put our current token list on the word sequence.
+% \begin{macrocode}
+ \tl_if_empty:NF \l_@@_tmpa_tl
+ {
+ \seq_put_right:NV \l_@@_word_seq \l_@@_tmpa_tl
+ \tl_clear:N \l_@@_tmpa_tl
+ }
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_index:n}
+% Parse an index, saving it in a sequence with the two indices such that the first goes over the second.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_parse_index:n #1
+{
+ \seq_set_from_clist:Nn \l_@@_crossing_seq {#1}
+ \int_compare:nT {\seq_count:N \l_@@_crossing_seq == 1}
+ {
+ \seq_put_right:Nx \l_@@_crossing_seq {\int_eval:n {#1 + 1} }
+ }
+ \bool_if:NT \l_@@_swap_crossing_bool
+ {
+ \seq_pop_left:NN \l_@@_crossing_seq \l_@@_tmpa_tl
+ \seq_put_right:NV \l_@@_crossing_seq \l_@@_tmpa_tl
+ }
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_exponent:n}
+% Parse an exponent, basically testing to see if it is \(-1\) in which case our crossing numbers should be reversed..
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_parse_exponent:n #1
+{
+ \int_compare:nTF {#1 == -1}
+ {
+ \bool_set_true:N \l_@@_swap_crossing_bool
+ }
+ {
+ \bool_set_false:N \l_@@_swap_crossing_bool
+ }
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_do_identity:}
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_do_identity:
+{
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_count:NNN}
+% Work out how big the braid is by counting strands and levels.
+% We also figure out the permutation from the start to end of the strands.
+% This is useful for labelling various parts of the braid.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_count:
+{
+ \int_zero:N \l_@@_length_int
+ \int_set:Nn \l_@@_strands_int {\@@_value:n {number~of~strands}}
+ \prop_clear:N \l_@@_permutation_prop
+ \prop_clear:N \l_@@_crossing_permutation_prop
+ \prop_clear:N \l_@@_anchor_prop
+ \prop_clear:N \l_@@_inverse_prop
+
+ \seq_map_inline:Nn \l_@@_word_seq
+ {
+% \end{macrocode}
+% Clear the crossing sequence and assume we're going to step the level.
+% \begin{macrocode}
+ \seq_clear:N \l_@@_crossing_seq
+ \bool_set_true:N \l_@@_step_level_bool
+ \bool_set_false:N \l_@@_swap_crossing_bool
+% \end{macrocode}
+% Run the details of this crossing.
+% \begin{macrocode}
+ ##1
+% \end{macrocode}
+% If we're increasing the level (no hyphen), do so.
+% \begin{macrocode}
+ \bool_if:NT \l_@@_step_level_bool
+ {
+ \int_incr:N \l_@@_length_int
+ }
+% \end{macrocode}
+% If we have a crossing, check we have enough strands to cover it.
+% \begin{macrocode}
+ \seq_if_empty:NF \l_@@_crossing_seq
+ {
+ \int_set:Nn \l_@@_strands_int
+ {
+ \int_max:nn
+ {
+ \int_max:nn {\l_@@_strands_int}
+ { \seq_item:Nn \l_@@_crossing_seq {1}}
+ }
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ }
+ }
+ }
+ }
+% \end{macrocode}
+% Now that we know how many strands we have, we can initialise our permutation props.
+% One will hold the overall permutation, the other will keep track of our current permutation.
+% \begin{macrocode}
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_put:Nnn \l_@@_permutation_prop {##1} {##1}
+ \prop_put:Nnn \l_@@_anchor_prop {##1} {##1}
+ \prop_put:Nnn \l_@@_crossing_permutation_prop {##1} {##1}
+ }
+% \end{macrocode}
+% Now we step through the braid word again and record the permutations so that we can calculate the overall permutation defined by the braid.
+%
+% We will also figure out our shift from the anchor, so first we need to get some information about the anchor.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpa_tl {\@@_value:n {anchor}}
+ \seq_set_split:NnV \l_@@_anchor_seq {-} \l_@@_tmpa_tl
+
+ \tl_set:Nx \l_@@_tmpa_tl {\seq_item:Nn \l_@@_anchor_seq {1}}
+ \tl_if_eq:VnTF \l_@@_tmpa_tl {rev}
+ {
+ \tl_set:Nx \l_@@_anchor_strand_tl {\seq_item:Nn \l_@@_anchor_seq {2}}
+ \tl_set:Nx \l_@@_anchor_level_tl {\seq_item:Nn \l_@@_anchor_seq {3}}
+ }
+ {
+ \tl_set:Nx \l_@@_anchor_strand_tl {\seq_item:Nn \l_@@_anchor_seq {1}}
+ \tl_set:Nx \l_@@_anchor_level_tl {\seq_item:Nn \l_@@_anchor_seq {2}}
+ }
+% \end{macrocode}
+% The important information is as to the level at which the requested anchor resides.
+% If it is at the end or start of a strand, we set the level to \(-1\) so that it never matches a level number.
+% \begin{macrocode}
+ \tl_if_eq:VnTF \l_@@_anchor_level_tl {s}
+ {
+ \int_set:Nn \l_@@_anchor_level_int {-1}
+ }
+ {
+ \tl_if_eq:VnTF \l_@@_anchor_level_tl {e}
+ {
+ \int_set:Nn \l_@@_anchor_level_int {-1}
+ }
+ {
+ \int_set:Nn \l_@@_anchor_level_int
+ {\tl_use:N \l_@@_anchor_level_tl}
+ }
+ }
+
+ \int_zero:N \l_@@_crossing_int
+ \int_incr:N \l_@@_crossing_int
+% \end{macrocode}
+%
+% \begin{macrocode}
+ \seq_map_inline:Nn \l_@@_word_seq
+ {
+ \bool_set_true:N \l_@@_step_level_bool
+ \seq_clear:N \l_@@_crossing_seq
+ \bool_set_false:N \l_@@_swap_crossing_bool
+ ##1
+ \seq_if_empty:NF \l_@@_crossing_seq
+ {
+ \prop_get:NxN \l_@@_permutation_prop
+ {
+ \seq_item:Nn \l_@@_crossing_seq {1}
+ } \l_@@_tmpa_tl
+ \prop_get:NxN \l_@@_permutation_prop
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ } \l_@@_tmpb_tl
+
+ \prop_put:NxV \l_@@_permutation_prop
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ } \l_@@_tmpa_tl
+ \prop_put:NxV \l_@@_permutation_prop
+ {
+ \seq_item:Nn \l_@@_crossing_seq {1}
+ } \l_@@_tmpb_tl
+ }
+% \end{macrocode}
+% See if the current level is what was requested by the anchor.
+% \begin{macrocode}
+ \int_compare:nT {\l_@@_crossing_int = \l_@@_anchor_level_int}
+ {
+ \prop_set_eq:NN \l_@@_anchor_prop \l_@@_permutation_prop
+ }
+ \bool_if:NT \l_@@_step_level_bool
+ {
+ \int_incr:N \l_@@_crossing_int
+ }
+ }
+% \end{macrocode}
+% This inverts the anchor permutation.
+% \begin{macrocode}
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_get:NnN \l_@@_anchor_prop {##1} \l_@@_tmpa_tl
+ \prop_put:NVn \l_@@_inverse_prop \l_@@_tmpa_tl {##1}
+ }
+ \prop_set_eq:NN \l_@@_anchor_prop \l_@@_inverse_prop
+% \end{macrocode}
+% This inverts the full permutation.
+% \begin{macrocode}
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_get:NnN \l_@@_permutation_prop {##1} \l_@@_tmpa_tl
+ \prop_put:NVn \l_@@_inverse_prop \l_@@_tmpa_tl {##1}
+ }
+% \end{macrocode}
+% Now that we have the inverse, we can figure out our anchor.
+% First, see if we requested a strand by its position at the end of the braid.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpa_tl {\seq_item:Nn \l_@@_anchor_seq {1}}
+ \tl_if_eq:VnT \l_@@_tmpa_tl {rev}
+ {
+ \prop_get:NVN \l_@@_permutation_prop
+ \l_@@_anchor_strand_tl \l_@@_anchor_strand_tl
+ }
+ \tl_if_eq:VnF \l_@@_anchor_level_tl {s}
+ {
+ \tl_if_eq:VnTF \l_@@_anchor_level_tl {e}
+ {
+ \prop_get:NVN \l_@@_inverse_prop
+ \l_@@_anchor_strand_tl \l_@@_anchor_strand_tl
+ }
+ {
+ \prop_get:NVN \l_@@_anchor_prop
+ \l_@@_anchor_strand_tl \l_@@_anchor_strand_tl
+ }
+ }
+% \end{macrocode}
+% \begin{macrocode}
+}
+% \end{macrocode}
+%
+%
+% \end{macro}
+%
+%
+% \begin{macro}{\@@_dim_value:n, \@@_value:n}
+% Extract a length or a value from a PGF key.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_dim_value:n #1
+{
+ \dim_to_fp:n {\pgfkeysvalueof{/tikz/braid/#1}}
+}
+\cs_new_nopar:Npn \@@_value:n #1
+{
+ \pgfkeysvalueof{/tikz/braid/#1}
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_render:}
+% This is the macro that converts the braid word into TikZ paths.
+% \begin{macrocode}
+\cs_generate_variant:Nn \prop_get:NnN {NxN}
+\cs_generate_variant:Nn \prop_put:Nnn {NxV}
+\cs_generate_variant:Nn \tl_if_eq:nnTF {VnTF}
+\cs_generate_variant:Nn \tl_if_eq:nnF {VnF}
+\cs_generate_variant:Nn \tl_if_eq:nnT {VnT}
+
+\cs_new_nopar:Npn \@@_render:
+{
+% \end{macrocode}
+%
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_anchor_x_fp { - 1 * (\tl_use:N \l_@@_anchor_strand_tl - 1) * \@@_dim_value:n {width} }
+
+ \tl_if_eq:VnTF \l_@@_anchor_level_tl {s}
+ {
+ \fp_set:Nn \l_@@_anchor_y_fp {0}
+ }
+ {
+ \tl_if_eq:VnTF \l_@@_anchor_level_tl {e}
+ {
+ \fp_set:Nn \l_@@_anchor_y_fp {
+ -1 * \l_@@_length_int * \@@_dim_value:n {height}
+ - sign(\@@_dim_value:n {height})
+ * 2 * \@@_dim_value:n {border~ height}
+ }
+ }
+ {
+ \fp_set:Nn \l_@@_anchor_y_fp {
+ -1 * \l_@@_anchor_level_tl * \@@_dim_value:n {height}
+ - sign(\@@_dim_value:n {height})
+ * \@@_dim_value:n {border~ height}
+ }
+ }
+ }
+
+ \begin{scope}[
+ shift={
+ (\fp_to_decimal:N \l_@@_anchor_x_fp pt,
+ \fp_to_decimal:N \l_@@_anchor_y_fp pt
+ )
+ }
+ ]
+% \end{macrocode}
+% Initialise a prop for the individual strands.
+% \begin{macrocode}
+ \prop_clear:N \l_@@_strands_prop
+% \end{macrocode}
+% Initialise some lengths.
+% \begin{macrocode}
+ \fp_zero:N \l_@@_height_fp
+ \fp_zero:N \l_@@_nudge_fp
+ \fp_zero:N \l_@@_control_fp
+% \end{macrocode}
+% This holds our current \Verb+height+ of our strands.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_height_fp
+ {
+ sign(\@@_dim_value:n {height})
+ * \@@_dim_value:n {border~ height}
+ }
+% \end{macrocode}
+% This holds the total \Verb+width+ of our strands.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_width_fp
+ {
+ (\l_@@_strands_int - 1) * \@@_dim_value:n {width}
+ + 2 * sign(\@@_dim_value:n{width})
+ * \@@_dim_value:n {floor~ border}
+ }
+% \end{macrocode}
+% Each crossing actually starts a little bit into the crossing space, as defined by the \Verb+nudge factor+.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_nudge_fp
+ {
+ \@@_value:n {nudge~ factor} * \@@_dim_value:n {height}
+ }
+% \end{macrocode}
+% This sets where the control points for the crossing curves will be.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_control_fp
+ {
+ \@@_value:n {control~ factor} * \@@_dim_value:n {height}
+ }
+ \fp_sub:Nn \l_@@_control_fp {\l_@@_nudge_fp}
+% \end{macrocode}
+% Initialise our strand paths with a \Verb+\draw+.
+% \begin{macrocode}
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_get:NnN \l_@@_inverse_prop {##1} \l_@@_tmpa_tl
+ \prop_put:Nnx \l_@@_strands_prop {##1}
+ {
+ \exp_not:N \draw[
+ braid/every~ strand/.try,
+ braid/strand~ ##1/.try
+ ]
+ \exp_not:N \@@_moveto:nn {
+ \fp_eval:n {(##1 - 1) * \@@_dim_value:n {width} }
+ } {0}
+ \exp_not:N \@@_lineto:nn {
+ \fp_eval:n {(##1 - 1) * \@@_dim_value:n {width} }
+ } { \fp_to_decimal:N \l_@@_height_fp}
+ }
+% \end{macrocode}
+% Add a load of coordinates at the start of each strand, indexed by both forward and backward strand numbers.
+% \begin{macrocode}
+ \@@_coordinate:xxxx {-##1-s} {-rev-\l_@@_tmpa_tl-s}
+ {\fp_eval:n {(##1 - 1) * \@@_dim_value:n {width} }} {0}
+
+ \@@_coordinate:xxxx {-##1-0} {-rev-\l_@@_tmpa_tl-0}
+ {\fp_eval:n {(##1 - 1) * \@@_dim_value:n {width} }}
+ { \fp_to_decimal:N \l_@@_height_fp}
+ }
+% \end{macrocode}
+%
+% Run through any extra floors requested.
+% \begin{macrocode}
+ \seq_map_inline:Nn \l_@@_floors_seq
+ {
+ \tl_set:Nx \l_@@_tmpa_tl {\clist_item:nn {##1} {5}}
+ \@@_do_floor:Vxxxx \l_@@_tmpa_tl
+ {\fp_eval:n
+ {
+ -1*sign(\@@_dim_value:n{width})
+ * \@@_dim_value:n {floor~ border}
+ + (\@@_dim_value:n {width}) * (\clist_item:nn {##1} {1} - 1)
+ }
+ pt
+ }
+ {\fp_eval:n
+ {
+ \l_@@_height_fp + ( \@@_dim_value:n {height} ) * (\clist_item:nn {##1} {2})
+ }
+ pt
+ }
+ {\fp_eval:n {
+ ( (\clist_item:nn {##1} {3}) * \@@_dim_value:n {width}
+ + 2 * sign(\@@_dim_value:n{width})
+ * \@@_dim_value:n {floor~ border} ) / \dim_to_fp:n {1cm}
+ }
+ }
+ {\fp_eval:n {
+ (\clist_item:nn {##1} {4}) * ( \@@_dim_value:n {height} ) / \dim_to_fp:n {1cm}
+ }
+ }
+ }
+% \end{macrocode}
+%
+% Keep track of the crossing level for the floor.
+% \begin{macrocode}
+ \int_zero:N \l_@@_crossing_int
+ \int_incr:N \l_@@_crossing_int
+
+ \seq_map_inline:Nn \l_@@_word_seq
+ {
+% \end{macrocode}
+% Clear the flags for this segment of the braid word
+% \begin{macrocode}
+ \seq_clear:N \l_@@_crossing_seq
+ \bool_set_true:N \l_@@_step_level_bool
+ \bool_set_false:N \l_@@_floor_bool
+ \bool_set_false:N \l_@@_swap_crossing_bool
+ ##1
+% \end{macrocode}
+% If we're drawing a floor, do so straightaway.
+% \begin{macrocode}
+ \bool_if:NT \l_@@_floor_bool
+ {
+ \@@_do_floor:Vxxxx \l_@@_crossing_int
+ {\fp_eval:n
+ {
+ -1*sign(\@@_dim_value:n{width})
+ * \@@_dim_value:n {floor~ border}
+ }
+ pt
+ }
+ {\fp_to_decimal:N \l_@@_height_fp pt}
+ {\fp_eval:n { \l_@@_width_fp / \dim_to_fp:n {1cm} }}
+ {\fp_eval:n { ( \@@_dim_value:n {height} ) / \dim_to_fp:n {1cm}}}
+ }
+% \end{macrocode}
+% If we have a crossing, process it.
+% \begin{macrocode}
+ \seq_if_empty:NF \l_@@_crossing_seq
+ {
+% \end{macrocode}
+% Keep track of the current permutation.
+% \begin{macrocode}
+ \prop_get:NxN \l_@@_crossing_permutation_prop
+ {\seq_item:Nn \l_@@_crossing_seq {1}} \l_@@_tmpa_tl
+ \prop_get:NxN \l_@@_crossing_permutation_prop
+ {\seq_item:Nn \l_@@_crossing_seq {2}} \l_@@_tmpb_tl
+
+ \prop_put:NxV \l_@@_crossing_permutation_prop
+ {\seq_item:Nn \l_@@_crossing_seq {2}} \l_@@_tmpa_tl
+ \prop_put:NxV \l_@@_crossing_permutation_prop
+ {\seq_item:Nn \l_@@_crossing_seq {1}} \l_@@_tmpb_tl
+% \end{macrocode}
+% Now get the strands corresponding to the ones involved in the crossing.
+% \begin{macrocode}
+ \prop_get:NxN \l_@@_strands_prop
+ {\seq_item:Nn \l_@@_crossing_seq {1}} \l_@@_tmpa_tl
+ \prop_get:NxN \l_@@_strands_prop
+ {\seq_item:Nn \l_@@_crossing_seq {2}} \l_@@_tmpb_tl
+% \end{macrocode}
+% The over-strand is easy as that's a single curve.
+% \begin{macrocode}
+ \tl_put_right:Nx \l_@@_tmpa_tl
+ {
+ \exp_not:N \@@_lineto:nn
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1} - 1)
+ * \@@_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n { \l_@@_height_fp + \l_@@_nudge_fp } }
+
+ \exp_not:N \@@_curveto:nnnnnn
+
+ {0}
+ {\fp_eval:n { \l_@@_control_fp}}
+
+ {0}
+ {\fp_eval:n {- \l_@@_control_fp}}
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {2} - 1)
+ * \@@_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n
+ {
+ \l_@@_height_fp
+ + \@@_dim_value:n {height}
+ - \l_@@_nudge_fp
+ }
+ }
+ }
+% \end{macrocode}
+% The under-strand is a bit more complicated as we need to break it in the middle.
+% \begin{macrocode}
+ \tl_put_right:Nx \l_@@_tmpb_tl
+ {
+ \exp_not:N \@@_lineto:nn
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {2} - 1)
+ * \@@_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n { \l_@@_height_fp + \l_@@_nudge_fp } }
+
+ \exp_not:N \@@_curveto:nnnnnn
+
+ {0}
+ {
+ \fp_eval:n {
+ \l_@@_control_fp * (.5 - \@@_value:n {gap} )
+ }
+ }
+
+ {
+ \fp_eval:n {
+ - (.5 - \@@_value:n {gap} ) / 3 *
+ \@@_bezier_tangent:nnnnn
+ {.5 - \@@_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ -(.5 - \@@_value:n {gap} ) / 3 *
+ \@@_bezier_tangent:nnnnn
+ {.5 - \@@_value:n {gap} }
+ {0}
+ {\l_@@_control_fp}
+ {
+ \@@_dim_value:n {height}
+ - 2* \l_@@_nudge_fp
+ - \l_@@_control_fp
+ }
+ {\@@_dim_value:n {height} - 2* \l_@@_nudge_fp}
+ }
+ }
+
+ {
+ \fp_eval:n {
+ (\seq_item:Nn \l_@@_crossing_seq {2} - 1)
+ * \@@_dim_value:n {width} +
+ \@@_bezier_point:nnnnn
+ {.5 - \@@_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ \l_@@_height_fp + \l_@@_nudge_fp +
+ \@@_bezier_point:nnnnn
+ {.5 - \@@_value:n {gap} }
+ {0}
+ {\l_@@_control_fp}
+ {
+ \@@_dim_value:n {height}
+ - 2* \l_@@_nudge_fp
+ - \l_@@_control_fp
+ }
+ {\@@_dim_value:n {height} - 2* \l_@@_nudge_fp}
+ }
+ }
+
+ \exp_not:N \@@_moveto:nn
+ {
+ \fp_eval:n {
+ (\seq_item:Nn \l_@@_crossing_seq {2} - 1)
+ * \@@_dim_value:n {width} +
+ \@@_bezier_point:nnnnn
+ {.5 + \@@_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ \l_@@_height_fp + \l_@@_nudge_fp +
+ \@@_bezier_point:nnnnn
+ {.5 + \@@_value:n {gap} }
+ {0}
+ {\l_@@_control_fp}
+ {
+ \@@_dim_value:n {height} - 2* \l_@@_nudge_fp
+ - \l_@@_control_fp
+ }
+ {\@@_dim_value:n {height} - 2* \l_@@_nudge_fp}
+ }
+ }
+
+ \exp_not:N \@@_curveto:nnnnnn
+
+ {
+ \fp_eval:n {
+ (.5 - \@@_value:n {gap} ) / 3 *
+ \@@_bezier_tangent:nnnnn
+ {.5 + \@@_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1}
+ - \seq_item:Nn \l_@@_crossing_seq {2})
+ * \@@_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ (.5 - \@@_value:n {gap} ) / 3 *
+ \@@_bezier_tangent:nnnnn
+ {.5 + \@@_value:n {gap} }
+ {0}
+ {\l_@@_control_fp}
+ {
+ \@@_dim_value:n {height} - 2* \l_@@_nudge_fp
+ - \l_@@_control_fp
+ }
+ {\@@_dim_value:n {height} - 2* \l_@@_nudge_fp}
+ }
+ }
+
+ {0}
+ { \fp_eval:n {
+ -\l_@@_control_fp * (.5 - \@@_value:n {gap} )
+ }
+ }
+
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l_@@_crossing_seq {1} - 1)
+ * \@@_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n
+ {
+ \l_@@_height_fp + \@@_dim_value:n {height}
+ - \l_@@_nudge_fp
+ }
+ }
+
+ }
+% \end{macrocode}
+% Now put those new strands back in the prop.
+% \begin{macrocode}
+ \prop_put:NxV \l_@@_strands_prop
+ {\seq_item:Nn \l_@@_crossing_seq {2}} \l_@@_tmpa_tl
+ \prop_put:NxV \l_@@_strands_prop
+ {\seq_item:Nn \l_@@_crossing_seq {1}} \l_@@_tmpb_tl
+% \end{macrocode}
+% If the strands are more than one apart, the intermediate strands need to be broken as well.
+% \begin{macrocode}
+ \int_compare:nT
+ {
+ \int_max:nn
+ {
+ \seq_item:Nn \l_@@_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ }
+ -
+ \int_min:nn
+ {
+ \seq_item:Nn \l_@@_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ }
+ > 1
+ }
+ {
+ \int_step_inline:nnnn
+ {
+ \int_min:nn
+ {
+ \seq_item:Nn \l_@@_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ }
+ + 1}
+ {1}
+ {
+ \int_max:nn
+ {
+ \seq_item:Nn \l_@@_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l_@@_crossing_seq {2}
+ }
+ - 1
+ }
+ {
+
+ \prop_get:NnN \l_@@_strands_prop {####1} \l_@@_tmpa_tl
+ \tl_put_right:Nx \l_@@_tmpa_tl
+ {
+ \exp_not:N \@@_lineto:nn
+ {\fp_eval:n {(####1 - 1) * \@@_dim_value:n {width} }}
+ {\fp_eval:n
+ {
+ \l_@@_height_fp + \l_@@_nudge_fp
+ + .5 * \l_@@_control_fp
+ }
+ }
+ \exp_not:N \@@_moveto:nn
+ {\fp_eval:n {(####1 - 1) * \@@_dim_value:n {width} }}
+ {\fp_eval:n
+ {
+ \l_@@_height_fp + \@@_dim_value:n {height}
+ - \l_@@_nudge_fp - .5 * \l_@@_control_fp
+ }
+ }
+ }
+
+ \prop_put:NnV \l_@@_strands_prop {####1} \l_@@_tmpa_tl
+ }
+ }
+ }
+% \end{macrocode}
+% If we're to step the level, increase the height and add a load of coordinates.
+% \begin{macrocode}
+ \bool_if:NT \l_@@_step_level_bool
+ {
+ \fp_add:Nn \l_@@_height_fp { \@@_dim_value:n {height} }
+
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_get:NnN \l_@@_crossing_permutation_prop
+ {####1} \l_@@_tmpb_tl
+ \prop_get:NVN \l_@@_inverse_prop
+ \l_@@_tmpb_tl \l_@@_tmpa_tl
+
+ \@@_coordinate:xxxx
+ {-\l_@@_tmpb_tl-\int_use:N \l_@@_crossing_int}
+ {-rev-\l_@@_tmpa_tl-\int_use:N \l_@@_crossing_int }
+ {\fp_eval:n { (####1 - 1) * \@@_dim_value:n {width} }}
+ {\fp_to_decimal:N \l_@@_height_fp}
+ }
+
+ \int_incr:N \l_@@_crossing_int
+ }
+ }
+
+ \fp_add:Nn \l_@@_height_fp
+ {
+ sign(\@@_dim_value:n {height})
+ * \@@_dim_value:n {border~ height}
+ }
+% \end{macrocode}
+% Add a little bit to the end of each strand, together with some coordinates.
+% \begin{macrocode}
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_get:NxN \l_@@_strands_prop {##1} \l_@@_tmpa_tl
+ \prop_get:NxN \l_@@_permutation_prop {##1} \l_@@_tmpb_tl
+
+ \tl_put_right:Nx \l_@@_tmpa_tl {
+ \exp_not:N \@@_lineto:nn
+ {\fp_eval:n { (##1 - 1) * \@@_dim_value:n {width} }}
+ {\fp_to_decimal:N \l_@@_height_fp}
+ coordinate (-rev-##1-e)
+ coordinate (-\l_@@_tmpb_tl-e)
+ ;
+ }
+
+ \prop_put:NnV \l_@@_strands_prop {##1} \l_@@_tmpa_tl
+ }
+% \end{macrocode}
+% This is where we actually carry out the drawing commands.
+% \begin{macrocode}
+ \int_step_inline:nnnn {1} {1} {\l_@@_strands_int}
+ {
+ \prop_get:NnN \l_@@_strands_prop {##1} \l_@@_tmpa_tl
+ \tl_use:N \l_@@_tmpa_tl
+ }
+ \end{scope}
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_moveto:nn, \@@_lineto:nn, \@@_curveto:nnnnnn, \@@_coordinate:nnnn}
+% These are our interfaces to the TikZ code.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_moveto:nn #1#2
+{
+ (#1 pt, #2 pt)
+}
+\cs_new_nopar:Npn \@@_lineto:nn #1#2
+{
+ -- (#1 pt, #2 pt)
+}
+\cs_new_nopar:Npn \@@_curveto:nnnnnn #1#2#3#4#5#6
+{
+ .. controls +(#1 pt, #2 pt) and +(#3 pt, #4 pt)
+ .. (#5 pt, #6 pt)
+}
+\cs_new_nopar:Npn \@@_coordinate:nnnn #1#2#3#4
+{
+ \coordinate[alias=#2] (#1) at (#3 pt,#4 pt);
+}
+\cs_generate_variant:Nn \@@_coordinate:nnnn {xxxx}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\@@_bezier_point:nnnnn, \@@_bezier_tangent:nnnnn}
+% Used to calculate intermediate points and tangents on a bezier curve.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_bezier_point:nnnnn #1#2#3#4#5
+{
+ \fp_eval:n
+ {
+ (1 - (#1)) * (1 - (#1)) * (1 - (#1)) * (#2)
+ +
+ 3 * (1 - (#1)) * (1 - (#1)) * (#1) * (#3)
+ +
+ 3 * (1 - (#1)) * (#1) * (#1) * (#4)
+ +
+ (#1) * (#1) * (#1) * (#5)
+ }
+}
+\cs_new_nopar:Npn \@@_bezier_tangent:nnnnn #1#2#3#4#5
+{
+ \fp_eval:n
+ {
+ 3 * (1 - (#1)) * (1 - (#1)) * (#3 - (#2))
+ +
+ 6 * (1 - (#1)) * (#1) * (#4 - (#3))
+ +
+ 3 * (#1) * (#1) * (#5 - (#4))
+ }
+}
+\cs_new_nopar:Npn \@@_do_floor:nnnnn #1#2#3#4#5
+{
+ \pic[pic~ type=floor,
+ xscale=#4,
+ yscale=#5,
+ at={(#2,#3)},
+ braid/every~ floor/.try,
+ braid/floor~#1/.try,
+ ];
+}
+\cs_generate_variant:Nn \@@_do_floor:nnnnn {Vxxxx}
+% \end{macrocode}
+% \end{macro}
+% \begin{macrocode}
+\ExplSyntaxOff
+% \end{macrocode}
+%
+% \iffalse
+%</library>
+% \fi
+%
+% \Finale
+
+\endinput
Property changes on: trunk/Master/texmf-dist/source/latex/braids/braids_code.dtx
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/source/latex/braids/braids_code.ins
===================================================================
--- trunk/Master/texmf-dist/source/latex/braids/braids_code.ins (rev 0)
+++ trunk/Master/texmf-dist/source/latex/braids/braids_code.ins 2019-05-08 21:15:00 UTC (rev 51048)
@@ -0,0 +1,83 @@
+%%
+%% This is file `braids_code.ins',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% braids_code.dtx (with options: `install')
+%% ----------------------------------------------------------------
+%% braids --- a style file for drawing braid diagrams with TikZ/PGF
+%% E-mail: loopspace at mathforge.org
+%% Released under the LaTeX Project Public License v1.3c or later
+%% See http://www.latex-project.org/lppl.txt
+%% ----------------------------------------------------------------
+%%
+\input l3docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\preamble
+----------------------------------------------------------------
+braids --- a style file for drawing braid diagrams with TikZ/PGF
+E-mail: loopspace at 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) 2011-2019 by Andrew Stacey <loopspace at 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 braids.dtx
+ braids_doc.tex
+and the derived files README.txt,
+ braids.ins,
+ braids.pdf,
+ braids.sty,
+ tikzlibrarybraids.code.tex,
+ braids_doc.pdf.
+
+\endpostamble
+\usedir{tex/latex/braids}
+\generate{
+ \file{braids.sty}{\from{\jobname.dtx}{package}}
+}
+\generate{
+ \file{tikzlibrarybraids.code.tex}{\from{\jobname.dtx}{library}}
+}
+\endbatchfile
+
+%%
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace at 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 braids.dtx
+%% braids_doc.tex
+%% and the derived files README.txt,
+%% braids.ins,
+%% braids.pdf,
+%% braids.sty,
+%% tikzlibrarybraids.code.tex,
+%% braids_doc.pdf.
+%%
+%%
+%% End of file `braids_code.ins'.
Modified: trunk/Master/texmf-dist/tex/latex/braids/braids.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/braids/braids.sty 2019-05-08 21:09:31 UTC (rev 51047)
+++ trunk/Master/texmf-dist/tex/latex/braids/braids.sty 2019-05-08 21:15:00 UTC (rev 51048)
@@ -4,21 +4,19 @@
%%
%% The original source files were:
%%
-%% braids.dtx (with options: `package')
+%% braids_code.dtx (with options: `package')
%% ----------------------------------------------------------------
%% braids --- a style file for drawing braid diagrams with TikZ/PGF
-%% E-mail: stacey at math.ntnu.no
+%% E-mail: loopspace at mathforge.org
%% Released under the LaTeX Project Public License v1.3c or later
%% See http://www.latex-project.org/lppl.txt
%% ----------------------------------------------------------------
%%
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{braids}[2011/05/07 v1.0 Tikz/PGF commands for drawing braid diagrams]
-\def\braid at pgfversion{2.10}%
-\ifx\pgfversion\braid at pgfversion
-\else
-\PackageWarning{braids}{This package was designed using PGF2.10; you are using \pgfversion.}%
-\fi
+\ProvidesPackage{braids}[2011/10/18 v1.1 Tikz/PGF commands for drawing braid diagrams]
+\PackageWarning{braids}{%
+ This package has been reimplemented as a TikZ library; if starting with a fresh document, please consider using that instead.%
+}%
\long\def\ge at addto@macro#1#2{%
\begingroup
\toks@\expandafter\expandafter\expandafter{\expandafter#1#2}%
@@ -71,7 +69,14 @@
\ifx\braid at token-
\braid at increase@levelfalse
\else
- \ifx\braid at token[
+ \ifx\braid at token1%
+ \ifbraid at increase@level
+ \stepcounter{braid at level}
+ \fi
+ \braid at increase@leveltrue
+ \ge at addto@macro\braid at label{\braid at token}%
+ \else
+ \ifx\braid at token[%
\let\braid at next=\braid at process@options
\else
\ifx\braid at token\braid at bar
@@ -84,6 +89,12 @@
\ifx\braid at token\egroup
\braid at endscope
\else
+ \ifx\braid at token\braid at olabel@strand
+ \let\braid at next=\braid at olabel@strand
+ \else
+ \ifx\braid at token\braid at clabel@strand
+ \let\braid at next=\braid at clabel@strand
+ \else
\ge at addto@macro\braid at label{\braid at token}%
\fi
\fi
@@ -93,6 +104,9 @@
\fi
\fi
\fi
+ \fi
+ \fi
+ \fi
\braid at next%
}
\def\braid at maybe@locate{%
@@ -140,9 +154,18 @@
\tikzset{#1}%
\braid at process%
}
-\def\braid at sup#1_#2{\g at addto@macro\braid at label{_{#2}^{#1}}\braid at add@crossing{#2}{#1}}
-\def\braid at sub#1{\@ifnextchar^{\braid@@sub{#1}}{\g at addto@macro\braid at label{_{#1}}\braid at add@crossing{#1}{1}}}
-\def\braid@@sub#1^#2{\g at addto@macro\braid at label{_{#1}^{#2}}\braid at add@crossing{#1}{#2}}
+\def\braid at sup#1_#2{%
+ \g at addto@macro\braid at label{_{#2}^{#1}}%
+ \braid at add@crossing{#2}{#1}%
+}
+\def\braid at sub#1{%
+ \@ifnextchar^{\braid@@sub{#1}}%
+ {\g at addto@macro\braid at label{_{#1}}\braid at add@crossing{#1}{1}}%
+}
+\def\braid@@sub#1^#2{%
+ \g at addto@macro\braid at label{_{#1}^{#2}}%
+ \braid at add@crossing{#1}{#2}%
+}
\def\braid at ne{1}
\def\braid at add@crossing#1#2{%
\edef\braid at crossing@type{#2}%
@@ -159,13 +182,14 @@
\braid at ny=\braid at ty
\advance\braid at nx by \braid at width
\advance\braid at ny by \braid at height
+ \advance\braid at ty by \braid at nf\braid at height
+ \advance\braid at ny by -\braid at nf\braid at height
\braid at cy=\braid at ty
\braid at dy=\braid at ny
- \advance\braid at cy by .5\braid at height
- \advance\braid at dy by -.5\braid at height
- \advance\braid at ty by .05\braid at height
- \advance\braid at ny by -.05\braid at height
- \expandafter\let\expandafter\braid at this@path at origin\csname braid at strand@\braid at this@strand @origin\endcsname
+ \advance\braid at cy by \braid at cf\braid at height
+ \advance\braid at dy by -\braid at cf\braid at height
+ \expandafter\let\expandafter\braid at this@path at origin%
+ \csname braid at strand@\braid at this@strand @origin\endcsname
\ifx\braid at this@path at origin\relax
\let\braid at this@path at origin\braid at this@strand
\pgfsyssoftpath at setcurrentpath{\@empty}
@@ -172,9 +196,11 @@
\pgfpathmoveto{\pgfpoint{\braid at tx}{0pt}}
\pgfsyssoftpath at getcurrentpath{\braid at this@path}
\else
- \expandafter\let\expandafter\braid at this@path\csname braid at strand@\braid at this@path at origin\endcsname
+ \expandafter\let\expandafter\braid at this@path%
+ \csname braid at strand@\braid at this@path at origin\endcsname
\fi
- \expandafter\let\expandafter\braid at next@path at origin\csname braid at strand@\braid at next@strand @origin\endcsname
+ \expandafter\let\expandafter\braid at next@path at origin%
+ \csname braid at strand@\braid at next@strand @origin\endcsname
\ifx\braid at next@path at origin\relax
\let\braid at next@path at origin\braid at next@strand
\pgfsyssoftpath at setcurrentpath{\@empty}
@@ -181,38 +207,172 @@
\pgfpathmoveto{\pgfpoint{\braid at nx}{0pt}}
\pgfsyssoftpath at getcurrentpath{\braid at next@path}
\else
- \expandafter\let\expandafter\braid at next@path\csname braid at strand@\braid at next@path at origin\endcsname
+ \expandafter\let\expandafter\braid at next@path%
+ \csname braid at strand@\braid at next@path at origin\endcsname
\fi
\pgfsyssoftpath at setcurrentpath{\braid at this@path}
\pgfpathlineto{\pgfqpoint{\braid at tx}{\braid at ty}}
+\pgfmathsetmacro{\braid at gst}{0.5 - \pgfkeysvalueof{/pgf/braid/gap}}%
+\pgfmathsetmacro{\braid at gend}{0.5 + \pgfkeysvalueof{/pgf/braid/gap}}%
\ifx\braid at crossing@type\braid at over@cross
-\pgfpathcurveto{\pgfqpoint{\braid at tx}{\braid at cy}}{\pgfqpoint{\braid at nx}{\braid at dy}}{\pgfqpoint{\braid at nx}{\braid at ny}}
+ \pgfpathcurveto{\pgfqpoint{\braid at tx}{\braid at cy}}%
+ {\pgfqpoint{\braid at nx}{\braid at dy}}%
+ {\pgfqpoint{\braid at nx}{\braid at ny}}
\else
-\pgfpathcurvebetweentimecontinue{0}{.4}{\pgfqpoint{\braid at tx}{\braid at ty}}{\pgfqpoint{\braid at tx}{\braid at cy}}{\pgfqpoint{\braid at nx}{\braid at dy}}{\pgfqpoint{\braid at nx}{\braid at ny}}
-\pgfpathcurvebetweentime{.6}{1}{\pgfqpoint{\braid at tx}{\braid at ty}}{\pgfqpoint{\braid at tx}{\braid at cy}}{\pgfqpoint{\braid at nx}{\braid at dy}}{\pgfqpoint{\braid at nx}{\braid at ny}}
+ \pgfpathcurvebetweentimecontinue{0}{\braid at gst}%
+ {\pgfqpoint{\braid at tx}{\braid at ty}}%
+ {\pgfqpoint{\braid at tx}{\braid at cy}}%
+ {\pgfqpoint{\braid at nx}{\braid at dy}}%
+ {\pgfqpoint{\braid at nx}{\braid at ny}}%
+ \pgfpathcurvebetweentime{\braid at gend}{1}%
+ {\pgfqpoint{\braid at tx}{\braid at ty}}%
+ {\pgfqpoint{\braid at tx}{\braid at cy}}%
+ {\pgfqpoint{\braid at nx}{\braid at dy}}%
+ {\pgfqpoint{\braid at nx}{\braid at ny}}
\fi
\pgfsyssoftpath at getcurrentpath{\braid at this@path}
\pgfsyssoftpath at setcurrentpath{\braid at next@path}
\pgfpathlineto{\pgfqpoint{\braid at nx}{\braid at ty}}
\ifx\braid at crossing@type\braid at over@cross
-\pgfpathcurvebetweentimecontinue{0}{.4}{\pgfqpoint{\braid at nx}{\braid at ty}}{\pgfqpoint{\braid at nx}{\braid at cy}}{\pgfqpoint{\braid at tx}{\braid at dy}}{\pgfqpoint{\braid at tx}{\braid at ny}}
-\pgfpathcurvebetweentime{.6}{1}{\pgfqpoint{\braid at nx}{\braid at ty}}{\pgfqpoint{\braid at nx}{\braid at cy}}{\pgfqpoint{\braid at tx}{\braid at dy}}{\pgfqpoint{\braid at tx}{\braid at ny}}
+ \pgfpathcurvebetweentimecontinue{0}{\braid at gst}%
+ {\pgfqpoint{\braid at nx}{\braid at ty}}%
+ {\pgfqpoint{\braid at nx}{\braid at cy}}%
+ {\pgfqpoint{\braid at tx}{\braid at dy}}%
+ {\pgfqpoint{\braid at tx}{\braid at ny}}
+ \pgfpathcurvebetweentime{\braid at gend}{1}%
+ {\pgfqpoint{\braid at nx}{\braid at ty}}%
+ {\pgfqpoint{\braid at nx}{\braid at cy}}%
+ {\pgfqpoint{\braid at tx}{\braid at dy}}%
+ {\pgfqpoint{\braid at tx}{\braid at ny}}
\else
- \pgfpathcurveto{\pgfqpoint{\braid at nx}{\braid at cy}}{\pgfqpoint{\braid at tx}{\braid at dy}}{\pgfqpoint{\braid at tx}{\braid at ny}}
+ \pgfpathcurveto{\pgfqpoint{\braid at nx}{\braid at cy}}%
+ {\pgfqpoint{\braid at tx}{\braid at dy}}%
+ {\pgfqpoint{\braid at tx}{\braid at ny}}
\fi
\pgfsyssoftpath at getcurrentpath{\braid at next@path}
- \expandafter\let\csname braid at strand@\braid at this@path at origin \endcsname\braid at this@path
- \expandafter\let\csname braid at strand@\braid at next@path at origin \endcsname\braid at next@path
- \expandafter\let\csname braid at strand@\braid at this@strand @origin\endcsname\braid at next@path at origin
- \expandafter\let\csname braid at strand@\braid at next@strand @origin\endcsname\braid at this@path at origin
- \pgfmathparse{\value{braid at strands} < \braid at next@strand ? "\noexpand\setcounter{braid at strands}{\braid at next@strand}" : ""}
+ \expandafter\let%
+ \csname braid at strand@\braid at this@path at origin \endcsname%
+ \braid at this@path
+ \expandafter\let%
+ \csname braid at strand@\braid at next@path at origin \endcsname%
+ \braid at next@path
+ \expandafter\let%
+ \csname braid at strand@\braid at this@strand @origin\endcsname%
+ \braid at next@path at origin
+ \expandafter\let%
+ \csname braid at strand@\braid at next@strand @origin\endcsname%
+ \braid at this@path at origin
+ \pgfmathparse{\value{braid at strands} < \braid at next@strand ?
+ "\noexpand\setcounter{braid at strands}{\braid at next@strand}" : ""}
\pgfmathresult
\braid at process%
}
+\newcommand{\braid at olabel@strand}[3][]{%
+ \edef\braid at tmp{{\the\value{braid at level}}}%
+ \expandafter\ifx\csname braid at strand@#2 at origin\endcsname\relax
+ \g at addto@macro\braid at tmp{{#2}}%
+ \else
+ \edef\braid at tmpa{{\csname braid at strand@#2 at origin\endcsname}}%
+ \ge at addto@macro\braid at tmp{\braid at tmpa}%
+ \fi
+ \g at addto@macro\braid at tmp{{#3}{#1}}%
+ \ge at addto@macro{\braid at strand@labels}{\braid at tmp}%
+ \braid at process%
+}
+\newcommand{\braid at clabel@strand}[3][]{%
+ \edef\braid at tmp{{\the\value{braid at level}}}%
+ \g at addto@macro\braid at tmp{{#2}{#3}{#1}}%
+ \ge at addto@macro{\braid at strand@labels}{\braid at tmp}%
+ \braid at process%
+}
\def\braid at floors@trim,{}
\def\braid at render@floor{%
\draw (\floorsx,\floorsy) rectangle (\floorex,\floorey);
}
+\def\braid at render@strand at labels#1{%
+ \def\braid at tmp{#1}%
+ \ifx\braid at tmp\pgfutil at empty
+ \let\braid at next=\pgfutil at gobble
+ \else
+ \let\braid at next=\braid@@render at strand@labels
+ \fi
+ \braid at next{#1}%
+}
+\def\braid@@render at strand@labels#1#2#3#4{%
+ \begingroup
+ \pgfscope
+ \let\tikz at options=\pgfutil at empty
+ \let\tikz at mode=\pgfutil at empty
+ \let\tik at transform=\pgfutil at empty
+ \let\tikz at fig@name=\pgfutil at empty
+ \tikzset{/pgf/braid/strand label,#4}%
+ \braid at nx=#2\braid at width
+ \braid at ny=#1\braid at height
+ \advance\braid at ny by \braid at eh
+ \advance\braid at ny by \braid at height
+ \pgftransformshift{\pgfqpoint{\braid at nx}{\braid at ny}}%
+ \tikz at options
+ \setbox\pgfnodeparttextbox=\hbox%
+ \bgroup%
+ \tikzset{every text node part/.try}%
+ \ifx\tikz at textopacity\pgfutil at empty%
+ \else%
+ \pgfsetfillopacity{\tikz at textopacity}%
+ \pgfsetstrokeopacity{\tikz at textopacity}%
+ \fi%
+ \pgfinterruptpicture%
+ \tikz at textfont%
+ \ifx\tikz at text@width\pgfutil at empty%
+ \else%
+ \begingroup%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@width}%
+ \pgfutil at minipage[t]{\pgf at x}\leavevmode\hbox{}%
+ \tikz at text@action%
+ \fi%
+ \tikz at atbegin@node%
+ \bgroup%
+ \aftergroup\unskip%
+ \ifx\tikz at textcolor\pgfutil at empty%
+ \else%
+ \pgfutil at colorlet{.}{\tikz at textcolor}%
+ \fi%
+ \pgfsetcolor{.}%
+ \setbox\tikz at figbox=\box\pgfutil at voidb@x%
+ \tikz at uninstallcommands%
+ \tikz at halign@check%
+ \ignorespaces%
+ #3
+ \egroup
+ \tikz at atend@node%
+ \ifx\tikz at text@width\pgfutil at empty%
+ \else%
+ \pgfutil at endminipage%
+ \endgroup%
+ \fi%
+ \endpgfinterruptpicture%
+ \egroup%
+ \ifx\tikz at text@width\pgfutil at empty%
+ \else%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@width}%
+ \wd\pgfnodeparttextbox=\pgf at x%
+ \fi%
+ \ifx\tikz at text@height\pgfutil at empty%
+ \else%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@height}%
+ \ht\pgfnodeparttextbox=\pgf at x%
+ \fi%
+ \ifx\tikz at text@depth\pgfutil at empty%
+ \else%
+ \pgfmathsetlength{\pgf at x}{\tikz at text@depth}%
+ \dp\pgfnodeparttextbox=\pgf at x%
+ \fi%
+ \pgfmultipartnode{\tikz at shape}{\tikz at anchor}{\tikz at fig@name}{%
+ {\begingroup\tikz at finish}%
+ }%
+ \endpgfscope
+ \endgroup
+ \braid at render@strand at labels%
+}
\def\braid at render{
\ifx\braid at floors\@empty
\else
@@ -237,7 +397,8 @@
\let\tikz at options=\pgfutil at empty
\expandafter\tikzset\expandafter{\braid at floors@style}
\pgfmathtruncatemacro{\braid at ff}{\braid at f+2}
- \expandafter\let\expandafter\braid at floor@style\csname braid at options@floor@\braid at ff\endcsname
+ \expandafter\let\expandafter\braid at floor@style%
+ \csname braid at options@floor@\braid at ff\endcsname
\ifx\braid at floor@style\relax
\else
\expandafter\tikzset\expandafter{\braid at floor@style}%
@@ -257,18 +418,21 @@
\braid at tx=\braid at k\braid at width
\braid at ty=\value{braid at level}\braid at height
\advance\braid at ty by 2\braid at eh
- \expandafter\let\expandafter\braid at path@origin\csname braid at strand@\braid at k @origin\endcsname
+ \expandafter\let\expandafter\braid at path@origin%
+ \csname braid at strand@\braid at k @origin\endcsname
\ifx\braid at path@origin\relax
\pgfsyssoftpath at setcurrentpath{\@empty}
\pgfpathmoveto{\pgfqpoint{\braid at tx}{0pt}}
\let\braid at path@origin\braid at k
\else
- \expandafter\let\expandafter\braid at path\csname braid at strand@\braid at path@origin\endcsname
+ \expandafter\let\expandafter\braid at path%
+ \csname braid at strand@\braid at path@origin\endcsname
\pgfsyssoftpath at setcurrentpath{\braid at path}
\fi
\pgflineto{\pgfqpoint{\braid at tx}{\braid at ty}}
\expandafter\tikzset\expandafter{\braid at style}
- \expandafter\let\expandafter\braid at style\csname braid at options@strand@\braid at path@origin\endcsname
+ \expandafter\let\expandafter\braid at style%
+ \csname braid at options@strand@\braid at path@origin\endcsname
\ifx\braid at style\relax
\else
\expandafter\tikzset\expandafter{\braid at style}
@@ -300,25 +464,40 @@
\braid at ty=.5\braid at ty
\coordinate (\braid at name) at (\braid at tx,\braid at ty);
\fi
+ \ifx\braid at strand@labels\pgfutil at empty
+ \else
+ \expandafter\braid at render@strand at labels\braid at strand@labels{}%
+ \fi
\pgfsys at endscope
\endgroup}
\def\braid at start#1{%
- \pgfsys at beginscope
- \setcounter{braid at level}{-1}%
- \let\braid at label\@empty
- \let\braid at floors\@empty
- \let\braid at name\empty
- \pgfkeys{/pgf/braid/.cd,#1}
- \let\braid at options\tikz at options
+ \pgfsys at beginscope
+ \setcounter{braid at level}{-1}%
+ \let\braid at label\@empty
+ \let\braid at strand@labels\@empty
+ \let\braid at floors\@empty
+ \let\braid at name\empty
+ \let\clabel=\braid at clabel@strand
+ \let\olabel=\braid at olabel@strand
+ \pgfkeys{/pgf/braid/.cd,#1}%
+ \ifbraid at strand@labels at origin
+ \let\label=\braid at olabel@strand
+ \else
+ \let\label=\braid at clabel@strand
+ \fi
+ \let\braid at options\tikz at options
\tikz at transform
- \setcounter{braid at strands}{\pgfkeysvalueof{/pgf/braid/number of strands}}%
- \braid at width=\pgfkeysvalueof{/pgf/braid/width}
- \braid at height=\pgfkeysvalueof{/pgf/braid/height}
- \braid at eh=\pgfkeysvalueof{/pgf/braid/border height}
- \braid at height=-\braid at height
- \braid at eh=-\braid at eh
- \braid at increase@leveltrue
- \braid at process@start
+ \setcounter{braid at strands}{%
+ \pgfkeysvalueof{/pgf/braid/number of strands}}%
+ \braid at width=\pgfkeysvalueof{/pgf/braid/width}%
+ \braid at height=\pgfkeysvalueof{/pgf/braid/height}%
+ \braid at eh=\pgfkeysvalueof{/pgf/braid/border height}%
+ \pgfkeysgetvalue{/pgf/braid/control factor}{\braid at cf}%
+ \pgfkeysgetvalue{/pgf/braid/nudge factor}{\braid at nf}%
+ \braid at height=-\braid at height
+ \braid at eh=-\braid at eh
+ \braid at increase@leveltrue
+ \braid at process@start
}
\newdimen\braid at width
\newdimen\braid at height
@@ -330,6 +509,7 @@
\newdimen\braid at dy
\newdimen\braid at eh
\newif\ifbraid at increase@level
+\newif\ifbraid at strand@labels at origin
\let\braid at style\pgfutil at empty
\let\braid at floors@style\pgfutil at empty
\def\braid at over@cross{1}
@@ -342,7 +522,10 @@
number of strands/.initial=0,
height/.initial=1cm,
width/.initial=1cm,
+ gap/.initial=.1,
border height/.initial=.25cm,
+ control factor/.initial=.5,
+ nudge factor/.initial=.05,
name/.code={%
\def\braid at name{#1}%
},
@@ -357,7 +540,8 @@
\braidset{style each strand/.list={#1}}%
},
style each strand/.code={%
- \expandafter\edef\csname braid at options@strand@#1\endcsname{\braid at temp}%
+ \expandafter\edef%
+ \csname braid at options@strand@#1\endcsname{\braid at temp}%
},
style floors/.code 2 args={%
\def\braid at temp{#2}%
@@ -364,17 +548,20 @@
\braidset{style each floor/.list={#1}}%
},
style each floor/.code={%
- \expandafter\edef\csname braid at options@floor@#1\endcsname{\braid at temp}%
+ \expandafter\edef%
+ \csname braid at options@floor@#1\endcsname{\braid at temp}%
},
style all floors/.code={%
\def\braid at floors@style{#1}
- }
+ },
+ strand label/.style={},
+ strand label by origin/.is if=braid at strand@labels at origin,
}
\def\braidset#1{%
\pgfkeys{/pgf/braid/.cd,#1}}
%%
-%% Copyright (C) 2011 by Andrew Stacey <stacey at math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace at mathforge.org>
%%
%% This work may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License (LPPL), either
@@ -392,6 +579,7 @@
%% braids.ins,
%% braids.pdf,
%% braids.sty,
+%% tikzlibrarybraids.code.tex,
%% braids_doc.pdf.
%%
%%
Added: trunk/Master/texmf-dist/tex/latex/braids/tikzlibrarybraids.code.tex
===================================================================
--- trunk/Master/texmf-dist/tex/latex/braids/tikzlibrarybraids.code.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/braids/tikzlibrarybraids.code.tex 2019-05-08 21:15:00 UTC (rev 51048)
@@ -0,0 +1,916 @@
+%%
+%% This is file `tikzlibrarybraids.code.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% braids_code.dtx (with options: `library')
+%% ----------------------------------------------------------------
+%% braids --- a style file for drawing braid diagrams with TikZ/PGF
+%% E-mail: loopspace at mathforge.org
+%% Released under the LaTeX Project Public License v1.3c or later
+%% See http://www.latex-project.org/lppl.txt
+%% ----------------------------------------------------------------
+%%
+\ProvidesFile{tikzlibrarybraids.code.tex}[%
+ 2019/03/20 v2.0 Tikz/PGF library for drawing braid diagrams%
+]
+\RequirePackage{expl3}
+\ExplSyntaxOn
+\tl_new:N \l__braid_tmpa_tl
+\tl_new:N \l__braid_tmpb_tl
+\tl_new:N \l__braid_tmpc_tl
+\tl_new:N \l__braid_tmpd_tl
+\tl_new:N \l__braid_anchor_strand_tl
+\tl_new:N \l__braid_anchor_level_tl
+\fp_new:N \l__braid_height_fp
+\fp_new:N \l__braid_width_fp
+\fp_new:N \l__braid_nudge_fp
+\fp_new:N \l__braid_control_fp
+\fp_new:N \l__braid_ctrlax_fp
+\fp_new:N \l__braid_ctrlay_fp
+\fp_new:N \l__braid_ctrlbx_fp
+\fp_new:N \l__braid_ctrlby_fp
+\fp_new:N \l__braid_endx_fp
+\fp_new:N \l__braid_endy_fp
+\fp_new:N \l__braid_anchor_x_fp
+\fp_new:N \l__braid_anchor_y_fp
+\int_new:N \l__braid_tmpa_int
+\int_new:N \l__braid_length_int
+\int_new:N \l__braid_strands_int
+\int_new:N \l__braid_crossing_int
+\int_new:N \l__braid_anchor_level_int
+\int_new:N \l__braid_floor_int
+\seq_new:N \l__braid_word_seq
+\seq_new:N \l__braid_crossing_seq
+\seq_new:N \l__braid_anchor_seq
+\seq_new:N \l__braid_floors_seq
+\str_new:N \l__braid_tmpa_str
+\str_new:N \l__braid_sup_str
+\str_set:Nn \l__braid_sup_str {^}
+\str_new:N \l__braid_sub_str
+\str_set:Nn \l__braid_sub_str {_}
+\str_new:N \l__braid_hyphen_str
+\str_set:Nn \l__braid_hyphen_str {-}
+\str_new:N \l__braid_bar_str
+\str_set:Nn \l__braid_bar_str {|}
+\str_new:N \l__braid_one_str
+\str_set:Nn \l__braid_one_str {1}
+\bool_new:N \l__braid_step_level_bool
+\bool_new:N \l__braid_swap_crossing_bool
+\bool_new:N \l__braid_floor_bool
+\prop_new:N \l__braid_strands_prop
+\prop_new:N \l__braid_permutation_prop
+\prop_new:N \l__braid_crossing_permutation_prop
+\prop_new:N \l__braid_inverse_prop
+\prop_new:N \l__braid_anchor_prop
+\tikzset{
+ braid/.pic={
+ code={
+ \__braid_parse_word:n {#1}
+ \__braid_count:
+ \__braid_render:
+ }
+ },
+ floor/.pic={
+ code={
+ \path[pic~ actions, draw=none] (0,0) rectangle (1,1);
+ \path[pic~ actions, fill=none] (0,0) -- (1,0) (0,1) -- (1,1);
+ }
+ },
+ /tikz/braid/.search~ also={/tikz},
+ braid/.cd,
+ anchor/.initial=1-s,
+ number~ of~ strands/.initial=0,
+ height/.initial=-1cm,
+ width/.initial=1cm,
+ gap/.initial=.05,
+ border~ height/.initial=.25cm,
+ floor~ border/.initial=.25cm,
+ add~ floor/.code={
+ \seq_push:Nn \l__braid_floors_seq {#1}
+ },
+ control~ factor/.initial=.5,
+ nudge~ factor/.initial=.05
+}
+\cs_new_nopar:Npn \__braid_parse_word:n #1
+{
+ \seq_clear:N \l__braid_word_seq
+ \tl_clear:N \l__braid_tmpa_tl
+ \tl_set:Nn \l__braid_tmpb_tl {#1}
+
+ \bool_until_do:nn { \tl_if_empty_p:N \l__braid_tmpb_tl }
+ {
+ \str_set:Nx \l__braid_tmpa_str {\tl_head:N \l__braid_tmpb_tl}
+ \tl_set:Nx \l__braid_tmpb_tl {\tl_tail:N \l__braid_tmpb_tl}
+ \str_case_e:nnTF {\l__braid_tmpa_str}
+ {
+ {_}
+ {
+ \tl_put_right:Nx \l__braid_tmpa_tl
+ {
+ \exp_not:N \__braid_parse_index:n {\tl_head:N \l__braid_tmpb_tl}
+ }
+ \tl_set:Nx \l__braid_tmpb_tl {\tl_tail:N \l__braid_tmpb_tl}
+ }
+ {^}
+ {
+ \tl_put_left:Nx \l__braid_tmpa_tl
+ {
+ \exp_not:N \__braid_parse_exponent:n {\tl_head:N \l__braid_tmpb_tl}
+ }
+ \tl_set:Nx \l__braid_tmpb_tl {\tl_tail:N \l__braid_tmpb_tl}
+ }
+ {|}
+ {
+ \tl_if_empty:NF \l__braid_tmpa_tl
+ {
+ \seq_put_right:NV \l__braid_word_seq \l__braid_tmpa_tl
+ \tl_clear:N \l__braid_tmpa_tl
+ }
+
+ \tl_set:Nn \l__braid_tmpa_tl {
+ \bool_set_false:N \l__braid_step_level_bool
+ \bool_set_true:N \l__braid_floor_bool
+ }
+ \seq_put_right:NV \l__braid_word_seq \l__braid_tmpa_tl
+ \tl_clear:N \l__braid_tmpa_tl
+ }
+ {-}
+ {
+ \tl_put_right:Nn \l__braid_tmpa_tl
+ {
+ \bool_set_false:N \l__braid_step_level_bool
+ }
+ }
+ {1}
+ {
+ \tl_if_empty:NF \l__braid_tmpa_tl
+ {
+ \seq_put_right:NV \l__braid_word_seq \l__braid_tmpa_tl
+ \tl_clear:N \l__braid_tmpa_tl
+ }
+ \tl_put_right:Nn \l__braid_tmpa_tl {\__braid_do_identity:}
+ }
+ {~}
+ {
+ }
+ }
+ {
+ }
+ {
+ \tl_if_empty:NF \l__braid_tmpa_tl
+ {
+ \seq_put_right:NV \l__braid_word_seq \l__braid_tmpa_tl
+ \tl_clear:N \l__braid_tmpa_tl
+ }
+ }
+ }
+ \tl_if_empty:NF \l__braid_tmpa_tl
+ {
+ \seq_put_right:NV \l__braid_word_seq \l__braid_tmpa_tl
+ \tl_clear:N \l__braid_tmpa_tl
+ }
+}
+\cs_new_nopar:Npn \__braid_parse_index:n #1
+{
+ \seq_set_from_clist:Nn \l__braid_crossing_seq {#1}
+ \int_compare:nT {\seq_count:N \l__braid_crossing_seq == 1}
+ {
+ \seq_put_right:Nx \l__braid_crossing_seq {\int_eval:n {#1 + 1} }
+ }
+ \bool_if:NT \l__braid_swap_crossing_bool
+ {
+ \seq_pop_left:NN \l__braid_crossing_seq \l__braid_tmpa_tl
+ \seq_put_right:NV \l__braid_crossing_seq \l__braid_tmpa_tl
+ }
+}
+\cs_new_nopar:Npn \__braid_parse_exponent:n #1
+{
+ \int_compare:nTF {#1 == -1}
+ {
+ \bool_set_true:N \l__braid_swap_crossing_bool
+ }
+ {
+ \bool_set_false:N \l__braid_swap_crossing_bool
+ }
+}
+\cs_new_nopar:Npn \__braid_do_identity:
+{
+}
+\cs_new_nopar:Npn \__braid_count:
+{
+ \int_zero:N \l__braid_length_int
+ \int_set:Nn \l__braid_strands_int {\__braid_value:n {number~of~strands}}
+ \prop_clear:N \l__braid_permutation_prop
+ \prop_clear:N \l__braid_crossing_permutation_prop
+ \prop_clear:N \l__braid_anchor_prop
+ \prop_clear:N \l__braid_inverse_prop
+
+ \seq_map_inline:Nn \l__braid_word_seq
+ {
+ \seq_clear:N \l__braid_crossing_seq
+ \bool_set_true:N \l__braid_step_level_bool
+ \bool_set_false:N \l__braid_swap_crossing_bool
+ ##1
+ \bool_if:NT \l__braid_step_level_bool
+ {
+ \int_incr:N \l__braid_length_int
+ }
+ \seq_if_empty:NF \l__braid_crossing_seq
+ {
+ \int_set:Nn \l__braid_strands_int
+ {
+ \int_max:nn
+ {
+ \int_max:nn {\l__braid_strands_int}
+ { \seq_item:Nn \l__braid_crossing_seq {1}}
+ }
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ }
+ }
+ }
+ }
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_put:Nnn \l__braid_permutation_prop {##1} {##1}
+ \prop_put:Nnn \l__braid_anchor_prop {##1} {##1}
+ \prop_put:Nnn \l__braid_crossing_permutation_prop {##1} {##1}
+ }
+ \tl_set:Nx \l__braid_tmpa_tl {\__braid_value:n {anchor}}
+ \seq_set_split:NnV \l__braid_anchor_seq {-} \l__braid_tmpa_tl
+
+ \tl_set:Nx \l__braid_tmpa_tl {\seq_item:Nn \l__braid_anchor_seq {1}}
+ \tl_if_eq:VnTF \l__braid_tmpa_tl {rev}
+ {
+ \tl_set:Nx \l__braid_anchor_strand_tl {\seq_item:Nn \l__braid_anchor_seq {2}}
+ \tl_set:Nx \l__braid_anchor_level_tl {\seq_item:Nn \l__braid_anchor_seq {3}}
+ }
+ {
+ \tl_set:Nx \l__braid_anchor_strand_tl {\seq_item:Nn \l__braid_anchor_seq {1}}
+ \tl_set:Nx \l__braid_anchor_level_tl {\seq_item:Nn \l__braid_anchor_seq {2}}
+ }
+ \tl_if_eq:VnTF \l__braid_anchor_level_tl {s}
+ {
+ \int_set:Nn \l__braid_anchor_level_int {-1}
+ }
+ {
+ \tl_if_eq:VnTF \l__braid_anchor_level_tl {e}
+ {
+ \int_set:Nn \l__braid_anchor_level_int {-1}
+ }
+ {
+ \int_set:Nn \l__braid_anchor_level_int
+ {\tl_use:N \l__braid_anchor_level_tl}
+ }
+ }
+
+ \int_zero:N \l__braid_crossing_int
+ \int_incr:N \l__braid_crossing_int
+ \seq_map_inline:Nn \l__braid_word_seq
+ {
+ \bool_set_true:N \l__braid_step_level_bool
+ \seq_clear:N \l__braid_crossing_seq
+ \bool_set_false:N \l__braid_swap_crossing_bool
+ ##1
+ \seq_if_empty:NF \l__braid_crossing_seq
+ {
+ \prop_get:NxN \l__braid_permutation_prop
+ {
+ \seq_item:Nn \l__braid_crossing_seq {1}
+ } \l__braid_tmpa_tl
+ \prop_get:NxN \l__braid_permutation_prop
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ } \l__braid_tmpb_tl
+
+ \prop_put:NxV \l__braid_permutation_prop
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ } \l__braid_tmpa_tl
+ \prop_put:NxV \l__braid_permutation_prop
+ {
+ \seq_item:Nn \l__braid_crossing_seq {1}
+ } \l__braid_tmpb_tl
+ }
+ \int_compare:nT {\l__braid_crossing_int = \l__braid_anchor_level_int}
+ {
+ \prop_set_eq:NN \l__braid_anchor_prop \l__braid_permutation_prop
+ }
+ \bool_if:NT \l__braid_step_level_bool
+ {
+ \int_incr:N \l__braid_crossing_int
+ }
+ }
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_get:NnN \l__braid_anchor_prop {##1} \l__braid_tmpa_tl
+ \prop_put:NVn \l__braid_inverse_prop \l__braid_tmpa_tl {##1}
+ }
+ \prop_set_eq:NN \l__braid_anchor_prop \l__braid_inverse_prop
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_get:NnN \l__braid_permutation_prop {##1} \l__braid_tmpa_tl
+ \prop_put:NVn \l__braid_inverse_prop \l__braid_tmpa_tl {##1}
+ }
+ \tl_set:Nx \l__braid_tmpa_tl {\seq_item:Nn \l__braid_anchor_seq {1}}
+ \tl_if_eq:VnT \l__braid_tmpa_tl {rev}
+ {
+ \prop_get:NVN \l__braid_permutation_prop
+ \l__braid_anchor_strand_tl \l__braid_anchor_strand_tl
+ }
+ \tl_if_eq:VnF \l__braid_anchor_level_tl {s}
+ {
+ \tl_if_eq:VnTF \l__braid_anchor_level_tl {e}
+ {
+ \prop_get:NVN \l__braid_inverse_prop
+ \l__braid_anchor_strand_tl \l__braid_anchor_strand_tl
+ }
+ {
+ \prop_get:NVN \l__braid_anchor_prop
+ \l__braid_anchor_strand_tl \l__braid_anchor_strand_tl
+ }
+ }
+}
+\cs_new_nopar:Npn \__braid_dim_value:n #1
+{
+ \dim_to_fp:n {\pgfkeysvalueof{/tikz/braid/#1}}
+}
+\cs_new_nopar:Npn \__braid_value:n #1
+{
+ \pgfkeysvalueof{/tikz/braid/#1}
+}
+\cs_generate_variant:Nn \prop_get:NnN {NxN}
+\cs_generate_variant:Nn \prop_put:Nnn {NxV}
+\cs_generate_variant:Nn \tl_if_eq:nnTF {VnTF}
+\cs_generate_variant:Nn \tl_if_eq:nnF {VnF}
+\cs_generate_variant:Nn \tl_if_eq:nnT {VnT}
+
+\cs_new_nopar:Npn \__braid_render:
+{
+ \fp_set:Nn \l__braid_anchor_x_fp { - 1 * (\tl_use:N \l__braid_anchor_strand_tl - 1) * \__braid_dim_value:n {width} }
+
+ \tl_if_eq:VnTF \l__braid_anchor_level_tl {s}
+ {
+ \fp_set:Nn \l__braid_anchor_y_fp {0}
+ }
+ {
+ \tl_if_eq:VnTF \l__braid_anchor_level_tl {e}
+ {
+ \fp_set:Nn \l__braid_anchor_y_fp {
+ -1 * \l__braid_length_int * \__braid_dim_value:n {height}
+ - sign(\__braid_dim_value:n {height})
+ * 2 * \__braid_dim_value:n {border~ height}
+ }
+ }
+ {
+ \fp_set:Nn \l__braid_anchor_y_fp {
+ -1 * \l__braid_anchor_level_tl * \__braid_dim_value:n {height}
+ - sign(\__braid_dim_value:n {height})
+ * \__braid_dim_value:n {border~ height}
+ }
+ }
+ }
+
+ \begin{scope}[
+ shift={
+ (\fp_to_decimal:N \l__braid_anchor_x_fp pt,
+ \fp_to_decimal:N \l__braid_anchor_y_fp pt
+ )
+ }
+ ]
+ \prop_clear:N \l__braid_strands_prop
+ \fp_zero:N \l__braid_height_fp
+ \fp_zero:N \l__braid_nudge_fp
+ \fp_zero:N \l__braid_control_fp
+ \fp_set:Nn \l__braid_height_fp
+ {
+ sign(\__braid_dim_value:n {height})
+ * \__braid_dim_value:n {border~ height}
+ }
+ \fp_set:Nn \l__braid_width_fp
+ {
+ (\l__braid_strands_int - 1) * \__braid_dim_value:n {width}
+ + 2 * sign(\__braid_dim_value:n{width})
+ * \__braid_dim_value:n {floor~ border}
+ }
+ \fp_set:Nn \l__braid_nudge_fp
+ {
+ \__braid_value:n {nudge~ factor} * \__braid_dim_value:n {height}
+ }
+ \fp_set:Nn \l__braid_control_fp
+ {
+ \__braid_value:n {control~ factor} * \__braid_dim_value:n {height}
+ }
+ \fp_sub:Nn \l__braid_control_fp {\l__braid_nudge_fp}
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_get:NnN \l__braid_inverse_prop {##1} \l__braid_tmpa_tl
+ \prop_put:Nnx \l__braid_strands_prop {##1}
+ {
+ \exp_not:N \draw[
+ braid/every~ strand/.try,
+ braid/strand~ ##1/.try
+ ]
+ \exp_not:N \__braid_moveto:nn {
+ \fp_eval:n {(##1 - 1) * \__braid_dim_value:n {width} }
+ } {0}
+ \exp_not:N \__braid_lineto:nn {
+ \fp_eval:n {(##1 - 1) * \__braid_dim_value:n {width} }
+ } { \fp_to_decimal:N \l__braid_height_fp}
+ }
+ \__braid_coordinate:xxxx {-##1-s} {-rev-\l__braid_tmpa_tl-s}
+ {\fp_eval:n {(##1 - 1) * \__braid_dim_value:n {width} }} {0}
+
+ \__braid_coordinate:xxxx {-##1-0} {-rev-\l__braid_tmpa_tl-0}
+ {\fp_eval:n {(##1 - 1) * \__braid_dim_value:n {width} }}
+ { \fp_to_decimal:N \l__braid_height_fp}
+ }
+ \seq_map_inline:Nn \l__braid_floors_seq
+ {
+ \tl_set:Nx \l__braid_tmpa_tl {\clist_item:nn {##1} {5}}
+ \__braid_do_floor:Vxxxx \l__braid_tmpa_tl
+ {\fp_eval:n
+ {
+ -1*sign(\__braid_dim_value:n{width})
+ * \__braid_dim_value:n {floor~ border}
+ + (\__braid_dim_value:n {width}) * (\clist_item:nn {##1} {1} - 1)
+ }
+ pt
+ }
+ {\fp_eval:n
+ {
+ \l__braid_height_fp + ( \__braid_dim_value:n {height} ) * (\clist_item:nn {##1} {2})
+ }
+ pt
+ }
+ {\fp_eval:n {
+ ( (\clist_item:nn {##1} {3}) * \__braid_dim_value:n {width}
+ + 2 * sign(\__braid_dim_value:n{width})
+ * \__braid_dim_value:n {floor~ border} ) / \dim_to_fp:n {1cm}
+ }
+ }
+ {\fp_eval:n {
+ (\clist_item:nn {##1} {4}) * ( \__braid_dim_value:n {height} ) / \dim_to_fp:n {1cm}
+ }
+ }
+ }
+ \int_zero:N \l__braid_crossing_int
+ \int_incr:N \l__braid_crossing_int
+
+ \seq_map_inline:Nn \l__braid_word_seq
+ {
+ \seq_clear:N \l__braid_crossing_seq
+ \bool_set_true:N \l__braid_step_level_bool
+ \bool_set_false:N \l__braid_floor_bool
+ \bool_set_false:N \l__braid_swap_crossing_bool
+ ##1
+ \bool_if:NT \l__braid_floor_bool
+ {
+ \__braid_do_floor:Vxxxx \l__braid_crossing_int
+ {\fp_eval:n
+ {
+ -1*sign(\__braid_dim_value:n{width})
+ * \__braid_dim_value:n {floor~ border}
+ }
+ pt
+ }
+ {\fp_to_decimal:N \l__braid_height_fp pt}
+ {\fp_eval:n { \l__braid_width_fp / \dim_to_fp:n {1cm} }}
+ {\fp_eval:n { ( \__braid_dim_value:n {height} ) / \dim_to_fp:n {1cm}}}
+ }
+ \seq_if_empty:NF \l__braid_crossing_seq
+ {
+ \prop_get:NxN \l__braid_crossing_permutation_prop
+ {\seq_item:Nn \l__braid_crossing_seq {1}} \l__braid_tmpa_tl
+ \prop_get:NxN \l__braid_crossing_permutation_prop
+ {\seq_item:Nn \l__braid_crossing_seq {2}} \l__braid_tmpb_tl
+
+ \prop_put:NxV \l__braid_crossing_permutation_prop
+ {\seq_item:Nn \l__braid_crossing_seq {2}} \l__braid_tmpa_tl
+ \prop_put:NxV \l__braid_crossing_permutation_prop
+ {\seq_item:Nn \l__braid_crossing_seq {1}} \l__braid_tmpb_tl
+ \prop_get:NxN \l__braid_strands_prop
+ {\seq_item:Nn \l__braid_crossing_seq {1}} \l__braid_tmpa_tl
+ \prop_get:NxN \l__braid_strands_prop
+ {\seq_item:Nn \l__braid_crossing_seq {2}} \l__braid_tmpb_tl
+ \tl_put_right:Nx \l__braid_tmpa_tl
+ {
+ \exp_not:N \__braid_lineto:nn
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1} - 1)
+ * \__braid_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n { \l__braid_height_fp + \l__braid_nudge_fp } }
+
+ \exp_not:N \__braid_curveto:nnnnnn
+
+ {0}
+ {\fp_eval:n { \l__braid_control_fp}}
+
+ {0}
+ {\fp_eval:n {- \l__braid_control_fp}}
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {2} - 1)
+ * \__braid_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n
+ {
+ \l__braid_height_fp
+ + \__braid_dim_value:n {height}
+ - \l__braid_nudge_fp
+ }
+ }
+ }
+ \tl_put_right:Nx \l__braid_tmpb_tl
+ {
+ \exp_not:N \__braid_lineto:nn
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {2} - 1)
+ * \__braid_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n { \l__braid_height_fp + \l__braid_nudge_fp } }
+
+ \exp_not:N \__braid_curveto:nnnnnn
+
+ {0}
+ {
+ \fp_eval:n {
+ \l__braid_control_fp * (.5 - \__braid_value:n {gap} )
+ }
+ }
+
+ {
+ \fp_eval:n {
+ - (.5 - \__braid_value:n {gap} ) / 3 *
+ \__braid_bezier_tangent:nnnnn
+ {.5 - \__braid_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ -(.5 - \__braid_value:n {gap} ) / 3 *
+ \__braid_bezier_tangent:nnnnn
+ {.5 - \__braid_value:n {gap} }
+ {0}
+ {\l__braid_control_fp}
+ {
+ \__braid_dim_value:n {height}
+ - 2* \l__braid_nudge_fp
+ - \l__braid_control_fp
+ }
+ {\__braid_dim_value:n {height} - 2* \l__braid_nudge_fp}
+ }
+ }
+
+ {
+ \fp_eval:n {
+ (\seq_item:Nn \l__braid_crossing_seq {2} - 1)
+ * \__braid_dim_value:n {width} +
+ \__braid_bezier_point:nnnnn
+ {.5 - \__braid_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ \l__braid_height_fp + \l__braid_nudge_fp +
+ \__braid_bezier_point:nnnnn
+ {.5 - \__braid_value:n {gap} }
+ {0}
+ {\l__braid_control_fp}
+ {
+ \__braid_dim_value:n {height}
+ - 2* \l__braid_nudge_fp
+ - \l__braid_control_fp
+ }
+ {\__braid_dim_value:n {height} - 2* \l__braid_nudge_fp}
+ }
+ }
+
+ \exp_not:N \__braid_moveto:nn
+ {
+ \fp_eval:n {
+ (\seq_item:Nn \l__braid_crossing_seq {2} - 1)
+ * \__braid_dim_value:n {width} +
+ \__braid_bezier_point:nnnnn
+ {.5 + \__braid_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ \l__braid_height_fp + \l__braid_nudge_fp +
+ \__braid_bezier_point:nnnnn
+ {.5 + \__braid_value:n {gap} }
+ {0}
+ {\l__braid_control_fp}
+ {
+ \__braid_dim_value:n {height} - 2* \l__braid_nudge_fp
+ - \l__braid_control_fp
+ }
+ {\__braid_dim_value:n {height} - 2* \l__braid_nudge_fp}
+ }
+ }
+
+ \exp_not:N \__braid_curveto:nnnnnn
+
+ {
+ \fp_eval:n {
+ (.5 - \__braid_value:n {gap} ) / 3 *
+ \__braid_bezier_tangent:nnnnn
+ {.5 + \__braid_value:n {gap} }
+ {0}
+ {0}
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1}
+ - \seq_item:Nn \l__braid_crossing_seq {2})
+ * \__braid_dim_value:n {width}
+ }
+ }
+ }
+ {
+ \fp_eval:n {
+ (.5 - \__braid_value:n {gap} ) / 3 *
+ \__braid_bezier_tangent:nnnnn
+ {.5 + \__braid_value:n {gap} }
+ {0}
+ {\l__braid_control_fp}
+ {
+ \__braid_dim_value:n {height} - 2* \l__braid_nudge_fp
+ - \l__braid_control_fp
+ }
+ {\__braid_dim_value:n {height} - 2* \l__braid_nudge_fp}
+ }
+ }
+
+ {0}
+ { \fp_eval:n {
+ -\l__braid_control_fp * (.5 - \__braid_value:n {gap} )
+ }
+ }
+
+ {\fp_eval:n
+ {
+ (\seq_item:Nn \l__braid_crossing_seq {1} - 1)
+ * \__braid_dim_value:n {width}
+ }
+ }
+ {\fp_eval:n
+ {
+ \l__braid_height_fp + \__braid_dim_value:n {height}
+ - \l__braid_nudge_fp
+ }
+ }
+
+ }
+ \prop_put:NxV \l__braid_strands_prop
+ {\seq_item:Nn \l__braid_crossing_seq {2}} \l__braid_tmpa_tl
+ \prop_put:NxV \l__braid_strands_prop
+ {\seq_item:Nn \l__braid_crossing_seq {1}} \l__braid_tmpb_tl
+ \int_compare:nT
+ {
+ \int_max:nn
+ {
+ \seq_item:Nn \l__braid_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ }
+ -
+ \int_min:nn
+ {
+ \seq_item:Nn \l__braid_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ }
+ > 1
+ }
+ {
+ \int_step_inline:nnnn
+ {
+ \int_min:nn
+ {
+ \seq_item:Nn \l__braid_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ }
+ + 1}
+ {1}
+ {
+ \int_max:nn
+ {
+ \seq_item:Nn \l__braid_crossing_seq {1}
+ }
+ {
+ \seq_item:Nn \l__braid_crossing_seq {2}
+ }
+ - 1
+ }
+ {
+
+ \prop_get:NnN \l__braid_strands_prop {####1} \l__braid_tmpa_tl
+ \tl_put_right:Nx \l__braid_tmpa_tl
+ {
+ \exp_not:N \__braid_lineto:nn
+ {\fp_eval:n {(####1 - 1) * \__braid_dim_value:n {width} }}
+ {\fp_eval:n
+ {
+ \l__braid_height_fp + \l__braid_nudge_fp
+ + .5 * \l__braid_control_fp
+ }
+ }
+ \exp_not:N \__braid_moveto:nn
+ {\fp_eval:n {(####1 - 1) * \__braid_dim_value:n {width} }}
+ {\fp_eval:n
+ {
+ \l__braid_height_fp + \__braid_dim_value:n {height}
+ - \l__braid_nudge_fp - .5 * \l__braid_control_fp
+ }
+ }
+ }
+
+ \prop_put:NnV \l__braid_strands_prop {####1} \l__braid_tmpa_tl
+ }
+ }
+ }
+ \bool_if:NT \l__braid_step_level_bool
+ {
+ \fp_add:Nn \l__braid_height_fp { \__braid_dim_value:n {height} }
+
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_get:NnN \l__braid_crossing_permutation_prop
+ {####1} \l__braid_tmpb_tl
+ \prop_get:NVN \l__braid_inverse_prop
+ \l__braid_tmpb_tl \l__braid_tmpa_tl
+
+ \__braid_coordinate:xxxx
+ {-\l__braid_tmpb_tl-\int_use:N \l__braid_crossing_int}
+ {-rev-\l__braid_tmpa_tl-\int_use:N \l__braid_crossing_int }
+ {\fp_eval:n { (####1 - 1) * \__braid_dim_value:n {width} }}
+ {\fp_to_decimal:N \l__braid_height_fp}
+ }
+
+ \int_incr:N \l__braid_crossing_int
+ }
+ }
+
+ \fp_add:Nn \l__braid_height_fp
+ {
+ sign(\__braid_dim_value:n {height})
+ * \__braid_dim_value:n {border~ height}
+ }
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_get:NxN \l__braid_strands_prop {##1} \l__braid_tmpa_tl
+ \prop_get:NxN \l__braid_permutation_prop {##1} \l__braid_tmpb_tl
+
+ \tl_put_right:Nx \l__braid_tmpa_tl {
+ \exp_not:N \__braid_lineto:nn
+ {\fp_eval:n { (##1 - 1) * \__braid_dim_value:n {width} }}
+ {\fp_to_decimal:N \l__braid_height_fp}
+ coordinate (-rev-##1-e)
+ coordinate (-\l__braid_tmpb_tl-e)
+ ;
+ }
+
+ \prop_put:NnV \l__braid_strands_prop {##1} \l__braid_tmpa_tl
+ }
+ \int_step_inline:nnnn {1} {1} {\l__braid_strands_int}
+ {
+ \prop_get:NnN \l__braid_strands_prop {##1} \l__braid_tmpa_tl
+ \tl_use:N \l__braid_tmpa_tl
+ }
+ \end{scope}
+}
+\cs_new_nopar:Npn \__braid_moveto:nn #1#2
+{
+ (#1 pt, #2 pt)
+}
+\cs_new_nopar:Npn \__braid_lineto:nn #1#2
+{
+ -- (#1 pt, #2 pt)
+}
+\cs_new_nopar:Npn \__braid_curveto:nnnnnn #1#2#3#4#5#6
+{
+ .. controls +(#1 pt, #2 pt) and +(#3 pt, #4 pt)
+ .. (#5 pt, #6 pt)
+}
+\cs_new_nopar:Npn \__braid_coordinate:nnnn #1#2#3#4
+{
+ \coordinate[alias=#2] (#1) at (#3 pt,#4 pt);
+}
+\cs_generate_variant:Nn \__braid_coordinate:nnnn {xxxx}
+\cs_new_nopar:Npn \__braid_bezier_point:nnnnn #1#2#3#4#5
+{
+ \fp_eval:n
+ {
+ (1 - (#1)) * (1 - (#1)) * (1 - (#1)) * (#2)
+ +
+ 3 * (1 - (#1)) * (1 - (#1)) * (#1) * (#3)
+ +
+ 3 * (1 - (#1)) * (#1) * (#1) * (#4)
+ +
+ (#1) * (#1) * (#1) * (#5)
+ }
+}
+\cs_new_nopar:Npn \__braid_bezier_tangent:nnnnn #1#2#3#4#5
+{
+ \fp_eval:n
+ {
+ 3 * (1 - (#1)) * (1 - (#1)) * (#3 - (#2))
+ +
+ 6 * (1 - (#1)) * (#1) * (#4 - (#3))
+ +
+ 3 * (#1) * (#1) * (#5 - (#4))
+ }
+}
+\cs_new_nopar:Npn \__braid_do_floor:nnnnn #1#2#3#4#5
+{
+ \pic[pic~ type=floor,
+ xscale=#4,
+ yscale=#5,
+ at={(#2,#3)},
+ braid/every~ floor/.try,
+ braid/floor~#1/.try,
+ ];
+}
+\cs_generate_variant:Nn \__braid_do_floor:nnnnn {Vxxxx}
+\ExplSyntaxOff
+
+%%
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace at 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 braids.dtx
+%% braids_doc.tex
+%% and the derived files README.txt,
+%% braids.ins,
+%% braids.pdf,
+%% braids.sty,
+%% tikzlibrarybraids.code.tex,
+%% braids_doc.pdf.
+%%
+%%
+%% End of file `tikzlibrarybraids.code.tex'.
Property changes on: trunk/Master/texmf-dist/tex/latex/braids/tikzlibrarybraids.code.tex
___________________________________________________________________
Added: svn:eol-style
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+native
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