mirror of
https://github.com/MartinThoma/LaTeX-examples.git
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2049 lines
71 KiB
TeX
2049 lines
71 KiB
TeX
% \iffalse meta-comment
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%<*internal>
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\iffalse
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%</internal>
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%<*readme>
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----------------------------------------------------------------
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brunnian --- a style file for drawing link diagrams with TikZ/PGF
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E-mail: stacey@math.ntnu.no
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Released under the LaTeX Project Public License v1.3c or later
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See http://www.latex-project.org/lppl.txt
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----------------------------------------------------------------
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This package defines some commands and styles useful for drawing knot and link diagrams with TikZ/PGF.
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Some are geared towards drawing very specific links (the iterated Hopf and Brunnian links) whilst others will be more generally useful for arbitrary knots and links.
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%</readme>
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%<*internal>
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\fi
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\def\nameofplainTeX{plain}
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\ifx\fmtname\nameofplainTeX\else
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\expandafter\begingroup
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\fi
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%</internal>
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%<*install>
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\input docstrip.tex
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\keepsilent
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\askforoverwritefalse
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\preamble
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----------------------------------------------------------------
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brunnian --- a style file for drawing link diagrams with TikZ/PGF
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E-mail: stacey@math.ntnu.no
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Released under the LaTeX Project Public License v1.3c or later
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See http://www.latex-project.org/lppl.txt
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----------------------------------------------------------------
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\endpreamble
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\postamble
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Copyright (C) 2011 by Andrew Stacey <stacey@math.ntnu.no>
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This work may be distributed and/or modified under the
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conditions of the LaTeX Project Public License (LPPL), either
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version 1.3c of this license or (at your option) any later
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version. The latest version of this license is in the file:
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http://www.latex-project.org/lppl.txt
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This work is "maintained" (as per LPPL maintenance status) by
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Andrew Stacey.
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This work consists of the file brunnian.dtx
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and the derived files brunnian.ins,
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brunnain.pdf, and
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brunnian.sty.
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\endpostamble
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\usedir{tex/latex/brunnian}
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\generate{
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\file{\jobname.sty}{\from{\jobname.dtx}{package}}
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}
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%</install>
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%<install>\endbatchfile
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%<*internal>
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\usedir{source/latex/brunnian}
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\generate{
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\file{\jobname.ins}{\from{\jobname.dtx}{install}}
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}
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\nopreamble\nopostamble
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\usedir{doc/latex/demopkg}
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\generate{
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\file{README.txt}{\from{\jobname.dtx}{readme}}
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}
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\ifx\fmtname\nameofplainTeX
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\expandafter\endbatchfile
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\else
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\expandafter\endgroup
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\fi
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%</internal>
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%<*package>
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\NeedsTeXFormat{LaTeX2e}
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\ProvidesPackage{brunnian}[2011/03/10 v1.0 Tikz/PGF commands for drawing knots and links]
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%</package>
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%<*driver>
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\documentclass{ltxdoc}
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\usepackage[T1]{fontenc}
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\usepackage{lmodern}
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\usepackage{morefloats}
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\usepackage{\jobname}
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\usepackage[numbered]{hypdoc}
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\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9}
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\usepackage{listings}
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\lstloadlanguages{[LaTeX]TeX}
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\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
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\usepackage{fancyvrb}
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\newenvironment{example}
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{\VerbatimEnvironment
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\begin{VerbatimOut}[gobble=2]{example.out}}
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{\end{VerbatimOut}
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\begin{center}
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\vspace{1ex}
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\setlength{\parindent}{0pt}
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\fbox{\begin{minipage}{.9\linewidth}
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\lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
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\lstinputlisting[]{example.out}
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\end{minipage}}
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\fbox{\begin{minipage}{.9\linewidth}
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\small\input{example.out}
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\end{minipage}}
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\vspace{1ex}
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\end{center}
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}
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\EnableCrossrefs
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\CodelineIndex
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\RecordChanges
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\begin{document}
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\DocInput{\jobname.dtx}
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\end{document}
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%</driver>
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% \fi
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%
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% \CheckSum{2860}
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%
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% \CharacterTable
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% {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
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% 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
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% Digits \0\1\2\3\4\5\6\7\8\9
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% Exclamation \! Double quote \" Hash (number) \#
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% Dollar \$ Percent \% Ampersand \&
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% Acute accent \' Left paren \( Right paren \)
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% Asterisk \* Plus \+ Comma \,
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% Minus \- Point \. Solidus \/
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% Colon \: Semicolon \; Less than \<
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% Equals \= Greater than \> Question mark \?
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% Commercial at \@ Left bracket \[ Backslash \\
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% Right bracket \] Circumflex \^ Underscore \_
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% Grave accent \` Left brace \{ Vertical bar \|
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% Right brace \} Tilde \~}
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%
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%
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% \changes{1.0}{2011/03/10}{Converted to DTX file}
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%
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% \DoNotIndex{\newcommand,\newenvironment}
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%
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% \providecommand*{\url}{\texttt}
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% \GetFileInfo{brunnian.dtx}
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% \title{The \textsf{brunnian} package}
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% \author{Andrew Stacey \\ \url{stacey@math.ntnu.no}}
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% \date{\fileversion~from \filedate}
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%
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% \maketitle
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%
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% \section{Introduction}
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%
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% This package defines some commands and styles for drawing knots and links with Ti\emph{k}Z/PGF.
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% The original motivation for the commands was to draw iterated Hopf and Brunnian links and so many of the commands are specifically for those diagrams.
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% There are also more general styles and commands that will be useful for general knot and link diagrams.
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% For example, the trefoil knot can be rendered using the following code.
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%
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% \begin{example}
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% \tikzset{every path/.style={red,line width=2pt},every node/.style={transform shape,knot crossing,inner sep=1.5pt}}
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% \begin{center}
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% \begin{tikzpicture}
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% \foreach \brk in {0,1,2} {
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% \begin{scope}[rotate=\brk * 120]
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% \node (k\brk) at (0,-1) {};
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% \end{scope}
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% }
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% \foreach \brk in {0,1,2} {
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% \pgfmathparse{int(Mod(\brk - 1,3))}
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% \edef\brl{\pgfmathresult}
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% \draw (k\brk) .. controls (k\brk.4 north west) and (k\brl.4 north east) .. (k\brl.center);
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% \draw (k\brk.center) .. controls (k\brk.16 south west) and (k\brl.16 south east) .. (k\brl);
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% }
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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%
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% \section{Usage}
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%
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% Using this package is very easy.
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% Once it is installed, simply put\\
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% \Verb+\usepackage{brunnian}+\\
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% in the preamble of your document.
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% This package automatically loads several other packages: \Verb+xcolor+ (with the \Verb+svgnames+ option), \Verb+tikz+, and \Verb+colorinfo+.
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% (These can be loaded before this package, though note that loading \Verb+xcolor+ with a different set of colours will result in an error about option clashes.)
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% It also detects whether \Verb+htlatex+ is being used and sets up PGF to produce SVG if so.
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%
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% \subsection{User Commands}
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%
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% The user interface provided by this package splits into two parts.
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% One part consists of the jigsaw pieces needed to construct complicated link diagrams.
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% The other part consists of various Ti\emph{k}Z styles and oddments that are designed to make it easier to draw knots and links.
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% As this second part is probably more widely applicable, we shall describe it first.
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% \subsubsection{Knots and Links}
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%
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% This package defines four styles for paths for Ti\emph{k}Z: \Verb+knot+, \Verb+thin knot+, \Verb+thick knot+, and \Verb+string+.
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% The first three define paths which have an extra thickness set to the colour of the background meaning that they ``chop out'' part of anything that they pass over.
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% To specify a colour for one of these styles, one has to pass the option \Verb+double=colour+ rather than the colour itself.
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% This is because the styles work by using the \Verb+double+ style of Ti\emph{k}Z paths, wherein the colour of the path becomes the \emph{outside} colour.
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% As we want it to be the inside colour, we have to specify the colour differently.
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%
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% \begin{example}
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% \begin{center}
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% \begin{tikzpicture}[every path/.style={double=Red}]
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% \draw[thin knot] (-1,-1) -- (1,1);
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% \draw[thin knot] (-1,1) -- (1,-1);
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% \begin{scope}[xshift=2.5cm]
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% \draw[knot] (-1,-1) -- (1,1);
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% \draw[knot] (-1,1) -- (1,-1);
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% \end{scope}
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% \begin{scope}[xshift=5cm]
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% \draw[thick knot] (-1,-1) -- (1,1);
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% \draw[thick knot] (-1,1) -- (1,-1);
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% \end{scope}
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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% The last style, \Verb+string+, does not have this overhand but is designed to be compatible with \Verb+knot+ and so can be used whenever the overhang might get in the way.
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%
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% This package also defines some node shapes to help draw knot and link diagrams.
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% The idea with these is to place a node of the appropriate type at each crossing and then link them accordingly.
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% The node shapes are \Verb+knot crossing+, \Verb+knot over cross+, \Verb+knot under cross+, \Verb+knot vert+, \Verb+knot horiz+.
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% The \Verb+knot over cross+ and \Verb+knot under cross+ two are crossings, \Verb+knot vert+ and \Verb+knot horiz+ are for when resolving the crossings in a diagram.
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% By judicious use of the \Verb+\foreach+ command, a family of resolved link diagrams can be produced.
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%
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% \begin{example}
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% \begin{center}
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% \begin{tikzpicture}[every node/.style={draw,Red}]
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% \node[knot over cross] at (1,0) {};
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% \node[knot under cross] at (2,0) {};
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% \node[knot vert] at (3,0) {};
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% \node[knot horiz] at (4,0) {};
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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% The node \Verb+knot crossing+ is not meant to be drawn, it is an empty shape.
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% Its value is in that it defines more anchors than the usual rectangle shape.
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% For each of the 8 main compass directions, it defines anchors at 2, 4, 8, 16, and 32 times further out.
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% This can be useful for designing curves that enter and exit the crossing gracefully at particular directions.
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% When using this node shape, the crossing itself is easiest to draw by using the \Verb+center+ anchor for the strands that form the over cross.
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%
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% \begin{example}
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% \begin{center}
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% \begin{tikzpicture}[every path/.style={string,Red}, every node/.style={transform shape, knot crossing, inner sep=1.5pt}]
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% \node[rotate=45] (tl) at (-1,1) {};
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% \node[rotate=-45] (tr) at (1,1) {};
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% \node (m) at (0,-1) {};
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% \node (b) at (0,-2) {};
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% \draw (b) .. controls (b.4 north west) and (m.4 south west) .. (m.center);
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% \draw (b.center) .. controls (b.4 north east) and (m.4 south east) .. (m);
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% \draw (m) .. controls (m.8 north west) and (tl.3 south west) .. (tl.center);
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% \draw (m.center) .. controls (m.8 north east) and (tr.3 south east) .. (tr);
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% \draw (tl.center) .. controls (tl.16 north east) and (tr.16 north west) .. (tr);
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% \draw (b) .. controls (b.16 south east) and (tr.16 north east) .. (tr.center);
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% \draw (b.center) .. controls (b.16 south west) and (tl.16 north west) .. (tl);
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% \draw (tl) -- (tr.center);
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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% \subsection{Higher Order Link Diagrams}
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%
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% Many of the commands in this package were developed to draw examples of specific families of higher order links, particularly involving the Brunnian and Hopfian families.
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% These commands are built up in sections from some basic jigsaw pieces.
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%
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% \DescribeMacro{\brunnian}
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% \DescribeMacro{\outbrunnian}
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% \DescribeMacro{\midbrunnian}
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% \DescribeMacro{\hopfring}
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% \DescribeMacro{\brunniantwo}
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% \DescribeMacro{\outbrunniantwo}
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% \DescribeMacro{\hopftwo}
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% \DescribeMacro{\outhopftwo}
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% \DescribeMacro{\brunnianhopf}
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% \DescribeMacro{\hopfbrunnian}
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% Let us start with the commands that render a full diagram.
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%
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% \begin{itemize}
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% \item \cmd{\brunnian}\oarg{double}\marg{radius}\marg{number} \\
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% \cmd{\outbrunnian}\oarg{double}\marg{radius}\marg{number} \\
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% \cmd{\midbrunnian}\oarg{double}\marg{radius}\marg{number}
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%
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% This draws a Brunnian ring of radius \marg{radius} with \marg{number} components.
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% If \oarg{double} is specified (as a positive integer) then each strand is doubled by that amount.
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% The default is to draw them with the junctions pointing inwards, the second variant has them outwards whilst the third makes them balanced.
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%
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% \item \cmd{\hopfring}\marg{radius}\marg{number}
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%
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% This draws a Hopf ring of radius \marg{radius} with \marg{number} components.
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%
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% \item \cmd{\brunniantwo}\marg{radius}\marg{level2}\marg{level1} \\
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% \cmd{\outbrunniantwo}\marg{radius}\marg{level2}\marg{level1}
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%
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% This draws a level two Brunnian ring of radius \marg{radius} with \marg{level2} level two families each of \marg{level1} components.
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% The \cmd{\outbrunniantwo} variant draws it with the main junctions pointing outwards.
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%
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% \item \cmd{\hopftwo}\marg{radius}\marg{level2}\marg{level1} \\
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% \cmd{\outhopftwo}\marg{radius}\marg{level2}\marg{level1}
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%
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% This draws a level two Hopf ring of radius \marg{radius} with \marg{level2} level two families each of \marg{level1} components.
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% The \cmd{\outhopftwo} variant draws it with the main junctions pointing outwards.
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%
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% \item \cmd{\brunnianhopf}\marg{radius}\marg{level2}\marg{level1} \\
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% \cmd{\hopfbrunnian}\marg{radius}\marg{level2}\marg{level1}
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%
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% These draw level two structures of radius \marg{radius} with \marg{level2} level two families each of \marg{level1} components.
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% The level two families in the first are linked by Brunnian linkages and the level one linkages are Hopfian.
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% In the second, these are the other way around.
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% \end{itemize}
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%
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% The main pieces that these diagrams are built from are \emph{linkages}.
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% By the term \emph{linkage} we mean that part of a link diagram where crossings occur.
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% For the Brunnian links, the command that generates the linkages is the \Verb+\junction+ command.
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% The Hopfian links are generated by \Verb+\hopfjunction+.
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% There are some other variants as well.
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%
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% \DescribeMacro{\junction}
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% \DescribeMacro{\flatjunction}
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% \DescribeMacro{\hopfjunction}
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% These commands all take the same arguments.
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% For example, \\
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% \cmd{\junction}\marg{level}\marg{radius}\marg{direction}\marg{clockwise}\marg{anticlockwise}\\
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% renders a Brunnian junction according to the specifications.
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% The argument \marg{level} sets the level of iteration of the linkage.
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% The \marg{radius} is the starting radius of the junction, whilst \marg{direction} determines whether it points in or out.
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% The angles \marg{clockwise} and \marg{anticlockwise} determine how far around the strands will extend on either side of the junction.
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% (It is possible that the strands will extend further than the given angles as there is a minimum which depends on the other parameters.)
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% The command \Verb+\flatjunction+ renders the same linkage but as part of a flat link diagram (that is, not one that forms a circle).
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% At the moment, \Verb+\flatjunction+ does not use the angles; in some future version it will use these as lengths.
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% Lastly, \Verb+\hopfjunction+ renders the linkages as used in the various Hopf rings.
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% The linkage is drawn at the bottom of the circle, obviously it can be rotated to suit.
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%
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% \begin{example}
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% \begin{center}
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% \begin{tikzpicture}
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% \colorlet{inner}{ring1}
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% \colorlet{outer}{ring2}
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% \flatjunction{2}{5}{1}{10}{100}
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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% \begin{example}
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% \begin{center}
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% \begin{tikzpicture}
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% \colorlet{inner}{ring1}
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% \colorlet{outer}{ring2}
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% \hopfjunction{3}{5}{1}{10}{20}
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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% The colours of the strands of the link are determined by colours named \Verb+innerINT+ and \Verb+outerINT+, where \Verb+INT+ is an (optional) integer.
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% On one side of the linkage, the colour of strand \(N\) is the colour specified in \Verb+innerM+ where \(M \le N\).
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% The other side uses the \Verb+outer+ colours.
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%
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%
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% \DescribeMacro{\fillin}
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% The more complicated diagrams are built from the various junction commands.
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% After all the junctions have been put in place, there are often some gaps that need to be filled in.
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% The command\\
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% \cmd{\fillin}\marg{radius}\marg{start}\marg{end}\marg{sangle}\marg{eangle}\marg{colour} \\
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% draws the arcs which correspond to the strands numbered from \marg{start} to \marg{end} given that the radius of the main diagram is \marg{radius}.
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% The arcs are drawn from angle \marg{sangle} to \marg{eangle}, with the proviso that the \(0\) is straight down.
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%
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%
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% \DescribeMacro{\chain}
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% \DescribeMacro{\leftchain}
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% \DescribeMacro{\rightchain}
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% \DescribeMacro{\leftcornerchain}
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% \DescribeMacro{\rightcornerchain}
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% The commands \cmd{\chain}, \cmd{\leftchain}, \cmd{\rightchain}, \cmd{\leftcornerchain}, and \cmd{\rightcornerchain} all draw the components for Brunnian chain mail.
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% The drawings are designed so that superimposing them will result in a correctly rendered diagram.
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% The colour of the chain element is determined by the colour \Verb+chain+.
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%
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% \begin{example}
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% \begin{center}
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% \begin{tikzpicture}
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% \colorlet{chain}{Green}
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% \chain
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% \begin{scope}[shift={(-2,-2)}]
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% \leftchain
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% \end{scope}
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% \begin{scope}[shift={(4,-2)}]
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% \rightcornerchain
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% \end{scope}
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% \end{tikzpicture}
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% \end{center}
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% \end{example}
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%
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%
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% \DescribeMacro{\brunnianlink}
|
|
% \DescribeMacro{\flatbrunnianlink}
|
|
% For the level one Brunnian structures, the pictures drawn are not the most elegant.
|
|
% A more pleasing rendition can be obtained by using the pieces rendered by \cmd{\flatbrunnianlink}\marg{scale} and \cmd{\brunnianlink}\marg{scale}\marg{angle}.
|
|
%
|
|
% \begin{example}
|
|
% \begin{center}
|
|
% \begin{tikzpicture}
|
|
% \pgfmathsetmacro{\brscale}{1}
|
|
% \begin{scope}[xshift=6.5 cm]
|
|
% \draw[knot,double=ring1] (-6.3*\brscale0,0) circle (\brscale);
|
|
% \draw[knot,double=ring2] (-1.5*\brscale,0) circle (\brscale);
|
|
% \foreach \brk in {5,...,3} {
|
|
% \begin{scope}[xshift=-\brk * \brscale cm]
|
|
% \colorlet{chain}{ring\brk}
|
|
% \flatbrunnianlink{\brscale}
|
|
% \end{scope}
|
|
% }
|
|
% \end{scope}
|
|
% \end{tikzpicture}
|
|
% \end{center}
|
|
% \end{example}
|
|
%
|
|
% \DescribeMacro{\brunniantwocpt}
|
|
% \DescribeMacro{\brunniancpt}
|
|
% \DescribeMacro{\brunniancptouter}
|
|
% More complicated link diagrams can be built from components.
|
|
% The command
|
|
%
|
|
% \cmd{\brunniantwocpt}\marg{radius}\marg{lvl2}\marg{lvl1}\marg{colour}
|
|
%
|
|
% renders a level two component from a Brunnian level two ring with base colour \marg{colour} (which must be one of the ring colours).
|
|
% It is rendered as if it were part of a level two Brunnian ring of radius \marg{radius} with \marg{lvl2} components at level two and \marg{lvl1} components at level one.
|
|
% The command \cmd{\brunniancpt} is the same but for level one Brunnian rings.
|
|
% As this only renders one link component, its colour is specified by the colour \Verb+brunnian+.
|
|
%
|
|
% \DescribeMacro{\brunnianlinkage}
|
|
% \DescribeMacro{\brunniantwoside}
|
|
% \DescribeMacro{\dblhopftwoside}
|
|
% \DescribeMacro{\dblhopfrctwoside}
|
|
% \DescribeMacro{\brunnianhalftwoside}
|
|
% \DescribeMacro{\brunnianringonetwoside}
|
|
% These commands draw a more schematic diagram of the various linkages.
|
|
% The \Verb+twoside+ versions draw two versions with a gap in the middle so that the gap can be filled by linking the various ends to draw different resolutions of the link diagrams.
|
|
% The ends of the strands in the middle are Ti\emph{k}Z coordinates with labels \((1)\) to \((8)\) running down the left-hand side and then down the right.
|
|
% Certain lengths need to be set before this is used, namely \Verb+\brover+, \Verb+\bradj+, \Verb+\brsep+, and \Verb+\brlen+.
|
|
% These control various aspects of how the diagram is rendered.
|
|
%
|
|
% \begin{example}
|
|
% \begin{center}
|
|
% \pgfmathsetmacro{\brover}{.25}
|
|
% \pgfmathsetmacro{\bradj}{.05}
|
|
% \pgfmathsetmacro{\brsep}{.25}
|
|
% \pgfmathsetmacro{\brlen}{1}
|
|
% \begin{tikzpicture}[every path/.style={thick knot,double=Red},every node/.style={text=black},baseline=0cm]
|
|
% \dblhopftwoside
|
|
% \draw[double=none,Red,line width=2pt] (1) -- (2) (3) -- (5) (4) -- (6) (7) -- (8) ;
|
|
% \end{tikzpicture}
|
|
% \end{center}
|
|
% \end{example}
|
|
%
|
|
%
|
|
% \subsection{Colours}
|
|
%
|
|
% \DescribeMacro{\resetbgcolour}
|
|
% The method of producing the complicated iterated diagrams is to define certain blocks which can then be put together in the correct fashion.
|
|
% The blocks corresponding to junctions (that is, where link components meet) comprise strands from several components.
|
|
% It is possible to show only certain strands by setting the colour of the others to the background colour.
|
|
% Such strands are not drawn.
|
|
% Rather than attempt to discover the \emph{actual} background colour of the picture, this package believes what it is told.
|
|
% At the begining of the document, it is told that the background is \Verb+white+.
|
|
% The command \cmd{\resetbgcolour} takes one argument, \marg{colour}, which it then believes to be the background (for the current group).
|
|
%
|
|
% \subsection{Lengths}
|
|
%
|
|
% \DescribeMacro{\setbrstep}
|
|
% Various aspects of the sizes of the various link diagrams are controlled by an internal parameter \cmd{\br@step}.
|
|
% The command \cmd{\brstep}\marg{number} is \Verb+let+ to this to enable its use in the main document, but changing \cmd{\brstep} doesn't change \cmd{\br@step}.
|
|
% The command \cmd{\setbrstep} takes one argument, \marg{number}, to which it then sets \cmd{\br@step}.
|
|
%
|
|
%
|
|
%
|
|
% \StopEventually{}
|
|
%
|
|
% \section{Implementation}
|
|
%
|
|
% \iffalse
|
|
%<*package>
|
|
% \fi
|
|
%
|
|
% \begin{macrocode}
|
|
\ProvidesPackage{brunnian}
|
|
% \end{macrocode}
|
|
%
|
|
% Test for \Verb+htlatex+ by looking for the \Verb+tex4ht+ package.
|
|
% If found, set the \Verb+pgfsysdriver+ to the appropriate one
|
|
%
|
|
% \begin{macrocode}
|
|
\newif\ifsvg
|
|
\@ifpackageloaded{tex4ht}{
|
|
\svgtrue
|
|
}{}
|
|
\ifsvg
|
|
\def\pgfsysdriver{pgfsys-tex4ht.def}
|
|
\fi
|
|
% \end{macrocode}
|
|
%
|
|
% Load in required packages
|
|
%
|
|
% \begin{macrocode}
|
|
\RequirePackage[svgnames]{xcolor}
|
|
\RequirePackage{tikz}
|
|
\RequirePackage{colorinfo}
|
|
\usetikzlibrary{calc}
|
|
% \end{macrocode}
|
|
%
|
|
% Handle background colour: set the default to \Verb+white+, define a command to reset it, and at the beginning of the document, we read in the colour information needed to recognise \Verb+white+ when we see it.
|
|
% (Not sure why that has to be at the beginning of the document and not here.)
|
|
%
|
|
% \begin{macrocode}
|
|
\xglobal\colorlet{background}{white}
|
|
% \end{macrocode}
|
|
%
|
|
% \begin{macro}{\resetbgcolour}
|
|
% Allows for resetting the background colour.
|
|
% \begin{macrocode}
|
|
\newcommand{\resetbgcolour}[1]{%
|
|
\xglobal\colorlet{background}{#1}
|
|
\colorInfo{background}
|
|
\edef\br@white{\colorValue}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macrocode}
|
|
\AtBeginDocument{%
|
|
\colorInfo{background}%
|
|
\edef\br@white{\colorValue}%
|
|
}
|
|
% \end{macrocode}
|
|
%
|
|
% Now we set up the default colours for the rings.
|
|
%
|
|
% \begin{macrocode}
|
|
\xglobal\colorlet{ring1}{Red}
|
|
\xglobal\colorlet{ring2}{Green}
|
|
\xglobal\colorlet{ring3}{Blue}
|
|
\xglobal\colorlet{ring4}{Orange}
|
|
\xglobal\colorlet{ring5}{Purple}
|
|
\xglobal\colorlet{ring6}{Chartreuse}
|
|
\xglobal\colorlet{ring7}{Sienna}
|
|
\xglobal\colorlet{ring8}{DeepPink}
|
|
\xglobal\colorlet{ring9}{Gold}
|
|
\xglobal\colorlet{ring10}{DarkViolet}
|
|
\foreach \k in {1,2,3,4} {
|
|
\foreach \m in {1,2,3,4} {
|
|
\pgfmathparse{int(Mod(\m + \k - 2,4) + 1)}
|
|
\xglobal\colorlet{ring\k\m}{ring\k!50!ring\pgfmathresult}
|
|
\foreach \l in {1,2,3,4} {
|
|
\pgfmathparse{int(Mod(\l + \k - 2,4) + 1)}
|
|
\xglobal\colorlet{ring\k\m\l}{ring\k\m!50!ring\pgfmathresult}
|
|
}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
%
|
|
% Next step is to initialise the pgf layers.
|
|
%
|
|
% \begin{macrocode}
|
|
\pgfdeclarelayer{back}
|
|
\pgfdeclarelayer{front}
|
|
\pgfsetlayers{back,main,front}
|
|
% \end{macrocode}
|
|
%
|
|
% Now some default constants
|
|
%
|
|
% \begin{macrocode}
|
|
\pgfmathsetmacro{\br@step}{1/4}
|
|
\pgfmathsetmacro{\br@theta}{10}
|
|
\let\brstep=\br@step
|
|
\edef\br@one{1}
|
|
\edef\br@zero{0}
|
|
% \end{macrocode}
|
|
% \begin{macro}{\setbrste}
|
|
% \begin{macrocode}
|
|
\newcommand{\setbrstep}[1]{%
|
|
\def\br@step{#1}}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% These define some Ti\emph{k}Z styles for use with knot and link diagrams.
|
|
%
|
|
% \begin{macrocode}
|
|
\tikzset{knot/.style={double distance=1pt,line width=2pt,background}}
|
|
\tikzset{thin knot/.style={double distance=.5pt,line width=1pt,background}}
|
|
\tikzset{thick knot/.style={double distance=2pt,line width=4pt,background}}
|
|
\tikzset{string/.style={line width=1pt}}
|
|
% \end{macrocode}
|
|
%
|
|
% \begin{macro}{\getangle}
|
|
%
|
|
% Tells us the angles used by the junction command so we don't have to guess them later on, same parameters as the junction command (actually \cmd{\junction} should call this so we always know we do the same computation).
|
|
%
|
|
% \begin{macrocode}
|
|
\newcommand{\getangle}[5]{%
|
|
\pgfmathsetmacro{\br@num}{int(4 ^ (#1 - 1) + .5)}
|
|
\pgfmathsetmacro{\br@dir}{#3}
|
|
\pgfmathsetmacro{\br@innersep}{#1 == 1 ? 4 : 0}
|
|
\pgfmathsetmacro{\br@mr}{#2 -\br@step + (2*\br@num + .5) *\br@step * (1 - \br@dir)}
|
|
\pgfmathsetmacro{\br@angle}{atan((6 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
|
|
\ifx\relax#4\relax
|
|
\pgfmathparse{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathparse{int(#4 > \br@angle ? #4 : ceil(\br@angle))}
|
|
\fi
|
|
\xdef\clockangle{\pgfmathresult}
|
|
\ifx\relax#5\relax
|
|
\pgfmathparse{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathparse{int(#5 > \br@angle ? #5 : ceil(\br@angle))}
|
|
\fi
|
|
\xdef\aclockangle{\pgfmathresult}
|
|
\pgfmathparse{int(\clockangle + \aclockangle)}
|
|
\xdef\totalangle{\pgfmathresult}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\junction}
|
|
% Main junction command
|
|
%
|
|
% \begin{macrocode}
|
|
\newcommand{\junction}[5]{%
|
|
\pgfmathsetmacro{\br@midpt}{#3}
|
|
\pgfmathsetmacro{\br@dir}{(\br@midpt == 0 ? 1 : \br@midpt)}
|
|
\begin{scope}[xscale=\br@dir]
|
|
\pgfmathsetmacro{\br@num}{int(4 ^ (#1 - 1) + .5)}
|
|
\pgfmathsetmacro{\br@innersep}{#1 == 1 ? 4 : 0}
|
|
\pgfmathsetmacro{\br@mr}{#2 -\br@step + (2*\br@num + .5) *\br@step * (1 - \br@dir)}
|
|
\pgfmathsetmacro{\br@angle}{atan((6 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
|
|
\ifx\relax#4\relax
|
|
\pgfmathsetmacro{\br@outerangle}{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathsetmacro{\br@outerangle}{#4 > \br@angle ? #4 : ceil(\br@angle)}
|
|
\fi
|
|
\ifx\relax#5\relax
|
|
\pgfmathsetmacro{\br@innerangle}{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathsetmacro{\br@innerangle}{#5 > \br@angle ? #5 : ceil(\br@angle)}
|
|
\fi
|
|
\pgfmathsetmacro{\br@sin}{sin(\br@angle)}
|
|
\pgfmathsetmacro{\br@cos}{cos(\br@angle)}
|
|
\path (0,0) circle (2pt);
|
|
\edef\br@itstart{1}
|
|
\pgfmathsetmacro{\br@itend}{2*\br@num}
|
|
\edef\br@mcolor{outer}
|
|
\foreach \br@m in {\br@itstart,...,\br@itend} {
|
|
\@ifundefinedcolor{outer\br@m}{%
|
|
}{%
|
|
\global\edef\br@mcolor{outer\br@m}
|
|
}
|
|
\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 4 + 1 - \br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@x}{-1*\br@inr *\br@sin}
|
|
\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
|
|
\pgfmathsetmacro{\br@xx}{-1*\br@outr *\br@sin}
|
|
\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
|
|
\pgfmathsetmacro{\br@r}{(6*\br@num - 2*\br@m + \br@innersep)*\br@step/2}
|
|
\pgfmathsetmacro{\br@midr}{(\br@midpt == 0 ? (\br@inr + \br@outr)/2 + \br@r: \br@outr)}
|
|
\colorInfo{\br@mcolor}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) to[out=-\br@angle,in=180] (0,-\br@midr) arc(-\br@dir * 90:\br@dir * 90:\br@r) to[out=180,in=-\br@angle] (\br@x,\br@y);
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90-\br@angle:-90-\br@outerangle:\br@inr);
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90-\br@angle:-90-\br@outerangle:\br@outr);
|
|
\fi
|
|
}
|
|
\edef\br@itstart{1}
|
|
\pgfmathsetmacro{\br@itend}{2*\br@num}
|
|
\edef\br@mcolor{inner}
|
|
\foreach \br@m in {\br@itstart,...,\br@itend} {
|
|
\@ifundefinedcolor{inner\br@m}{%
|
|
}{%
|
|
\global\edef\br@mcolor{inner\br@m}
|
|
}
|
|
\pgfmathsetmacro{\br@inward}{2 * (-.5 + (\br@m > \br@num))}
|
|
\pgfmathsetmacro{\br@inr}{\br@mr + (\br@num+\br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outr}{\br@mr + (3*\br@num + 1 + \br@inward * 2*\br@num - \br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@inmidr}{\br@inr - \br@midpt * \br@innersep * \br@step / 2 - \br@num * \br@midpt * \br@step + .5*\br@midpt * \br@step}
|
|
\pgfmathsetmacro{\br@outmidr}{\br@outr - \br@midpt * \br@innersep * \br@step /2 + \br@inward * \br@dir * \br@innersep * \br@step/2 - \br@num * \br@midpt * \br@step + .5*\br@midpt * \br@step}
|
|
\pgfmathsetmacro{\br@x}{\br@inr *\br@sin}
|
|
\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
|
|
\pgfmathsetmacro{\br@xx}{\br@outr *\br@sin}
|
|
\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
|
|
\pgfmathsetmacro{\br@r}{(\br@num * (1 + \br@inward) - \br@inward * (\br@m - .5)) *\br@step + \br@innersep * \br@step/4}
|
|
\colorInfo{\br@mcolor}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) to[out=180+\br@angle,in=0] (0,-\br@outmidr) arc(\br@inward *\br@dir * 270:\br@inward *\br@dir * 90:\br@r);
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90+\br@angle:-90+\br@innerangle:\br@outr);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) to[out=180+\br@angle,in=0] (0,-\br@inmidr);
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90+\br@angle:-90+\br@innerangle:\br@inr);
|
|
\end{pgfonlayer}
|
|
\fi
|
|
}
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\flatjunction}
|
|
% The flat version of \cmd{\junction}
|
|
%
|
|
% \begin{macrocode}
|
|
\newcommand{\flatjunction}[5]{%
|
|
\begin{scope}[xscale=#3]
|
|
\pgfmathsetmacro{\br@num}{4 ^ (#1 - 1)}
|
|
\pgfmathsetmacro{\br@dir}{#3}
|
|
\pgfmathsetmacro{\br@innersep}{#1 == 1 ? 4 : 0}
|
|
\pgfmathsetmacro{\br@mr}{0}%#2 -\br@step + (2*\br@num + .5) *\br@step * (1 - \br@dir)}
|
|
\edef\br@itstart{1}
|
|
\pgfmathsetmacro{\br@itend}{2*\br@num}
|
|
\edef\br@mcolor{outer}
|
|
\foreach \br@m in {\br@itstart,...,\br@itend} {
|
|
\@ifundefinedcolor{outer\br@m}{%
|
|
}{%
|
|
\global\edef\br@mcolor{outer\br@m}
|
|
}
|
|
\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 4 + 1 - \br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@x}{-8*\br@step}
|
|
\pgfmathsetmacro{\br@y}{-1*\br@inr}
|
|
\pgfmathsetmacro{\br@xx}{-8*\br@step}
|
|
\pgfmathsetmacro{\br@yy}{-1*\br@outr}
|
|
\pgfmathsetmacro{\br@r}{(6*\br@num - 2*\br@m + \br@innersep)*\br@step/2}
|
|
\colorInfo{\br@mcolor}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) -- ++(8*\br@step,0) arc(-90:-90:\br@outr) arc(-\br@dir * 90:\br@dir * 90:\br@r) to[out=180,in=0] (\br@x,\br@y);
|
|
\fi
|
|
}
|
|
\edef\br@itstart{1}
|
|
\pgfmathsetmacro{\br@itend}{2*\br@num}
|
|
\edef\br@mcolor{inner}
|
|
\foreach \br@m in {\br@itstart,...,\br@itend} {
|
|
\@ifundefinedcolor{inner\br@m}{%
|
|
}{%
|
|
\global\edef\br@mcolor{inner\br@m}
|
|
}
|
|
\pgfmathsetmacro{\br@inward}{2 * (-.5 + (\br@m > \br@num))}
|
|
\pgfmathsetmacro{\br@inr}{\br@mr + (\br@num+\br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outr}{\br@mr + (3*\br@num + 1 + \br@inward * 2*\br@num - \br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@inmidr}{\br@inr - \br@dir * \br@innersep * \br@step / 2 - \br@num * \br@dir * \br@step + .5*\br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outmidr}{\br@outr - \br@dir * \br@innersep * \br@step /2 + \br@inward * \br@dir * \br@innersep * \br@step/2 - \br@num * \br@dir * \br@step + .5*\br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@x}{8*\br@step}
|
|
\pgfmathsetmacro{\br@y}{-1*\br@inr}
|
|
\pgfmathsetmacro{\br@xx}{8*\br@step}
|
|
\pgfmathsetmacro{\br@yy}{-1*\br@outr}
|
|
\pgfmathsetmacro{\br@r}{(\br@num * (1 + \br@inward) - \br@inward * (\br@m - .5)) *\br@step + \br@innersep * \br@step/4}
|
|
\colorInfo{\br@mcolor}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) to[out=180,in=0] (0,-\br@outmidr) arc(\br@inward *\br@dir * 270:\br@inward *\br@dir * 90:\br@r);
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) to[out=180,in=0] (0,-\br@inmidr);
|
|
\end{pgfonlayer}
|
|
\fi
|
|
}
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\gethopfangle}
|
|
% This is the Hopfian version of \cmd{\getangle}.
|
|
%
|
|
% \begin{macrocode}
|
|
\newcommand{\gethopfangle}[5]{%
|
|
\pgfmathsetmacro{\br@num}{2 ^ (#1 - 1)}
|
|
\pgfmathsetmacro{\br@dir}{#3}
|
|
\pgfmathsetmacro{\br@innersep}{2}%{#1 == 1 ? 2 : 0}
|
|
\pgfmathsetmacro{\br@mr}{#2 -\br@step + (\br@num + .5) *\br@step * (1 - \br@dir)}
|
|
\pgfmathsetmacro{\br@angle}{atan((3 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
|
|
\ifx\relax#4\relax
|
|
\pgfmathparse{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathparse{int(#4 > \br@angle ? #4 : ceil(\br@angle))}
|
|
\fi
|
|
\xdef\clockangle{\pgfmathresult}
|
|
\ifx\relax#5\relax
|
|
\pgfmathparse{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathparse{int(#5 > \br@angle ? #5 : ceil(\br@angle))}
|
|
\fi
|
|
\xdef\aclockangle{\pgfmathresult}
|
|
\pgfmathparse{int(\clockangle + \aclockangle)}
|
|
\xdef\totalangle{\pgfmathresult}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\hopfjunction}
|
|
% And the Hopfian version of \cmd{\junction}.
|
|
% \begin{macrocode}
|
|
\newcommand{\hopfjunction}[5]{%
|
|
\begin{scope}[xscale=#3]
|
|
\pgfmathsetmacro{\br@num}{2 ^ (#1 - 1)}
|
|
\pgfmathsetmacro{\br@dir}{#3}
|
|
\pgfmathsetmacro{\br@innersep}{2}%{#1 < 3 ? 2 : 0}
|
|
\pgfmathsetmacro{\br@mr}{#2 -\br@step + (\br@num + .5) *\br@step * (1 - \br@dir)}
|
|
\pgfmathsetmacro{\br@angle}{atan((3 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
|
|
\ifx\relax#4\relax
|
|
\pgfmathsetmacro{\br@outerangle}{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathsetmacro{\br@outerangle}{#4 > \br@angle ? #4 : ceil(\br@angle)}
|
|
\fi
|
|
\ifx\relax#5\relax
|
|
\pgfmathsetmacro{\br@innerangle}{ceil(\br@angle)}
|
|
\else
|
|
\pgfmathsetmacro{\br@innerangle}{#5 > \br@angle ? #5 : ceil(\br@angle)}
|
|
\fi
|
|
\pgfmathsetmacro{\br@sin}{sin(\br@angle)}
|
|
\pgfmathsetmacro{\br@cos}{cos(\br@angle)}
|
|
\path (0,0) circle (2pt);
|
|
\edef\br@itstart{1}
|
|
\pgfmathsetmacro{\br@itend}{\br@num}
|
|
\edef\br@mcolor{outer}
|
|
\foreach \br@m in {\br@itstart,...,\br@itend} {
|
|
\@ifundefinedcolor{outer\br@m}{%
|
|
}{%
|
|
\global\edef\br@mcolor{outer\br@m}
|
|
}
|
|
\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 2 + 1 - \br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@x}{-1*\br@inr *\br@sin}
|
|
\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
|
|
\pgfmathsetmacro{\br@xx}{-1*\br@outr *\br@sin}
|
|
\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
|
|
\pgfmathsetmacro{\br@r}{(\br@num - \br@m + \br@innersep + .5)*\br@step}
|
|
\colorInfo{\br@mcolor}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90-\br@angle:-90:\br@outr) arc(-\br@dir * 90:\br@dir * 90:\br@r) to[out=180,in=-\br@angle] (\br@x,\br@y);
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90-\br@angle:-90-\br@outerangle:\br@inr);
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90-\br@angle:-90-\br@outerangle:\br@outr);
|
|
\fi
|
|
}
|
|
\edef\br@itstart{1}
|
|
\pgfmathsetmacro{\br@itend}{\br@num}
|
|
\edef\br@mcolor{inner}
|
|
\foreach \br@m in {\br@itstart,...,\br@itend} {
|
|
\@ifundefinedcolor{inner\br@m}{%
|
|
}{%
|
|
\global\edef\br@mcolor{inner\br@m}
|
|
}
|
|
\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 2 + 1 - \br@m) * \br@dir * \br@step}
|
|
\pgfmathsetmacro{\br@x}{\br@inr *\br@sin}
|
|
\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
|
|
\pgfmathsetmacro{\br@xx}{\br@outr *\br@sin}
|
|
\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
|
|
\pgfmathsetmacro{\br@r}{-(\br@num - \br@m + \br@innersep + .5)*\br@step}
|
|
\colorInfo{\br@mcolor}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90+\br@angle:-90:\br@outr) arc(\br@dir * 90:0:\br@r);
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) to[out=180+\br@angle,in=0] (0,-\br@outr - \br@dir * 2*\br@r) arc(-\br@dir * 90:0:\br@r);
|
|
\end{pgfonlayer}
|
|
\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90+\br@angle:-90+\br@innerangle:\br@inr);
|
|
\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90+\br@angle:-90+\br@innerangle:\br@outr);
|
|
\fi
|
|
}
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
%
|
|
% \begin{macro}{\brunnian}
|
|
% Level One: Brunnian rings of radius \#2 with \#3 components, \#1 is a "doubling" parameter
|
|
% \begin{macrocode}
|
|
\newcommand{\brunnian}[3][1]{%
|
|
\pgfmathsetmacro{\br@n}{#3}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@n}
|
|
\pgfmathsetmacro{\br@psi}{180/\br@n}
|
|
\foreach \br@k in {1,...,\br@n} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@n : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@m}
|
|
\colorlet{inner}{ring\br@k}
|
|
\junction{#1}{#2}{1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\outbrunnian}
|
|
% Level One: Outward Brunnian rings of radius \#2 with \#3 components, \#1 is a "doubling" parameter.
|
|
% This one points outwards
|
|
% \begin{macrocode}
|
|
\newcommand{\outbrunnian}[3][1]{%
|
|
\pgfmathsetmacro{\br@n}{#3}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@n}
|
|
\pgfmathsetmacro{\br@psi}{180/\br@n}
|
|
\foreach \br@k in {1,...,\br@n} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@n : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{inner}{ring\br@m}
|
|
\colorlet{outer}{ring\br@k}
|
|
\junction{#1}{#2}{-1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\midbrunnian}
|
|
% Level One: Midward Brunnian rings of radius \#2 with \#3 components, \#1 is a "doubling" parameter.
|
|
% This one is symmetrical.
|
|
%
|
|
% \begin{macrocode}
|
|
\newcommand{\midbrunnian}[3][1]{%
|
|
\pgfmathsetmacro{\br@n}{#3}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@n}
|
|
\pgfmathsetmacro{\br@psi}{180/\br@n}
|
|
\foreach \br@k in {1,...,\br@n} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@n : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@m}
|
|
\colorlet{inner}{ring\br@k}
|
|
\junction{#1}{#2}{0}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\brunniantwo}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunniantwo}[3]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathparse{int(mod(\br@q,2))}
|
|
\edef\br@qodd{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (ceil(\br@q/2)+1))}
|
|
\foreach \br@k in {1,...,\br@p} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@p : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@k\br@qtwo}
|
|
\colorlet{outer5}{ring\br@k\br@qmo}
|
|
\colorlet{inner}{ring\br@m\br@qmo}
|
|
\junction{2}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{(\br@i - (1 - mod(\br@i,2))*(1 - \br@qodd) - ceil(\br@q/2)) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{ring\br@k\br@i}
|
|
\colorlet{inner}{ring\br@k\br@j}
|
|
\junction{1}{\br@radius+12 * \br@mi * \br@step}{\br@modi}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\ifx\br@qodd\br@one
|
|
\fillin{\br@radius}{1}{4}{\br@psi}{(1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qtwo}
|
|
\fillin{\br@radius}{1}{4}{\br@phi -\br@psi}{\br@phi - (1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qmo}
|
|
\fi
|
|
\fillin{\br@radius}{5}{12}{\br@psi}{\br@phi - \br@psi}{ring\br@k\br@qmo}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\fillin}
|
|
% \begin{macrocode}
|
|
\newcommand{\fillin}[6]{%
|
|
\colorInfo{#6}
|
|
\ifx\colorValue\br@white
|
|
\else
|
|
\pgfmathsetmacro{\br@sin}{sin(#4)};
|
|
\pgfmathsetmacro{\br@cos}{cos(#4)}
|
|
\foreach \br@fk in {#2,...,#3} {
|
|
\pgfmathsetmacro{\br@r}{#1 + (\br@fk - 1) * \br@step}
|
|
\draw[knot,double=#6] (\br@r * \br@sin, -\br@r * \br@cos) arc(-90+#4:-90+#5:\br@r);
|
|
}
|
|
\fi
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\hopfring}
|
|
% \begin{macrocode}
|
|
\newcommand{\hopfring}[2]{%
|
|
\pgfmathsetmacro{\br@n}{#2}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@n}
|
|
\gethopfangle{1}{#1}{1}{}{}
|
|
\pgfmathsetmacro{\br@psi}{360/\br@n - \clockangle}
|
|
\foreach \br@k in {1,...,\br@n} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@n : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@m}
|
|
\colorlet{inner}{ring\br@k}
|
|
\hopfjunction{1}{#1}{1}{}{}
|
|
\pgfmathparse{Mod(\br@k,2) == 0 ? "\noexpand\fillin{#1}{1}{2}{\clockangle}{\br@psi}{inner}" : ""}
|
|
\begin{pgfonlayer}{back}
|
|
\pgfmathresult
|
|
\end{pgfonlayer}
|
|
\pgfmathparse{Mod(\br@k,2) == 0 ? "" : "\noexpand\fillin{#1}{1}{2}{\clockangle}{\br@psi}{inner}"}
|
|
\pgfmathresult
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\hopftwo}
|
|
% \begin{macrocode}
|
|
\newcommand{\hopftwo}[3]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathsetmacro{\br@qodd}{mod(\br@q,2)}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (ceil(\br@q/2)+1))}
|
|
\foreach \br@k in {1,...,\br@p} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@p : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@k\br@qtwo}
|
|
\colorlet{outer5}{ring\br@k\br@qmo}
|
|
\colorlet{inner}{ring\br@m\br@qmo}
|
|
\hopfjunction{2}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{(\br@i - (1 - mod(\br@i,2))*(1 - \br@qodd) - ceil(\br@q/2)) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{ring\br@k\br@i}
|
|
\colorlet{inner}{ring\br@k\br@j}
|
|
\hopfjunction{1}{\br@radius+2 * \br@mi * \br@step}{\br@modi}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\fillin{\br@radius}{1}{2}{\br@psi}{(1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qtwo}
|
|
\fillin{\br@radius}{1}{2}{\br@phi -\br@psi}{\br@phi - (1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qmo}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\chain}
|
|
% \begin{macrocode}
|
|
\newcommand{\chain}{%
|
|
\begin{scope}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=chain] (-1.1,0.7) -- ++(0,-1.8) -- ++(.3,0);
|
|
\draw[knot,double=chain] (1.1,0.7) -- ++(0,-1.8) -- ++(-.3,0);
|
|
\draw[knot,double=chain] (-.9,0.7) -- ++(0,-1.6) -- ++(.1,0);
|
|
\draw[knot,double=chain] (.9,0.7) -- ++(0,-1.6) -- ++(-.1,0);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (-.8,-.9) -- ++(1.6,0);
|
|
\draw[knot,double=chain] (-.8,-1.1) -- ++(1.6,0);
|
|
\end{pgfonlayer}
|
|
\draw[knot,double=chain] (-1,1) circle (.4);
|
|
\draw[background,line width=1.8mm] (-1,0.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (-1.1,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (-.9,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (1,1) circle (.4);
|
|
\draw[background,line width=1.8mm] (1,0.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (1.1,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (.9,0.5) -- ++(0,.1);
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\leftchain}
|
|
% \begin{macrocode}
|
|
\newcommand{\leftchain}{%
|
|
\begin{scope}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=chain] (-1.1,2.7) -- ++(0,-3.8) -- ++(.3,0);
|
|
\draw[knot,double=chain] (1.1,0.7) -- ++(0,-1.8) -- ++(-.3,0);
|
|
\draw[knot,double=chain] (-.9,2.7) -- ++(0,-3.6) -- ++(.1,0);
|
|
\draw[knot,double=chain] (.9,0.7) -- ++(0,-1.6) -- ++(-.1,0);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (-.8,-.9) -- ++(1.6,0);
|
|
\draw[knot,double=chain] (-.8,-1.1) -- ++(1.6,0);
|
|
\end{pgfonlayer}
|
|
\draw[knot,double=chain] (-1,3) circle (.4);
|
|
\draw[background,line width=1.8mm] (-1,2.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (-1.1,2.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (-.9,2.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (1,1) circle (.4);
|
|
\draw[background,line width=1.8mm] (1,0.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (1.1,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (.9,0.5) -- ++(0,.1);
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\rightchain}
|
|
% \begin{macrocode}
|
|
\newcommand{\rightchain}{%
|
|
\begin{scope}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=chain] (1.1,2.7) -- ++(0,-3.8) -- ++(-.3,0);
|
|
\draw[knot,double=chain] (-1.1,0.7) -- ++(0,-1.8) -- ++(.3,0);
|
|
\draw[knot,double=chain] (.9,2.7) -- ++(0,-3.6) -- ++(-.1,0);
|
|
\draw[knot,double=chain] (-.9,0.7) -- ++(0,-1.6) -- ++(.1,0);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (-.8,-.9) -- ++(1.6,0);
|
|
\draw[knot,double=chain] (-.8,-1.1) -- ++(1.6,0);
|
|
\end{pgfonlayer}
|
|
\draw[knot,double=chain] (1,3) circle (.4);
|
|
\draw[background,line width=1.8mm] (1,2.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (1.1,2.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (.9,2.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (-1,1) circle (.4);
|
|
\draw[background,line width=1.8mm] (-1,0.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (-1.1,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (-.9,0.5) -- ++(0,.1);
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\leftcornerchain}
|
|
% \begin{macrocode}
|
|
\newcommand{\leftcornerchain}{%
|
|
\begin{scope}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=chain] (.5,3.1) -- ++(-1.6,0) -- ++(0,-4.2) -- ++(.3,0);
|
|
\draw[knot,double=chain] (1.1,0.7) -- ++(0,-1.8) -- ++(-.3,0);
|
|
\draw[knot,double=chain] (.5,2.9) -- ++(-1.4,0) -- ++(0,-3.8) -- ++(.1,0);
|
|
\draw[knot,double=chain] (.9,0.7) -- ++(0,-1.6) -- ++(-.1,0);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (-.8,-.9) -- ++(1.6,0);
|
|
\draw[knot,double=chain] (-.8,-1.1) -- ++(1.6,0);
|
|
\end{pgfonlayer}
|
|
\draw[knot,double=chain] (1,3) circle (.4);
|
|
\draw[background,line width=1.8mm] (.5,3) -- ++(.2,0);
|
|
\draw[knot,double=chain] (.5,3.1) -- ++(.1,0);
|
|
\draw[knot,double=chain] (.5,2.9) -- ++(.1,0);
|
|
\draw[knot,double=chain] (1,1) circle (.4);
|
|
\draw[background,line width=1.8mm] (1,0.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (1.1,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (.9,0.5) -- ++(0,.1);
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\rightcornerchain}
|
|
% \begin{macrocode}
|
|
\newcommand{\rightcornerchain}{%
|
|
\begin{scope}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=chain] (-.5,3.1) -- ++(1.6,0) -- ++(0,-4.2) -- ++(-.3,0);
|
|
\draw[knot,double=chain] (-1.1,0.7) -- ++(0,-1.8) -- ++(.3,0);
|
|
\draw[knot,double=chain] (-.5,2.9) -- ++(1.4,0) -- ++(0,-3.8) -- ++(-.1,0);
|
|
\draw[knot,double=chain] (-.9,0.7) -- ++(0,-1.6) -- ++(.1,0);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (-.8,-.9) -- ++(1.6,0);
|
|
\draw[knot,double=chain] (-.8,-1.1) -- ++(1.6,0);
|
|
\end{pgfonlayer}
|
|
\draw[knot,double=chain] (-1,3) circle (.4);
|
|
\draw[background,line width=1.8mm] (-.5,3) -- ++(-.2,0);
|
|
\draw[knot,double=chain] (-.5,3.1) -- ++(-.1,0);
|
|
\draw[knot,double=chain] (-.5,2.9) -- ++(-.1,0);
|
|
\draw[knot,double=chain] (-1,1) circle (.4);
|
|
\draw[background,line width=1.8mm] (-1,0.5) -- ++(0,.2);
|
|
\draw[knot,double=chain] (-1.1,0.5) -- ++(0,.1);
|
|
\draw[knot,double=chain] (-.9,0.5) -- ++(0,.1);
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\brunnianhopf}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunnianhopf}[3]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathparse{int(mod(\br@q,2))}
|
|
\edef\br@qodd{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (ceil(\br@q/2)+1))}
|
|
\foreach \br@k in {1,...,\br@p} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@p : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@k\br@qtwo}
|
|
\colorlet{outer3}{ring\br@k\br@qmo}
|
|
\colorlet{inner}{ring\br@m\br@qmo}
|
|
\junction{1.5}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{(\br@i - (1 - mod(\br@i,2))*(1 - \br@qodd) - ceil(\br@q/2)) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{ring\br@k\br@i}
|
|
\colorlet{inner}{ring\br@k\br@j}
|
|
\hopfjunction{1}{\br@radius+6 * \br@mi * \br@step}{\br@modi}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\ifx\br@qodd\br@one
|
|
\fillin{\br@radius}{1}{2}{\br@psi}{(1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qtwo}
|
|
\fillin{\br@radius}{1}{2}{\br@phi -\br@psi}{\br@phi - (1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qmo}
|
|
\fi
|
|
\fillin{\br@radius}{3}{6}{\br@psi}{\br@phi - \br@psi}{ring\br@k\br@qmo}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\hopfbrunnian}
|
|
% \begin{macrocode}
|
|
\newcommand{\hopfbrunnian}[3]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathparse{int(mod(\br@q,2))}
|
|
\edef\br@qodd{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (ceil(\br@q/2)+1))}
|
|
\foreach \br@k in {1,...,\br@p} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@p : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@k\br@qtwo}
|
|
\colorlet{inner}{ring\br@m\br@qmo}
|
|
\hopfjunction{3}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{(\br@i - (1 - mod(\br@i,2))*(1 - \br@qodd) - ceil(\br@q/2)) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{ring\br@k\br@i}
|
|
\colorlet{inner}{ring\br@k\br@j}
|
|
\junction{1}{\br@radius+4 * \br@mi * \br@step}{\br@modi}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\ifx\br@qodd\br@one
|
|
\fillin{\br@radius}{1}{4}{\br@psi}{(1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qtwo}
|
|
\fillin{\br@radius}{1}{4}{\br@phi -\br@psi}{\br@phi - (1.5 + \br@qodd/2)*\br@psi}{ring\br@k\br@qmo}
|
|
\fi
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\outerhopftwo}
|
|
% \begin{macrocode}
|
|
\newcommand{\outerhopftwo}[3]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathsetmacro{\br@qodd}{mod(\br@q,2)}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (\br@q+1))}
|
|
\foreach \br@k in {1,...,\br@p} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@p : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@k\br@qtwo}
|
|
\colorlet{outer5}{ring\br@k\br@qmo}
|
|
\colorlet{inner}{ring\br@m\br@qtwo}
|
|
\hopfjunction{2}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{2*(\br@i - (\br@q+1)/2 ) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{ring\br@k\br@i}
|
|
\colorlet{inner}{ring\br@k\br@j}
|
|
\hopfjunction{1}{\br@radius+2 * \br@step}{-1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\fillin{\br@radius}{1}{2}{\br@psi}{180 - \br@psi}{ring\br@k\br@qtwo}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\outerbrunniantwo}
|
|
% \begin{macrocode}
|
|
\newcommand{\outerbrunniantwo}[3]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathsetmacro{\br@qodd}{mod(\br@q,2)}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (\br@q+1))}
|
|
\foreach \br@k in {1,...,\br@p} {
|
|
\pgfmathparse{int(\br@k == 1 ? \br@p : \br@k - 1)}
|
|
\edef\br@m{\pgfmathresult}
|
|
\begin{scope}[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{ring\br@k\br@qtwo}
|
|
\colorlet{inner}{ring\br@m\br@qtwo}
|
|
\junction{2}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{2*(\br@i - (\br@q+1)/2 ) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{ring\br@k\br@i}
|
|
\colorlet{inner}{ring\br@k\br@j}
|
|
\junction{1}{\br@radius+12 * \br@step}{-1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\fillin{\br@radius}{1}{12}{\br@psi}{180 - \br@psi}{ring\br@k\br@qtwo}
|
|
\end{scope}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\pgf@sh@@knotanchor}
|
|
% \begin{macrocode}
|
|
\def\pgf@sh@@knotanchor#1#2{%
|
|
\anchor{#2 north west}{%
|
|
\csname pgf@anchor@knot #1@north west\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 north east}{%
|
|
\csname pgf@anchor@knot #1@north east\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 south west}{%
|
|
\csname pgf@anchor@knot #1@south west\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 south east}{%
|
|
\csname pgf@anchor@knot #1@south east\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 north}{%
|
|
\csname pgf@anchor@knot #1@north\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 east}{%
|
|
\csname pgf@anchor@knot #1@east\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 west}{%
|
|
\csname pgf@anchor@knot #1@west\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
\anchor{#2 south}{%
|
|
\csname pgf@anchor@knot #1@south\endcsname%
|
|
\pgf@x=#2\pgf@x%
|
|
\pgf@y=#2\pgf@y%
|
|
}%
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macrocode}
|
|
\pgfdeclareshape{knot crossing}
|
|
{
|
|
\inheritsavedanchors[from=circle] % this is nearly a circle
|
|
\inheritanchorborder[from=circle]
|
|
\inheritanchor[from=circle]{north}
|
|
\inheritanchor[from=circle]{north west}
|
|
\inheritanchor[from=circle]{north east}
|
|
\inheritanchor[from=circle]{center}
|
|
\inheritanchor[from=circle]{west}
|
|
\inheritanchor[from=circle]{east}
|
|
\inheritanchor[from=circle]{mid}
|
|
\inheritanchor[from=circle]{mid west}
|
|
\inheritanchor[from=circle]{mid east}
|
|
\inheritanchor[from=circle]{base}
|
|
\inheritanchor[from=circle]{base west}
|
|
\inheritanchor[from=circle]{base east}
|
|
\inheritanchor[from=circle]{south}
|
|
\inheritanchor[from=circle]{south west}
|
|
\inheritanchor[from=circle]{south east}
|
|
\inheritanchorborder[from=circle]
|
|
\pgf@sh@@knotanchor{crossing}{2}
|
|
\pgf@sh@@knotanchor{crossing}{3}
|
|
\pgf@sh@@knotanchor{crossing}{4}
|
|
\pgf@sh@@knotanchor{crossing}{8}
|
|
\pgf@sh@@knotanchor{crossing}{16}
|
|
\pgf@sh@@knotanchor{crossing}{32}
|
|
\backgroundpath{
|
|
\pgfutil@tempdima=\radius%
|
|
\pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}%
|
|
\pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}%
|
|
\ifdim\pgf@xb<\pgf@yb%
|
|
\advance\pgfutil@tempdima by-\pgf@yb%
|
|
\else%
|
|
\advance\pgfutil@tempdima by-\pgf@xb%
|
|
\fi%
|
|
% \pgfpathcircle{\centerpoint}{\pgfutil@tempdima}%
|
|
}
|
|
}
|
|
\pgfdeclareshape{knot over cross}
|
|
{
|
|
\inheritsavedanchors[from=rectangle] % this is nearly a circle
|
|
\inheritanchorborder[from=rectangle]
|
|
\inheritanchor[from=rectangle]{north}
|
|
\inheritanchor[from=rectangle]{north west}
|
|
\inheritanchor[from=rectangle]{north east}
|
|
\inheritanchor[from=rectangle]{center}
|
|
\inheritanchor[from=rectangle]{west}
|
|
\inheritanchor[from=rectangle]{east}
|
|
\inheritanchor[from=rectangle]{mid}
|
|
\inheritanchor[from=rectangle]{mid west}
|
|
\inheritanchor[from=rectangle]{mid east}
|
|
\inheritanchor[from=rectangle]{base}
|
|
\inheritanchor[from=rectangle]{base west}
|
|
\inheritanchor[from=rectangle]{base east}
|
|
\inheritanchor[from=rectangle]{south}
|
|
\inheritanchor[from=rectangle]{south west}
|
|
\inheritanchor[from=rectangle]{south east}
|
|
\inheritanchorborder[from=rectangle]
|
|
\backgroundpath{
|
|
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
|
|
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
|
|
}
|
|
\foregroundpath{
|
|
% store lower right in xa/ya and upper right in xb/yb
|
|
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
|
|
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
|
|
}
|
|
}
|
|
\pgfdeclareshape{knot under cross}
|
|
{
|
|
\inheritsavedanchors[from=rectangle] % this is nearly a circle
|
|
\inheritanchorborder[from=rectangle]
|
|
\inheritanchor[from=rectangle]{north}
|
|
\inheritanchor[from=rectangle]{north west}
|
|
\inheritanchor[from=rectangle]{north east}
|
|
\inheritanchor[from=rectangle]{center}
|
|
\inheritanchor[from=rectangle]{west}
|
|
\inheritanchor[from=rectangle]{east}
|
|
\inheritanchor[from=rectangle]{mid}
|
|
\inheritanchor[from=rectangle]{mid west}
|
|
\inheritanchor[from=rectangle]{mid east}
|
|
\inheritanchor[from=rectangle]{base}
|
|
\inheritanchor[from=rectangle]{base west}
|
|
\inheritanchor[from=rectangle]{base east}
|
|
\inheritanchor[from=rectangle]{south}
|
|
\inheritanchor[from=rectangle]{south west}
|
|
\inheritanchor[from=rectangle]{south east}
|
|
\inheritanchorborder[from=rectangle]
|
|
\backgroundpath{
|
|
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
|
|
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
|
|
}
|
|
\foregroundpath{
|
|
% store lower right in xa/ya and upper right in xb/yb
|
|
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
|
|
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
|
|
}
|
|
}
|
|
\pgfdeclareshape{knot vert}
|
|
{
|
|
\inheritsavedanchors[from=rectangle] % this is nearly a circle
|
|
\inheritanchorborder[from=rectangle]
|
|
\inheritanchor[from=rectangle]{north}
|
|
\inheritanchor[from=rectangle]{north west}
|
|
\inheritanchor[from=rectangle]{north east}
|
|
\inheritanchor[from=rectangle]{center}
|
|
\inheritanchor[from=rectangle]{west}
|
|
\inheritanchor[from=rectangle]{east}
|
|
\inheritanchor[from=rectangle]{mid}
|
|
\inheritanchor[from=rectangle]{mid west}
|
|
\inheritanchor[from=rectangle]{mid east}
|
|
\inheritanchor[from=rectangle]{base}
|
|
\inheritanchor[from=rectangle]{base west}
|
|
\inheritanchor[from=rectangle]{base east}
|
|
\inheritanchor[from=rectangle]{south}
|
|
\inheritanchor[from=rectangle]{south west}
|
|
\inheritanchor[from=rectangle]{south east}
|
|
\inheritanchorborder[from=rectangle]
|
|
\backgroundpath{
|
|
% store lower right in xa/ya and upper right in xb/yb
|
|
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
|
|
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
|
|
}
|
|
}
|
|
\pgfdeclareshape{knot horiz}
|
|
{
|
|
\inheritsavedanchors[from=rectangle] % this is nearly a circle
|
|
\inheritanchorborder[from=rectangle]
|
|
\inheritanchor[from=rectangle]{north}
|
|
\inheritanchor[from=rectangle]{north west}
|
|
\inheritanchor[from=rectangle]{north east}
|
|
\inheritanchor[from=rectangle]{center}
|
|
\inheritanchor[from=rectangle]{west}
|
|
\inheritanchor[from=rectangle]{east}
|
|
\inheritanchor[from=rectangle]{mid}
|
|
\inheritanchor[from=rectangle]{mid west}
|
|
\inheritanchor[from=rectangle]{mid east}
|
|
\inheritanchor[from=rectangle]{base}
|
|
\inheritanchor[from=rectangle]{base west}
|
|
\inheritanchor[from=rectangle]{base east}
|
|
\inheritanchor[from=rectangle]{south}
|
|
\inheritanchor[from=rectangle]{south west}
|
|
\inheritanchor[from=rectangle]{south east}
|
|
\inheritanchorborder[from=rectangle]
|
|
\foregroundpath{
|
|
% store lower right in xa/ya and upper right in xb/yb
|
|
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
|
|
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
|
|
\pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
|
|
\pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
|
|
}
|
|
}
|
|
% \end{macrocode}
|
|
%
|
|
% \begin{macro}{\flatbrunnianlink}
|
|
% \begin{macrocode}
|
|
\newcommand{\flatbrunnianlink}[1]{%
|
|
\pgfmathsetmacro{\br@scale}{#1}%
|
|
\pgfmathsetmacro{\br@ctwenty}{cos(20)}
|
|
\pgfmathsetmacro{\br@stwenty}{sin(20)}
|
|
\draw[knot,double=chain] (-.5*\br@scale,0) arc(180:270:.5*\br@scale) node[coordinate] (a) {};
|
|
\draw[knot,double=chain] (-.6*\br@scale,0) arc(180:270:.6*\br@scale) node[coordinate] (c) {};
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (1.6*\br@scale,0) ++(-.9*\br@scale *\br@ctwenty,-.9*\br@scale *\br@stwenty) arc(0:-90:.2*\br@scale) to[out=180,in=0] (c);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{back}
|
|
\draw[knot,double=chain] (-.5*\br@scale,0) arc(180:90:.5*\br@scale) node[coordinate] (b) {};
|
|
\draw[knot,double=chain] (-.6*\br@scale,0) arc(180:90:.6*\br@scale) node[coordinate] (d) {};
|
|
\draw[knot,double=chain] (1.6*\br@scale,0) ++(-.9*\br@scale *\br@ctwenty,-.9*\br@scale *\br@stwenty) arc(0:135:.2*\br@scale) to[out=-135,in=0] (a);
|
|
\draw[knot,double=chain] (1.6*\br@scale,0) ++(-.9*\br@scale *\br@ctwenty,.9*\br@scale *\br@stwenty) arc(0:-135:.2*\br@scale) to[out=135,in=0] (b);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw[knot,double=chain] (1.6*\br@scale,0) ++(-.9*\br@scale *\br@ctwenty,.9*\br@scale *\br@stwenty) arc(0:90:.2*\br@scale) to[out=180,in=0] (d);
|
|
\end{pgfonlayer}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\brunnianlink}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunnianlink}[2]{%
|
|
\pgfmathsetmacro{\br@scale}{#1}
|
|
\pgfmathsetmacro{\br@angle}{#2}
|
|
\begin{scope}[every path/.style={knot,double=chain}]
|
|
\begin{scope}[rotate=-\br@angle + 5]
|
|
\draw (0,-\br@scale) arc (90:270:2.5*\br@step);
|
|
\draw (0,-\br@scale-\br@step) arc (90:270:1.5*\br@step);
|
|
\draw (0,-\br@scale) arc (-90:-85:\br@scale) coordinate (a);
|
|
\draw (0,-\br@scale-\br@step) arc (-90:-85:\br@scale+\br@step) coordinate (b);
|
|
\draw (0,-\br@scale-4*\br@step) arc (-90:-85:\br@scale+3*\br@step) coordinate (c);
|
|
\draw (0,-\br@scale-5*\br@step) arc (-90:-85:\br@scale+4*\br@step) coordinate (d);
|
|
\end{scope}
|
|
\begin{pgfonlayer}{back}
|
|
\draw (0,-\br@scale-2*\br@step) arc(-90:-100:\br@scale+2*\br@step) coordinate (B);
|
|
\draw (0,-\br@scale-3*\br@step) arc(-90:-100:\br@scale+3*\br@step) coordinate (C);
|
|
\end{pgfonlayer}
|
|
\begin{pgfonlayer}{front}
|
|
\draw (0,-\br@scale) arc (90:-90:\br@step);
|
|
\draw (0,-\br@scale) arc (-90:-100:\br@scale) coordinate (A);
|
|
\draw (0,-\br@scale-3*\br@step) arc (90:-90:\br@step);
|
|
\draw (0,-\br@scale-5*\br@step) arc (-90:-100:\br@scale+5*\br@step)coordinate (D);
|
|
\end{pgfonlayer}
|
|
\pgfmathsetmacro{\br@loose}{\br@angle == 180 ? 1.5 : 1}
|
|
\draw (a) to[out=-\br@angle+10,in=170,looseness=\br@loose] (A);
|
|
\draw (b) to[out=-\br@angle+10,in=170,looseness=\br@loose] (B);
|
|
\draw (c) to[out=-\br@angle+10,in=170,looseness=\br@loose] (C);
|
|
\draw (d) to[out=-\br@angle+10,in=170,looseness=\br@loose] (D);
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\brunniantwocpt}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunniantwocpt}[4]{%
|
|
\edef\br@p{#3}
|
|
\edef\br@q{#2}
|
|
\edef\br@colour{#4}
|
|
\pgfmathsetmacro{\br@radius}{#1}
|
|
\pgfmathparse{int(mod(\br@q,2))}
|
|
\edef\br@qodd{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q - 1 + \br@qodd)}
|
|
\edef\br@qmo{\pgfmathresult}
|
|
\pgfmathparse{int(\br@q == 1 ? 1 : 2)}
|
|
\edef\br@qtwo{\pgfmathresult}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@p}
|
|
\pgfmathsetmacro{\br@psi}{180/(\br@p * (ceil(\br@q/2)+1))}
|
|
\begin{scope}%[rotate=\br@m * \br@phi]
|
|
\colorlet{outer}{\br@colour\br@qtwo}
|
|
\colorlet{outer5}{\br@colour\br@qmo}
|
|
\colorlet{inner}{background}
|
|
\junction{2}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi]
|
|
\colorlet{outer}{background}
|
|
\colorlet{outer5}{background}
|
|
\colorlet{inner}{\br@colour\br@qmo}
|
|
\junction{2}{\br@radius}{-1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
\begin{scope}[rotate=\br@phi/2]
|
|
\foreach \br@i in {1,...,\br@q} {
|
|
\pgfmathsetmacro{\br@rho}{(\br@i - (1 - mod(\br@i,2))*(1 - \br@qodd) - ceil(\br@q/2)) * \br@psi}
|
|
\begin{scope}[rotate=\br@rho]
|
|
\pgfmathsetmacro{\br@mi}{mod(\br@i,2)}
|
|
\pgfmathsetmacro{\br@modi}{(-1)^\br@mi}
|
|
\pgfmathparse{int(\br@i == 1 || \br@i == \br@q - \br@qodd ? \br@i + \br@qtwo - 1 - 2*(1 - \br@qodd)*(1 - \br@mi) : \br@i + \br@modi * 2)}
|
|
\edef\br@j{\pgfmathresult}
|
|
\colorlet{outer}{\br@colour\br@i}
|
|
\colorlet{inner}{\br@colour\br@j}
|
|
\junction{1}{\br@radius+12 * \br@mi * \br@step}{\br@modi}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
\end{scope}
|
|
\ifx\br@qodd\br@one
|
|
\fillin{\br@radius}{1}{4}{\br@psi}{(1.5 + \br@qodd/2)*\br@psi}{\br@colour\br@qtwo}
|
|
\fillin{\br@radius}{1}{4}{\br@phi -\br@psi}{\br@phi - (1.5 + \br@qodd/2)*\br@psi}{\br@colour\br@qmo}
|
|
\fi
|
|
\fillin{\br@radius}{5}{12}{\br@psi}{\br@phi - \br@psi}{\br@colour\br@qmo}
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\brunniancpt}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunniancpt}[3][1]{%
|
|
\pgfmathsetmacro{\br@n}{#3}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@n}
|
|
\pgfmathsetmacro{\br@psi}{180/\br@n}
|
|
\colorlet{outer}{brunnian}
|
|
\colorlet{inner}{background}
|
|
\junction{#1}{#2}{1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=-\br@phi]
|
|
\colorlet{inner}{brunnian}
|
|
\colorlet{outer}{background}
|
|
\junction{#1}{#2}{1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\brunniancptouter}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunniancptouter}[3][1]{%
|
|
\pgfmathsetmacro{\br@n}{#3}
|
|
\pgfmathsetmacro{\br@phi}{360/\br@n}
|
|
\pgfmathsetmacro{\br@psi}{180/\br@n}
|
|
\colorlet{outer}{brunnian}
|
|
\colorlet{inner}{background}
|
|
\junction{#1}{#2}{-1}{\br@psi}{\br@psi}
|
|
\begin{scope}[rotate=\br@phi]
|
|
\colorlet{inner}{brunnian}
|
|
\colorlet{outer}{background}
|
|
\junction{#1}{#2}{-1}{\br@psi}{\br@psi}
|
|
\end{scope}
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \begin{macro}{\brunnianlinkage}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunnianlinkage}{%
|
|
\node (0) at (0,-\brlen) {};
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/1/1/-1,
|
|
2/-1/2/-1,
|
|
3/-1/1/-1,
|
|
4/1/1/1,
|
|
5/1/1/-1,
|
|
6/-1/1/1,
|
|
7/-1/2/1,
|
|
8/1/1/1
|
|
} {
|
|
\coordinate (\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0);
|
|
}
|
|
\draw (1) -- (4);
|
|
\draw (2) -- (7);
|
|
\draw (3) -- (6);
|
|
\draw (5) -- (8);
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\brunniantwoside}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunniantwoside}{%
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/1/1/-1,
|
|
2/-1/2/-1,
|
|
3/-1/1/-1,
|
|
4/1/1/1,
|
|
5/1/1/-1,
|
|
6/-1/1/1,
|
|
7/-1/2/1,
|
|
8/1/1/1
|
|
} {
|
|
\coordinate (l\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (l\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (le\bri);
|
|
}
|
|
\draw (l1) -- (l4);
|
|
\draw (l2) -- (l7);
|
|
\draw (l3) -- (l6);
|
|
\draw (l5) -- (l8);
|
|
\begin{scope}[xshift=4cm]
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/1/1/-1,
|
|
2/-1/2/-1,
|
|
3/-1/1/-1,
|
|
4/1/1/1,
|
|
5/1/1/-1,
|
|
6/-1/1/1,
|
|
7/-1/2/1,
|
|
8/1/1/1
|
|
} {
|
|
\coordinate (r\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (r\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (re\bri);
|
|
}
|
|
\draw (r1) -- (r4);
|
|
\draw (r2) -- (r7);
|
|
\draw (r3) -- (r6);
|
|
\draw (r5) -- (r8);
|
|
\end{scope}
|
|
\draw
|
|
(le2) -- ++(\brsep,0) coordinate (1)
|
|
(le7) -- ++(\brsep,0) coordinate (4)
|
|
(re1) -- ++(-\brsep,0) coordinate (5)
|
|
(re8) -- ++(-\brsep,0) coordinate (8)
|
|
;
|
|
\path
|
|
coordinate (2) at (le3)
|
|
coordinate (3) at (le6)
|
|
coordinate (6) at (re4)
|
|
coordinate (7) at (re5)
|
|
coordinate (lb) at ($(4)!.5!(8)+(0,-1)$)
|
|
;
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\dblhopftwoside}
|
|
% \begin{macrocode}
|
|
\newcommand{\dblhopftwoside}{%
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/-1/2/-1,
|
|
2/-1/1/-1,
|
|
3/1/2/-1,
|
|
4/1/1/-1,
|
|
5/-1/1/1,
|
|
6/-1/2/1,
|
|
7/1/1/1,
|
|
8/1/2/1
|
|
} {
|
|
\coordinate (l\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (l\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (le\bri);
|
|
}
|
|
\draw (l1) -- (l6);
|
|
\draw (l2) -- (l5);
|
|
\draw (l3) -- (l8);
|
|
\draw (l4) -- (l7);
|
|
\begin{scope}[xshift=4cm]
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/-1/2/-1,
|
|
2/-1/1/-1,
|
|
3/1/2/-1,
|
|
4/1/1/-1,
|
|
5/-1/1/1,
|
|
6/-1/2/1,
|
|
7/1/1/1,
|
|
8/1/2/1
|
|
} {
|
|
\coordinate (r\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (r\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (re\bri);
|
|
}
|
|
\draw (r1) -- (r6);
|
|
\draw (r2) -- (r5);
|
|
\draw (r3) -- (r8);
|
|
\draw (r4) -- (r7);
|
|
\end{scope}
|
|
\draw
|
|
(le1) -- ++(\brsep,0) coordinate (1)
|
|
(le6) -- ++(\brsep,0) coordinate (4)
|
|
(re3) -- ++(-\brsep,0) coordinate (5)
|
|
(re8) -- ++(-\brsep,0) coordinate (8)
|
|
;
|
|
\path
|
|
coordinate (2) at (le2)
|
|
coordinate (3) at (le5)
|
|
coordinate (6) at (re4)
|
|
coordinate (7) at (re7)
|
|
coordinate (lb) at ($(4)!.5!(8)+(0,-1)$)
|
|
;
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\dblhopfrctwoside}
|
|
% \begin{macrocode}
|
|
\newcommand{\dblhopfrctwoside}{%
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/-1/2/-1,
|
|
2/-1/1/-1,
|
|
3/1/2/-1,
|
|
4/1/1/-1,
|
|
5/-1/1/1,
|
|
6/-1/2/1,
|
|
7/1/1/1,
|
|
8/1/2/1
|
|
} {
|
|
\coordinate (l\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (l\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (le\bri);
|
|
}
|
|
\draw (l1) -- (l6);
|
|
\draw (l2) -- (l5);
|
|
\draw (l3) -- (l8);
|
|
\draw (l4) -- (l7);
|
|
\begin{scope}[xshift=4cm]
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/-1/2/-1,
|
|
2/-1/1/-1,
|
|
3/1/2/-1,
|
|
4/1/1/-1,
|
|
5/-1/1/1,
|
|
6/-1/2/1,
|
|
7/1/1/1,
|
|
8/1/2/1
|
|
} {
|
|
\coordinate (r\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (r\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (re\bri);
|
|
}
|
|
\draw (r1) -- (r6);
|
|
\draw (r2) -- (r5);
|
|
\draw (r3) -- (r8);
|
|
\draw (r4) -- (r7);
|
|
\end{scope}
|
|
\draw
|
|
(le1) -- ++(\brsep,0) coordinate (1)
|
|
(le6) -- ++(\brsep,0) coordinate (4)
|
|
(re3) -- ++(-\brsep,0) coordinate (5)
|
|
(re8) -- ++(-\brsep,0) coordinate (8)
|
|
;
|
|
\path
|
|
coordinate (2) at (le2)
|
|
coordinate (3) at (le5)
|
|
coordinate (6) at (re4)
|
|
coordinate (7) at (re7)
|
|
coordinate (lb) at ($(4)!.5!(8)+(0,-1)$)
|
|
;
|
|
\draw[double=none,Red,line width=2pt] (2) -- (3);
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\brunnianhalftwoside}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunnianhalftwoside}{%
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/1/1/-1,
|
|
2/-1/2/-1,
|
|
3/-1/1/-1,
|
|
4/1/1/1,
|
|
5/1/1/-1,
|
|
6/-1/1/1,
|
|
7/-1/2/1,
|
|
8/1/1/1
|
|
} {
|
|
\coordinate (l\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (l\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (le\bri);
|
|
}
|
|
\draw (l1) -- (l4);
|
|
\draw (l2) -- (l7);
|
|
\draw (l3) -- (l6);
|
|
\draw (l5) -- (l8);
|
|
\begin{scope}[xshift=4cm]
|
|
\foreach \bri/\brdir/\brnud/\brv in {
|
|
1/1/1/-1,
|
|
2/-1/2/-1,
|
|
3/-1/1/-1,
|
|
4/1/1/1,
|
|
5/1/1/-1,
|
|
6/-1/1/1,
|
|
7/-1/2/1,
|
|
8/1/1/1
|
|
} {
|
|
\coordinate (r\bri) at (\brover * \brdir * \brnud,-\bri * \brsep + \brv * \bradj);
|
|
\draw (r\bri) -- ++(0,-\brv * \bradj) -- +(-\brdir * \brlen - \brover * \brdir * \brnud,0) coordinate (re\bri);
|
|
}
|
|
\draw (r1) -- (r4);
|
|
\draw (r2) -- (r7);
|
|
\draw (r3) -- (r6);
|
|
\draw (r5) -- (r8);
|
|
\end{scope}
|
|
\draw
|
|
(le2) -- ++(\brsep,0) coordinate (1)
|
|
(le7) -- ++(\brsep,0) coordinate (4)
|
|
(re1) -- ++(-\brsep,0) coordinate (5)
|
|
(re8) coordinate (6)
|
|
;
|
|
\path
|
|
coordinate (2) at (le3)
|
|
coordinate (3) at (le6)
|
|
coordinate (8) at (re4)
|
|
coordinate (7) at (re5)
|
|
coordinate (lb) at ($(4)!.5!(8)+(0,-1)$)
|
|
;
|
|
\draw[double=none,Red,line width=2pt] (6) -- (7);
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
% \begin{macro}{\brunnianringonetwoside}
|
|
% \begin{macrocode}
|
|
\newcommand{\brunnianringonetwoside}{
|
|
\fill[gray] (-\brlen,-.5*\brsep) rectangle (\brlen, .5*\brsep);
|
|
\draw[double=none,Red,line width=2pt]
|
|
(-\brlen,-.5*\brsep)
|
|
++(-\brsep,-\brsep) coordinate (1)
|
|
++(-\brsep,-\brsep) coordinate (2)
|
|
++(-\brsep,-\brsep) coordinate (c3) -- +(\brsep,0) coordinate (3)
|
|
++(-\brsep,-\brsep) coordinate (c4) -- +(4*\brsep,0) coordinate (4)
|
|
(\brlen,-.5*\brsep)
|
|
++(\brsep,-\brsep) coordinate (5)
|
|
++(\brsep,-\brsep) coordinate (6)
|
|
++(\brsep,-\brsep) coordinate (c7) -- +(-\brsep,0) coordinate (7)
|
|
++(\brsep,-\brsep) coordinate (c8) -- +(-4*\brsep,0) coordinate (8)
|
|
;
|
|
\draw[double=none,Red,line width=2pt]
|
|
(1) -- ++(0,3*\brsep) -| (5)
|
|
(2) -- ++(0,5*\brsep) -| (6)
|
|
(c3) -- ++(0,7*\brsep) -| (c7)
|
|
(c4) -- ++(0,9*\brsep) -| (c8)
|
|
;
|
|
}
|
|
% \end{macrocode}
|
|
% \end{macro}
|
|
%
|
|
%
|
|
% \iffalse
|
|
%</package>
|
|
% \fi
|
|
%
|
|
% \Finale
|
|
\endinput
|