mirror of
https://github.com/MartinThoma/LaTeX-examples.git
synced 2025-04-19 11:38:05 +02:00
1331 lines
47 KiB
TeX
1331 lines
47 KiB
TeX
%%
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%% This is file `brunnian.sty',
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%% generated with the docstrip utility.
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%%
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%% The original source files were:
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%%
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%% brunnian.dtx (with options: `package')
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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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%%
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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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\ProvidesPackage{brunnian}
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\newif\ifsvg
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\@ifpackageloaded{tex4ht}{
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\svgtrue
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}{}
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\ifsvg
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\def\pgfsysdriver{pgfsys-tex4ht.def}
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\fi
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\RequirePackage[svgnames]{xcolor}
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\RequirePackage{tikz}
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\RequirePackage{colorinfo}
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\usetikzlibrary{calc}
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\xglobal\colorlet{background}{white}
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\newcommand{\resetbgcolour}[1]{%
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\xglobal\colorlet{background}{#1}
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\colorInfo{background}
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\edef\br@white{\colorValue}
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}
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\AtBeginDocument{%
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\colorInfo{background}%
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\edef\br@white{\colorValue}%
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}
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\xglobal\colorlet{ring1}{Red}
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\xglobal\colorlet{ring2}{Green}
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\xglobal\colorlet{ring3}{Blue}
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\xglobal\colorlet{ring4}{Orange}
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\xglobal\colorlet{ring5}{Purple}
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\xglobal\colorlet{ring6}{Chartreuse}
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\xglobal\colorlet{ring7}{Sienna}
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\xglobal\colorlet{ring8}{DeepPink}
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\xglobal\colorlet{ring9}{Gold}
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\xglobal\colorlet{ring10}{DarkViolet}
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\foreach \k in {1,2,3,4} {
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\foreach \m in {1,2,3,4} {
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\pgfmathparse{int(Mod(\m + \k - 2,4) + 1)}
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\xglobal\colorlet{ring\k\m}{ring\k!50!ring\pgfmathresult}
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\foreach \l in {1,2,3,4} {
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\pgfmathparse{int(Mod(\l + \k - 2,4) + 1)}
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\xglobal\colorlet{ring\k\m\l}{ring\k\m!50!ring\pgfmathresult}
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}
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}
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}
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\pgfdeclarelayer{back}
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\pgfdeclarelayer{front}
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\pgfsetlayers{back,main,front}
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\pgfmathsetmacro{\br@step}{1/4}
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\pgfmathsetmacro{\br@theta}{10}
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\let\brstep=\br@step
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\edef\br@one{1}
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\edef\br@zero{0}
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\newcommand{\setbrstep}[1]{%
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\def\br@step{#1}}
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\tikzset{knot/.style={double distance=1pt,line width=2pt,background}}
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\tikzset{thin knot/.style={double distance=.5pt,line width=1pt,background}}
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\tikzset{thick knot/.style={double distance=2pt,line width=4pt,background}}
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\tikzset{string/.style={line width=1pt}}
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\newcommand{\getangle}[5]{%
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\pgfmathsetmacro{\br@num}{int(4 ^ (#1 - 1) + .5)}
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\pgfmathsetmacro{\br@dir}{#3}
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\pgfmathsetmacro{\br@innersep}{#1 == 1 ? 4 : 0}
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\pgfmathsetmacro{\br@mr}{#2 -\br@step + (2*\br@num + .5) *\br@step * (1 - \br@dir)}
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\pgfmathsetmacro{\br@angle}{atan((6 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
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\ifx\relax#4\relax
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\pgfmathparse{ceil(\br@angle)}
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\else
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\pgfmathparse{int(#4 > \br@angle ? #4 : ceil(\br@angle))}
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\fi
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\xdef\clockangle{\pgfmathresult}
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\ifx\relax#5\relax
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\pgfmathparse{ceil(\br@angle)}
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\else
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\pgfmathparse{int(#5 > \br@angle ? #5 : ceil(\br@angle))}
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\fi
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\xdef\aclockangle{\pgfmathresult}
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\pgfmathparse{int(\clockangle + \aclockangle)}
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\xdef\totalangle{\pgfmathresult}
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}
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\newcommand{\junction}[5]{%
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\pgfmathsetmacro{\br@midpt}{#3}
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\pgfmathsetmacro{\br@dir}{(\br@midpt == 0 ? 1 : \br@midpt)}
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\begin{scope}[xscale=\br@dir]
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\pgfmathsetmacro{\br@num}{int(4 ^ (#1 - 1) + .5)}
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\pgfmathsetmacro{\br@innersep}{#1 == 1 ? 4 : 0}
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\pgfmathsetmacro{\br@mr}{#2 -\br@step + (2*\br@num + .5) *\br@step * (1 - \br@dir)}
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\pgfmathsetmacro{\br@angle}{atan((6 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
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\ifx\relax#4\relax
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\pgfmathsetmacro{\br@outerangle}{ceil(\br@angle)}
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\else
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\pgfmathsetmacro{\br@outerangle}{#4 > \br@angle ? #4 : ceil(\br@angle)}
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\fi
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\ifx\relax#5\relax
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\pgfmathsetmacro{\br@innerangle}{ceil(\br@angle)}
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\else
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\pgfmathsetmacro{\br@innerangle}{#5 > \br@angle ? #5 : ceil(\br@angle)}
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\fi
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\pgfmathsetmacro{\br@sin}{sin(\br@angle)}
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\pgfmathsetmacro{\br@cos}{cos(\br@angle)}
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\path (0,0) circle (2pt);
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\edef\br@itstart{1}
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\pgfmathsetmacro{\br@itend}{2*\br@num}
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\edef\br@mcolor{outer}
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\foreach \br@m in {\br@itstart,...,\br@itend} {
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\@ifundefinedcolor{outer\br@m}{%
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}{%
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\global\edef\br@mcolor{outer\br@m}
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}
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\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
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\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 4 + 1 - \br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@x}{-1*\br@inr *\br@sin}
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\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
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\pgfmathsetmacro{\br@xx}{-1*\br@outr *\br@sin}
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\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
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\pgfmathsetmacro{\br@r}{(6*\br@num - 2*\br@m + \br@innersep)*\br@step/2}
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\pgfmathsetmacro{\br@midr}{(\br@midpt == 0 ? (\br@inr + \br@outr)/2 + \br@r: \br@outr)}
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\colorInfo{\br@mcolor}
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\ifx\colorValue\br@white
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\else
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\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);
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\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90-\br@angle:-90-\br@outerangle:\br@inr);
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\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90-\br@angle:-90-\br@outerangle:\br@outr);
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\fi
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}
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\edef\br@itstart{1}
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\pgfmathsetmacro{\br@itend}{2*\br@num}
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\edef\br@mcolor{inner}
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\foreach \br@m in {\br@itstart,...,\br@itend} {
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\@ifundefinedcolor{inner\br@m}{%
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}{%
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\global\edef\br@mcolor{inner\br@m}
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}
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\pgfmathsetmacro{\br@inward}{2 * (-.5 + (\br@m > \br@num))}
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\pgfmathsetmacro{\br@inr}{\br@mr + (\br@num+\br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@outr}{\br@mr + (3*\br@num + 1 + \br@inward * 2*\br@num - \br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@inmidr}{\br@inr - \br@midpt * \br@innersep * \br@step / 2 - \br@num * \br@midpt * \br@step + .5*\br@midpt * \br@step}
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\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}
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\pgfmathsetmacro{\br@x}{\br@inr *\br@sin}
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\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
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\pgfmathsetmacro{\br@xx}{\br@outr *\br@sin}
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\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
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\pgfmathsetmacro{\br@r}{(\br@num * (1 + \br@inward) - \br@inward * (\br@m - .5)) *\br@step + \br@innersep * \br@step/4}
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\colorInfo{\br@mcolor}
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\ifx\colorValue\br@white
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\else
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\begin{pgfonlayer}{front}
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\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);
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\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90+\br@angle:-90+\br@innerangle:\br@outr);
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\end{pgfonlayer}
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\begin{pgfonlayer}{back}
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\draw[knot,double=\br@mcolor] (\br@x,\br@y) to[out=180+\br@angle,in=0] (0,-\br@inmidr);
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\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90+\br@angle:-90+\br@innerangle:\br@inr);
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\end{pgfonlayer}
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\fi
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}
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\end{scope}
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}
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\newcommand{\flatjunction}[5]{%
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\begin{scope}[xscale=#3]
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\pgfmathsetmacro{\br@num}{4 ^ (#1 - 1)}
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\pgfmathsetmacro{\br@dir}{#3}
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\pgfmathsetmacro{\br@innersep}{#1 == 1 ? 4 : 0}
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\pgfmathsetmacro{\br@mr}{0}%#2 -\br@step + (2*\br@num + .5) *\br@step * (1 - \br@dir)}
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\edef\br@itstart{1}
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\pgfmathsetmacro{\br@itend}{2*\br@num}
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\edef\br@mcolor{outer}
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\foreach \br@m in {\br@itstart,...,\br@itend} {
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\@ifundefinedcolor{outer\br@m}{%
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}{%
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\global\edef\br@mcolor{outer\br@m}
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}
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\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
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\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 4 + 1 - \br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@x}{-8*\br@step}
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\pgfmathsetmacro{\br@y}{-1*\br@inr}
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\pgfmathsetmacro{\br@xx}{-8*\br@step}
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\pgfmathsetmacro{\br@yy}{-1*\br@outr}
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\pgfmathsetmacro{\br@r}{(6*\br@num - 2*\br@m + \br@innersep)*\br@step/2}
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\colorInfo{\br@mcolor}
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\ifx\colorValue\br@white
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\else
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\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);
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\fi
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}
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\edef\br@itstart{1}
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\pgfmathsetmacro{\br@itend}{2*\br@num}
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\edef\br@mcolor{inner}
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\foreach \br@m in {\br@itstart,...,\br@itend} {
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\@ifundefinedcolor{inner\br@m}{%
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}{%
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\global\edef\br@mcolor{inner\br@m}
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}
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\pgfmathsetmacro{\br@inward}{2 * (-.5 + (\br@m > \br@num))}
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\pgfmathsetmacro{\br@inr}{\br@mr + (\br@num+\br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@outr}{\br@mr + (3*\br@num + 1 + \br@inward * 2*\br@num - \br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@inmidr}{\br@inr - \br@dir * \br@innersep * \br@step / 2 - \br@num * \br@dir * \br@step + .5*\br@dir * \br@step}
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\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}
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\pgfmathsetmacro{\br@x}{8*\br@step}
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\pgfmathsetmacro{\br@y}{-1*\br@inr}
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\pgfmathsetmacro{\br@xx}{8*\br@step}
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\pgfmathsetmacro{\br@yy}{-1*\br@outr}
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\pgfmathsetmacro{\br@r}{(\br@num * (1 + \br@inward) - \br@inward * (\br@m - .5)) *\br@step + \br@innersep * \br@step/4}
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\colorInfo{\br@mcolor}
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\ifx\colorValue\br@white
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\else
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\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);
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\begin{pgfonlayer}{back}
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\draw[knot,double=\br@mcolor] (\br@x,\br@y) to[out=180,in=0] (0,-\br@inmidr);
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\end{pgfonlayer}
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\fi
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}
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\end{scope}
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}
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\newcommand{\gethopfangle}[5]{%
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\pgfmathsetmacro{\br@num}{2 ^ (#1 - 1)}
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\pgfmathsetmacro{\br@dir}{#3}
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\pgfmathsetmacro{\br@innersep}{2}%{#1 == 1 ? 2 : 0}
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\pgfmathsetmacro{\br@mr}{#2 -\br@step + (\br@num + .5) *\br@step * (1 - \br@dir)}
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\pgfmathsetmacro{\br@angle}{atan((3 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
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\ifx\relax#4\relax
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\pgfmathparse{ceil(\br@angle)}
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\else
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\pgfmathparse{int(#4 > \br@angle ? #4 : ceil(\br@angle))}
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\fi
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\xdef\clockangle{\pgfmathresult}
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\ifx\relax#5\relax
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\pgfmathparse{ceil(\br@angle)}
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\else
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\pgfmathparse{int(#5 > \br@angle ? #5 : ceil(\br@angle))}
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\fi
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\xdef\aclockangle{\pgfmathresult}
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\pgfmathparse{int(\clockangle + \aclockangle)}
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\xdef\totalangle{\pgfmathresult}
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}
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\newcommand{\hopfjunction}[5]{%
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\begin{scope}[xscale=#3]
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\pgfmathsetmacro{\br@num}{2 ^ (#1 - 1)}
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\pgfmathsetmacro{\br@dir}{#3}
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\pgfmathsetmacro{\br@innersep}{2}%{#1 < 3 ? 2 : 0}
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\pgfmathsetmacro{\br@mr}{#2 -\br@step + (\br@num + .5) *\br@step * (1 - \br@dir)}
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\pgfmathsetmacro{\br@angle}{atan((3 * \br@num + 2*\br@innersep) * \br@step/\br@mr)}
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\ifx\relax#4\relax
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\pgfmathsetmacro{\br@outerangle}{ceil(\br@angle)}
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\else
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\pgfmathsetmacro{\br@outerangle}{#4 > \br@angle ? #4 : ceil(\br@angle)}
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\fi
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\ifx\relax#5\relax
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\pgfmathsetmacro{\br@innerangle}{ceil(\br@angle)}
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\else
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\pgfmathsetmacro{\br@innerangle}{#5 > \br@angle ? #5 : ceil(\br@angle)}
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\fi
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\pgfmathsetmacro{\br@sin}{sin(\br@angle)}
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\pgfmathsetmacro{\br@cos}{cos(\br@angle)}
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\path (0,0) circle (2pt);
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\edef\br@itstart{1}
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\pgfmathsetmacro{\br@itend}{\br@num}
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\edef\br@mcolor{outer}
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\foreach \br@m in {\br@itstart,...,\br@itend} {
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\@ifundefinedcolor{outer\br@m}{%
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}{%
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\global\edef\br@mcolor{outer\br@m}
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}
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\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
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\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 2 + 1 - \br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@x}{-1*\br@inr *\br@sin}
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\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
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\pgfmathsetmacro{\br@xx}{-1*\br@outr *\br@sin}
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\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
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\pgfmathsetmacro{\br@r}{(\br@num - \br@m + \br@innersep + .5)*\br@step}
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\colorInfo{\br@mcolor}
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\ifx\colorValue\br@white
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\else
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\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);
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\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90-\br@angle:-90-\br@outerangle:\br@inr);
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\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90-\br@angle:-90-\br@outerangle:\br@outr);
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\fi
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}
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\edef\br@itstart{1}
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\pgfmathsetmacro{\br@itend}{\br@num}
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\edef\br@mcolor{inner}
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\foreach \br@m in {\br@itstart,...,\br@itend} {
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\@ifundefinedcolor{inner\br@m}{%
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}{%
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\global\edef\br@mcolor{inner\br@m}
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}
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\pgfmathsetmacro{\br@inr}{\br@mr + \br@m * \br@dir * \br@step}
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\pgfmathsetmacro{\br@outr}{\br@mr + (\br@num * 2 + 1 - \br@m) * \br@dir * \br@step}
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\pgfmathsetmacro{\br@x}{\br@inr *\br@sin}
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\pgfmathsetmacro{\br@y}{-1*\br@inr *\br@cos}
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\pgfmathsetmacro{\br@xx}{\br@outr *\br@sin}
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\pgfmathsetmacro{\br@yy}{-1*\br@outr *\br@cos}
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\pgfmathsetmacro{\br@r}{-(\br@num - \br@m + \br@innersep + .5)*\br@step}
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\colorInfo{\br@mcolor}
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\ifx\colorValue\br@white
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\else
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\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90+\br@angle:-90:\br@outr) arc(\br@dir * 90:0:\br@r);
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\begin{pgfonlayer}{back}
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\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);
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\end{pgfonlayer}
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\draw[knot,double=\br@mcolor] (\br@x,\br@y) arc(-90+\br@angle:-90+\br@innerangle:\br@inr);
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\draw[knot,double=\br@mcolor] (\br@xx,\br@yy) arc(-90+\br@angle:-90+\br@innerangle:\br@outr);
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\fi
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}
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\end{scope}
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}
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\newcommand{\brunnian}[3][1]{%
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\pgfmathsetmacro{\br@n}{#3}
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|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
}
|
|
\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%
|
|
}%
|
|
}
|
|
\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%
|
|
}
|
|
}
|
|
\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{
|
|
\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{
|
|
\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{
|
|
\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{
|
|
\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}}
|
|
}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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}
|
|
}
|
|
\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);
|
|
}
|
|
\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 ($(4)!.5!(8)+(0,-1)$)
|
|
;
|
|
}
|
|
\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 ($(4)!.5!(8)+(0,-1)$)
|
|
;
|
|
}
|
|
\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);
|
|
}
|
|
\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);
|
|
}
|
|
\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)
|
|
;
|
|
}
|
|
%%
|
|
%% Copyright (C) 2011 by Andrew Stacey <stacey@math.ntnu.no>
|
|
%%
|
|
%% This work may be distributed and/or modified under the
|
|
%% conditions of the LaTeX Project Public License (LPPL), either
|
|
%% version 1.3c of this license or (at your option) any later
|
|
%% version. The latest version of this license is in the file:
|
|
%%
|
|
%% http://www.latex-project.org/lppl.txt
|
|
%%
|
|
%% This work is "maintained" (as per LPPL maintenance status) by
|
|
%% Andrew Stacey.
|
|
%%
|
|
%% This work consists of the file brunnian.dtx
|
|
%% and the derived files brunnian.ins,
|
|
%% brunnain.pdf, and
|
|
%% brunnian.sty.
|
|
%%
|
|
%%
|
|
%% End of file `brunnian.sty'.
|