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tpath_poster_figures.tex
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tpath_poster_figures.tex
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% !TEX root = poster.tex
\usepackage{tikz,tikz-cd} %
\usetikzlibrary{arrows,shapes,trees}
\usetikzlibrary{backgrounds}
\usetikzlibrary{calc,decorations.pathmorphing,patterns}
\usetikzlibrary{decorations.markings}
% new for poster
%\usetikzlibrary{decorations.pathreplacing,shapes,arrows}
\usetikzlibrary{positioning} % to use right= of
%\usetikzlibrary{calc}
%%% start of NEW NEW
\tikzstyle{NooseArrowAtPosStyleTwo}=[decoration={ markings, mark=at position 0.2 with {\arrow[line width=1.5pt]{stealth};}}, postaction={decorate}]
\tikzstyle{NooseArrowAtPosStyleThree}=[decoration={ markings, mark=at position 0.3 with {\arrow[line width=1.5pt]{stealth};}}, postaction={decorate}]
\tikzstyle{NooseArrowAtPosStyleFour}=[decoration={ markings, mark=at position 0.4 with {\arrow[line width=1.5pt]{stealth};}}, postaction={decorate}]
\tikzstyle{NooseArrowAtPosStyleFive}=[decoration={ markings, mark=at position 0.5 with {\arrow[line width=1.5pt]{stealth};}}, postaction={decorate}]
\tikzstyle{NooseArrowAtPosStyleSix}=[decoration={ markings, mark=at position 0.6 with {\arrow[line width=1.5pt]{stealth};}}, postaction={decorate}]
\tikzstyle{NooseArrowAtPosStyleSeven}=[decoration={ markings, mark=at position 0.7 with {\arrow[line width=1.5pt]{stealth};}}, postaction={decorate}]
\newcommand\PathArrowLineWidth{1.8pt}
\newcommand\PathArrowStyle{to}
\tikzstyle{PathArrowAtPosStyleOne}=[decoration={ markings, mark=at position 0.1 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleTwo}=[decoration={ markings, mark=at position 0.2 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleTwoSmall}=[decoration={ markings, mark=at position 0.2 with {\arrow[line width=0.7*\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleThree}=[decoration={ markings, mark=at position 0.3 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleThreeSmall}=[decoration={ markings, mark=at position 0.3 with {\arrow[line width=0.7*\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleFour}=[decoration={ markings, mark=at position 0.4 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleFourSmall}=[decoration={ markings, mark=at position 0.4 with {\arrow[line width=0.7*\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleFive}=[decoration={ markings, mark=at position 0.5 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleSix}=[decoration={ markings, mark=at position 0.6 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleSixSmall}=[decoration={ markings, mark=at position 0.6 with {\arrow[line width=0.7*\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleSeven}=[decoration={ markings, mark=at position 0.7 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleSevenSmall}=[decoration={ markings, mark=at position 0.7 with {\arrow[line width=0.7*\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleEight}=[decoration={ markings, mark=at position 0.8 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleEightSmall}=[decoration={ markings, mark=at position 0.8 with {\arrow[line width=0.7*\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleNine}=[decoration={ markings, mark=at position 0.9 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleEnd}=[decoration={ markings, mark=at position 1 with {\arrow[line width=\PathArrowLineWidth]{\PathArrowStyle};}}, postaction={decorate}]
\tikzstyle{PathArrowAtPosStyleReversedFive}=[decoration={ markings, mark=at position 0.5 with {\arrow{to reversed};}}, postaction={decorate}]
\tikzstyle{NonOrientedTriangulationStyle}=[style=thick]
\tikzstyle{TPathStyle}=[blue, very thick,
%line width=5pt,
style=dashed]
\tikzstyle{orientedTriangulationStyle}=[style=thick]
\tikzstyle{inducedmapTPathStyle}=[
blue, very thick,%line width = 2pt,
->, style=dashed, rounded corners = 20pt,
decoration={ markings, mark=at position .6 with {\arrow[blue, line width=2.5pt]{to};}}]
\tikzstyle{inducedmapTPathonCnStyle}=[
blue, very thick, %line width = 2pt,
style=dashed, rounded corners = 30pt,
decoration={ markings, mark=at position .6 with {\arrow[blue, line width=2.5pt]{to};}}]
%%% start of new
\tikzstyle{RedGammaStyle}=[very thick, dashed, red]
\tikzstyle{CyanGammaStyle}=[very thick, dashed, cyan]
\tikzstyle{CyanBetaStyle}=[very thick, dashed, cyan]
\tikzstyle{CyanTilBetaStyle}=[line width=2pt, dashed, cyan]
\tikzstyle{RedTilSigmaStyle}=[line width=2pt, dashed, red]
\tikzstyle{RedSigmaStyle}=[very thick, dashed, red]
\newcommand\TikzPunctureSize{0.04}
\newcommand\TikzPointSize{0.03}
\newcommand\TikzIntersectionSize{0.03}
%%% ending triangle_0 is self-folded, including \a and \b
\newcommand \MacroLiftedTriangleOneTwoNoArrow {
\coordinate (P) at (0,0); \coordinate (v1) at (\Tikzn,0); \coordinate (v2) at (0,\Tikzn); \coordinate (y) at (\Tikzn,\Tikzn);
\draw (P) --(v1);% node[pos=0.5, below] {$r$};
\draw (P) -- (v2);% node[pos=0.5,left] {$\ccr$};
\draw (v2) -- (y);% node[pos=0.5,above]{$\a$};
\draw (v1) -- (y);% node[pos=0.5,right]{$\b$};
\draw (v2) -- (v1);% node[pos=0.7,right] {$\ell$};
\foreach \pos in {(v1),(v2)}
{\draw [fill=olive] \pos circle (\TikzPointSize*\Tikzn);}
\foreach \pos in {(P),(y)}
{\draw [fill=violet] \pos circle (\TikzPunctureSize*\Tikzn);}
}
\newcommand \MacroLiftedTriangleOneTwo {
\coordinate (P) at (0,0); \coordinate (v1) at (\Tikzn,0); \coordinate (v2) at (0,\Tikzn); \coordinate (y) at (\Tikzn,\Tikzn);
\draw (P) --(v1) node[pos=0.5, below] {$r$};
\draw (P) -- (v2) node[pos=0.5,left] {$\ccr$};
\draw (v2) -- (y) node[pos=0.5,above]{$\a$};
\draw (v1) -- (y) node[pos=0.5,right]{$\b$};
\draw[NooseArrowAtPosStyleSix] (v2) -- (v1) node[pos=0.7,right] {$\ell$};
\foreach \pos in {(v1),(v2),(y)}
{\draw [fill=olive] \pos circle (\TikzPointSize*\Tikzn);}
\foreach \pos in {(P)}
{\draw [fill=violet] \pos circle (\TikzPunctureSize*\Tikzn);}
}
\newcommand\TikzLiftedTriangleOneTwoCrossesA[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleStyle]
\newcommand\Tikzn{2}
\MacroLiftedTriangleOneTwo
\draw [RedGammaStyle, ->] (P) --(0.8*\Tikzn,1.2*\Tikzn) node[pos=0.4,left] {$\ga$};
\begin{scope}[gray]
\draw (\Tikzn * 0.4,\Tikzn * 0.22) node {$\tilblacktri{0}$};
\draw (\Tikzn * 0.75,\Tikzn *0.72) node {$\tilblacktri{1}$};
\end{scope}
\end{tikzpicture}
}
\newcommand\TikzLiftedTriangleOneTwo[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleStyle]
\newcommand\Tikzn{2}
\MacroLiftedTriangleOneTwo
\draw [RedGammaStyle, <-] (0.5*\Tikzn,0.8*\Tikzn) -- (0.1,0.1);
\begin{scope}[gray]
\draw (\Tikzn * 0.4,\Tikzn * 0.22) node {$\tilblacktri{0}$};
\draw (\Tikzn * 0.75,\Tikzn *0.72) node {$\tilblacktri{1}$};
\end{scope}
\end{tikzpicture}
}
\newcommand\TikzLiftedTriangleD[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleStyle]
\newcommand\Tikzn{2}
\MacroLiftedTriangleOneTwo
\draw [RedGammaStyle, ->] (0.5*\Tikzn,0.7*\Tikzn) -- (0.1,0.1);
\begin{scope}[gray]
\draw (\Tikzn * 0.4,\Tikzn * 0.22) node {$\tilblacktri{d}$};
\draw (\Tikzn * 0.75,\Tikzn *0.72) node {$\tilblacktri{d-1}$};
\end{scope}
\end{tikzpicture}
}
\newcommand\TikzCrossingNooseOne[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRAB
%\coordinate (P) at (0,\Tikzn);
\draw[RedGammaStyle, <- ] (-0.2*\Tikzn,1.6*\Tikzn) -- (P) node[blue,left, pos=0.4] {$p_1$};
\newcommand\TikzHeight{1.3}
\draw[fill=blue] (-0.1*\Tikzn,\Tikzn*\TikzHeight) circle (0.2*\Tikzn ex);
\end{tikzpicture}
}
\newcommand\TikzCrossingNooseOneAndA[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRAB
%\coordinate (P) at (0,\Tikzn);
\draw[RedGammaStyle, -> ]% (-0.2*\Tikzn,1.6*\Tikzn)
(P) -- (-0.6*\Tikzn,2.1*\Tikzn) node[pos=0.45,left]{$\ga$};
\newcommand\TikzHeight{1.3}
\end{tikzpicture}
}
\newcommand\TikzCrossingNooseD[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRAB
%\coordinate (P) at (0,\Tikzn);
\draw[RedGammaStyle, -> ] (-0.2*\Tikzn,1.6*\Tikzn) -- (P) node[blue,left, pos=0.4] {$p_d$};
\newcommand\TikzHeight{1.3}
\draw[fill=blue] (-0.1*\Tikzn,\Tikzn*\TikzHeight) circle (0.2*\Tikzn ex);
\end{tikzpicture}
}
%%% ending triangle_0 is self-folded, including \a and \b
%% begins crossing self-folded triangle, including \a and \b
\newcommand\MacroCrossingLRAB{
\begin{scope}[thick, gray]
\coordinate (v) at (0,0);
\coordinate (P) at (0,0.9*\Tikzn);
\coordinate (y) at (0,2*\Tikzn);
\draw[thick] (0,0) -- (P);
\draw (0.08*\Tikzn,0.4*\Tikzn) node {$r$};
\draw (v) node[below,olive] {$v$}; \draw (y) node[below,olive] {$y$};
\begin{scope}[gray]
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.5,\Tikzn*0.5)}
\newcommand \TikzLowerPointerRight{(\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.5,\Tikzn)} \newcommand\TikzUpperPointerRight{(\Tikzn*0.5,\Tikzn)}
\draw[style = thick, rounded corners = 20pt,NooseArrowAtPosStyleSix]
(v) .. controls \TikzLowerPointerLeft and \TikzUpperPointerLeft .. (0,\Tikzn*1.5)
.. controls \TikzUpperPointerRight and \TikzLowerPointerRight .. (v) node[pos=0.3,right=3pt] {$\ell$};
\end{scope}
\newcommand\TikzLowerPointA{(-1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-\Tikzn,1.8*\Tikzn)}
\newcommand\TikzLowerPointB{(1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(\Tikzn,1.8*\Tikzn)}
\draw (v) .. controls \TikzLowerPointA and \TikzUpperPointA .. (y) node[pos=0.6,left] {$\a$};
\draw (v) .. controls \TikzLowerPointB and \TikzUpperPointB .. (y) node[pos=0.6,right] {$\b$};
\end{scope}
\draw [fill=violet, violet] (P) circle (\TikzPunctureSize*\Tikzn);
\foreach \pos in {(v),(y)}
{\draw [fill=olive, olive] \pos circle (\TikzPointSize*\Tikzn );}
}
\newcommand\TikzCrossingCounterclockwiseLRAB[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRAB
\newcommand\TikzHeight{0.6}
\draw [RedGammaStyle, dashed, ->] (-\Tikzn *0.6, \Tikzn * \TikzHeight) -- (\Tikzn *0.7, \Tikzn * \TikzHeight) node[blue,below, pos=0.1] {$p_k$};
\draw[fill=blue] (-0.4*\Tikzn,\Tikzn*\TikzHeight) circle (0.2*\Tikzn ex);
\end{tikzpicture}
}
\newcommand\TikzCrossingClockwiseLRAB[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRAB
\newcommand\TikzHeight{0.6}
\draw [RedGammaStyle, dashed, <-] (-\Tikzn *0.7, \Tikzn * \TikzHeight) -- (\Tikzn *0.7, \Tikzn * \TikzHeight)
node[blue,below, pos=0.9] {$p_k$};
\draw[fill=blue] (0.4*\Tikzn,\Tikzn*\TikzHeight) circle (0.2*\Tikzn ex);
\end{tikzpicture}
}
%%% end of crossing self-folded triangle, including \a and \b
%%%
\newcommand\MacroDoubleCrossingActualThetaOneThetaH{
\draw[gray, thick, rounded corners=5pt] (v) -- (-2.3*\Tikzn,0) -- (-2.3*\Tikzn,2*\Tikzn) -- (y)
(-2*\Tikzn,0) -- (-1*\Tikzn,2*\Tikzn) node [black,pos=0.5, left] {$\theta_1$};
}
\newcommand\TikzDoubleCrossingActualCrossingLR[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRAB
\MacroDoubleCrossingActualThetaOneThetaH
\newcommand\TikzHeightBelow{0.6}
\newcommand\TikzHeightExtraBelow{0.3}
\newcommand\TikzHeightAbove{1.5}
\draw [RedGammaStyle, dashed, ->, rounded corners=15pt] (-\Tikzn *2, \Tikzn * \TikzHeightBelow) -- (\Tikzn *0.2, \Tikzn * \TikzHeightBelow) -- (\Tikzn *0.2, \Tikzn * \TikzHeightAbove) -- (-2*\Tikzn, \Tikzn*\TikzHeightAbove)
node[pos=0.8, above] {$\si$};
\draw [CyanBetaStyle, dashed, ->] (-\Tikzn *2, \Tikzn * \TikzHeightExtraBelow) -- (\Tikzn *0.45, \Tikzn * \TikzHeightExtraBelow)
node[pos=0.2, below] {$\ga$};
% \draw[fill=blue] (-0.4*\Tikzn,\Tikzn*\TikzHeightBelow) circle (0.2*\Tikzn ex);
\end{tikzpicture}
}
\newcommand\TikzDoubleCrossingActualRhoOneRhoF[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\begin{scope}[thick, gray]
\coordinate (v) at (0,0);
\coordinate (P) at (0,0.9*\Tikzn);
\coordinate (y) at (0,2*\Tikzn);
\draw[thick] (0,0) -- (y) ;
\draw[black] (-0.1*\Tikzn,0.4*\Tikzn) node {$\rho_1$};
\draw[black] (-0.2*\Tikzn,1.3*\Tikzn) node {$\rho_f$};
\draw (v) node[below,white] {};%{$v$};% \draw (y) node[below,olive] {$y$};
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzLowerPointerRight{(\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.5,\Tikzn)} \newcommand\TikzUpperPointerRight{(\Tikzn*0.5,\Tikzn)}
% \draw[style = thick, rounded corners = 20pt,NooseArrowAtPosStyleSix]
% (v) .. controls \TikzLowerPointerLeft and \TikzUpperPointerLeft .. (0,\Tikzn*1.5)
% .. controls \TikzUpperPointerRight and \TikzLowerPointerRight .. (v) node[pos=0.3,right=3pt] {$\ell$};
\newcommand\TikzLowerPointA{(-1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-\Tikzn,1.8*\Tikzn)}
\newcommand\TikzLowerPointB{(1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(\Tikzn,1.8*\Tikzn)}
\draw (v) .. controls \TikzLowerPointA and \TikzUpperPointA .. (y) node[pos=0.5,black] {$\theta_h$};
\draw (v) .. controls \TikzLowerPointB and \TikzUpperPointB .. (y);% node[pos=0.6,right] {$\b$};
\end{scope}
\draw [fill=violet, violet] (P) circle (\TikzPunctureSize*\Tikzn);
\foreach \pos in {(v),(y)}
{\draw [fill=olive, olive] \pos circle (\TikzPointSize*\Tikzn );}
\MacroDoubleCrossingActualThetaOneThetaH
\newcommand\TikzHeightBelow{0.6}
\newcommand\TikzHeightExtraBelow{0.3}
\newcommand\TikzHeightAbove{1.5}
\draw [RedGammaStyle, dashed, ->, rounded corners=15pt] (-\Tikzn *2, \Tikzn * \TikzHeightBelow) -- (\Tikzn *0.5, \Tikzn * \TikzHeightBelow) -- (\Tikzn *0.5, \Tikzn * \TikzHeightAbove) -- (-2*\Tikzn, \Tikzn*\TikzHeightAbove)
node[pos=0.8, above] {$\si$};
\draw [CyanBetaStyle, dashed, ->] (-\Tikzn *2, \Tikzn * \TikzHeightExtraBelow) -- (\Tikzn *0.3, \Tikzn * \TikzHeightExtraBelow)
node[pos=0.2, below] {$\ga$};
\end{tikzpicture}
}
%%
\newcommand\MacroTwoFoldCoverCrossingRL{
\begin{scope}[thick, gray]
\coordinate (v) at (0,0);
\coordinate (P) at (0,1*\Tikzn);
\coordinate (y) at (0,2*\Tikzn);
\draw[thick] (0,0) -- (y);
\draw[black] (0.0*\Tikzn,0.6*\Tikzn) node {$r^1$};
\draw[black] (-0.0*\Tikzn,1.6*\Tikzn) node {$r^2$};
\draw (v) node[below,olive] {$v^1$}; \draw (y) node[above,olive] {$v^2$};
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.6,\Tikzn*0.5)}
\newcommand\TikzLowerPointerRight{(\Tikzn*0.6,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.6,1.5*\Tikzn)}
\newcommand\TikzUpperPointerRight{(\Tikzn*0.6,1.5*\Tikzn)}
\draw[style = thick, NooseArrowAtPosStyleThree,NooseArrowAtPosStyleSeven]
(v) .. controls \TikzLowerPointerLeft and \TikzUpperPointerLeft .. (y) node[black,pos=0.7] {$\ell^1$}
(y) .. controls \TikzUpperPointerRight and \TikzLowerPointerRight .. (v) node[black,pos=0.5] {$\ell^2$};
\newcommand\TikzLowerPointA{(-1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-0.7*\Tikzn,1.8*\Tikzn)}
\newcommand\TikzLowerPointB{(0.7*\Tikzn,0.2*\Tikzn)} \newcommand\TikzUpperPointB{(1.3*\Tikzn,1.7*\Tikzn)}
\draw (v) .. controls \TikzLowerPointA and \TikzUpperPointA .. (-1.4,2*\Tikzn) node[black,pos=0.6] {$\a^1$};
\draw (1.4,0*\Tikzn) .. controls \TikzLowerPointB and \TikzUpperPointB .. (y) node[black,pos=0.6] {$\a^2$};
\draw[fill=olive] (-1.4,2*\Tikzn) circle (\TikzPointActualSize) node [olive, above] {$y^2$};
\draw (-0.8,2.1*\Tikzn) node {$\b$};
\draw[fill=olive] (1.4,0*\Tikzn) circle (\TikzPointActualSize) node [olive, below] {$y^1$};
\draw (0.8,-0.1*\Tikzn) node {$\b$};
\end{scope}
\draw [fill=violet, violet] (P) circle (\TikzPunctureActualSize);
\foreach \pos in {(v),(y)}
{\draw [fill=olive, olive] \pos circle (\TikzPointSize*\Tikzn );}
}
\newcommand\TikzTwoFoldCoverCrossingLR[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroTwoFoldCoverCrossingRL
\newcommand\TikzWidth{2}
\draw[gray, thick,rounded corners=5pt] (v) -- (-\TikzWidth*\Tikzn,0) -- (-\TikzWidth*\Tikzn,2*\Tikzn) -- (y)
(-1.8*\Tikzn,0) -- (-1*\Tikzn,2*\Tikzn) node [black,pos=0.7, left] {$\theta_1^1$};
\draw[gray, thick,rounded corners=5pt] (v) -- (\TikzWidth*\Tikzn,0) -- (\TikzWidth*\Tikzn,2*\Tikzn) -- (y)
(1.8*\Tikzn,2*\Tikzn) -- (1*\Tikzn,0) node [black,pos=0.3, left] {$\theta_1^2$};
\newcommand\TikzHeightBelow{0.4}
\newcommand\TikzHeightAbove{0.8}
\draw [RedTilSigmaStyle, dashed, ->] (-\Tikzn *2, \Tikzn * \TikzHeightAbove) -- (\Tikzn *0.7, \Tikzn * \TikzHeightAbove) -- (2*\Tikzn, \Tikzn*\TikzHeightAbove) node[pos=0.7,above] {$\tilsi$};
\draw[fill=olive] (-\Tikzn *2, \Tikzn * \TikzHeightAbove) circle (\TikzPunctureActualSize) node[olive,left] {$\tils$};
\draw[fill=olive] (2*\Tikzn, \Tikzn*\TikzHeightAbove) circle (\TikzPunctureActualSize) node[olive,right] {$\tilt$};
\draw [CyanTilBetaStyle, dashed, ->] (-\Tikzn *1.5, \Tikzn * \TikzHeightBelow) -- (0.5*\Tikzn, \Tikzn*\TikzHeightBelow) node[pos=0.2, below] {$\tilbe$};
%node[blue,below, pos=0.1] {$p_k$};
%\draw[fill=blue] (-0.4*\Tikzn,\Tikzn*\TikzHeightBelow) circle (0.2*\Tikzn ex);
\end{tikzpicture}
}
\newcommand\MacroTwoFoldCoverCrossingRhoOneRhoF{
\begin{scope}[thick, gray]
\coordinate (v) at (0,0);
\coordinate (P) at (0,1*\Tikzn);
\coordinate (y) at (0,2*\Tikzn);
\draw[thick] (0,0) -- (y);
\draw[black] (0.0*\Tikzn,0.6*\Tikzn) node {$\rho_1^1$};
\draw[black] (-0.0*\Tikzn,1.6*\Tikzn) node {$\rho_1^2$};
\draw (-0.7*\Tikzn,2*\Tikzn) --
(0.7*\Tikzn,0)
node[black,pos=0.25] {$\rho_f^2$} node[black,pos=0.8] {$\rho_f^1$};
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.6,\Tikzn*0.5)}
\newcommand\TikzLowerPointerRight{(\Tikzn*0.6,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.6,1.5*\Tikzn)}
\newcommand\TikzUpperPointerRight{(\Tikzn*0.6,1.5*\Tikzn)}
\newcommand\TikzLowerPointA{(-0.8*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-0.8*\Tikzn,1.8*\Tikzn)}
\newcommand\TikzLowerPointB{(1*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(0.5*\Tikzn,1.8*\Tikzn)}
\draw (v) .. controls \TikzLowerPointA and \TikzUpperPointA .. (-0.7*\Tikzn,2*\Tikzn) node[black,pos=0.6] {$\theta_{h}^1$};
\draw (0.7*\Tikzn,0) .. controls \TikzLowerPointB and \TikzUpperPointB .. (y) node[black,pos=0.6] {$\theta_{h}^2$};
\end{scope}
\draw [fill=violet, violet] (P) circle (\TikzPunctureActualSize);
\foreach \pos in {(v),(y),(0.7*\Tikzn,0), (-0.7*\Tikzn,2*\Tikzn)}
{\draw [fill=olive, olive] \pos circle (\TikzPointSize*\Tikzn );}
}
%
%\newcommand\TikzTwoFoldCoverCrossingRhoOneRhoF[1]{
%\begin{tikzpicture}[scale={#1}]
%\newcommand\Tikzn{2}
%\MacroTwoFoldCoverCrossingRhoOneRhoF
%\newcommand\TikzWidth{2}
%\draw[gray, thick,rounded corners=5pt] (v) -- (-\TikzWidth*\Tikzn,0) -- (-\TikzWidth*\Tikzn,2*\Tikzn) -- (y)
%(-1.8*\Tikzn,0) -- (-1*\Tikzn,2*\Tikzn) node [black,pos=0.7, left] {$\theta_1^1$};
%\draw[gray,thick, rounded corners=5pt] (v) -- (\TikzWidth*\Tikzn,0) -- (\TikzWidth*\Tikzn,2*\Tikzn) -- (y)
%(1.8*\Tikzn,2*\Tikzn) -- (1*\Tikzn,0) node [black,pos=0.25, left] {$\theta_1^2$};
%
%\newcommand\TikzHeightBelow{0.4}
%\newcommand\TikzHeightAbove{0.8}
%\draw [RedTilSigmaStyle, dashed, ->] (-\Tikzn *2, \Tikzn * \TikzHeightAbove) -- (\Tikzn *0.7, \Tikzn * \TikzHeightAbove) -- (2*\Tikzn, \Tikzn*\TikzHeightAbove) node[pos=0.7,above] {$\tilsi$};
%\draw[fill=olive] (-\Tikzn *2, \Tikzn * \TikzHeightAbove) circle (\TikzPunctureActualSize) node[olive,left] {$\tils$};
%\draw[fill=olive] (2*\Tikzn, \Tikzn*\TikzHeightAbove) circle (\TikzPunctureActualSize) node[olive,right] {$\tilt$};
%\draw [CyanTilBetaStyle, dashed, ->] (-\Tikzn *1.5, \Tikzn * \TikzHeightBelow) -- (0.3*\Tikzn, \Tikzn*\TikzHeightBelow) node[pos=0.2, below] {$\tilbe$};
%
%\draw (-1.4,2*\Tikzn) node [white, above] {$y^2$};
%\draw (1.4,0*\Tikzn) node [white, below] {$y^1$};
%\end{tikzpicture}
%}
%%%% current
\tikzstyle{LiftedPathStyle} = [blue, line width=2pt, dashed]
% begin of paths for k=1 or k=d
%% begins crossing self-folded triangle, including \a and \b
\newcommand\TikzNooseOneRLMinusA[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\newcommand\Tikzn{2}
\MacroLiftedTriangleOneTwoNoArrow
\draw [LiftedPathStyle, PathArrowAtPosStyleTwo, PathArrowAtPosStyleFour, PathArrowAtPosStyleEnd, rounded corners=5pt]
(P) --(v1) node[pos=0.4, below] {$r$}
-- (0.1,0.9*\Tikzn) node[pos=0.6,right] {$\ell$}
(0.1,0.9*\Tikzn)
-- (\Tikzn,0.9*\Tikzn) node[pos=0.3,above=3pt]{$\a$}
-- (\Tikzn,1.1*\Tikzn)
-- (0.6*\Tikzn,1.1*\Tikzn);
\end{tikzpicture}
}
\newcommand\TikzNooseOneRLPlusB[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\newcommand\Tikzn{2}
\MacroLiftedTriangleOneTwoNoArrow
\draw [LiftedPathStyle, PathArrowAtPosStyleTwo, PathArrowAtPosStyleFive, PathArrowAtPosStyleEnd, rounded corners=5pt]
(P) -- (v2) node[pos=0.3,left] {$\ccr$}
-- (v1) node[pos=0.6,right] {$\ell$}
-- (y) node[pos=0.5,right]{$\b$}
-- (0.3,\Tikzn) node[pos=0.5,above]{$\a$};
\end{tikzpicture}
}
\newcommand\TikzNooseOneRLPlusLMinus[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\newcommand\Tikzn{2}
\MacroLiftedTriangleOneTwoNoArrow
\draw [LiftedPathStyle, PathArrowAtPosStyleOne, PathArrowAtPosStyleSeven, PathArrowAtPosStyleEnd, rounded corners=5pt]
(P) -- (0,0.8*\Tikzn) node[pos=0.5,left] {$\ccr$}
-- (v1) -- (0.2,\Tikzn) node[pos=0.6,right] {$\ell$}
-- (y) node[pos=0.5,above]{$\a$};
\end{tikzpicture}
}
\newcommand\MacroCrossingLRABPlain{
\begin{scope}[thick, gray]
\coordinate (v) at (0,0);
\coordinate (P) at (0,0.9*\Tikzn);
\coordinate (y) at (0,2*\Tikzn);
\draw[thick] (0,0) -- (P);
\draw (0.08*\Tikzn,0.4*\Tikzn) node {$r$};
\draw (v) node[below,olive] {$v$}; \draw (y) node[below,olive] {$y$};
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.5,\Tikzn*0.5)}
\newcommand \TikzLowerPointerRight{(\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.5,\Tikzn)} \newcommand\TikzUpperPointerRight{(\Tikzn*0.5,\Tikzn)}
\draw[style = thick, rounded corners = 20pt]
(v) .. controls \TikzLowerPointerLeft and \TikzUpperPointerLeft .. (0,\Tikzn*1.5)
.. controls \TikzUpperPointerRight and \TikzLowerPointerRight .. (v);% node[pos=0.3,right=3pt] {$\ell$};
\newcommand\TikzLowerPointA{(-1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-\Tikzn,1.8*\Tikzn)}
\newcommand\TikzLowerPointB{(1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(\Tikzn,1.8*\Tikzn)}
\draw (v) .. controls \TikzLowerPointA and \TikzUpperPointA .. (y) ;%node[pos=0.6,left] {$\a$};
\draw (v) .. controls \TikzLowerPointB and \TikzUpperPointB .. (y) ;%node[pos=0.6,right] {$\b$};
\end{scope}
\draw [fill=violet, violet] (P) circle (\TikzPunctureSize*\Tikzn);
\foreach \pos in {(v),(y)}
{\draw [fill=olive, olive] \pos circle (\TikzPointSize*\Tikzn );}
}
\newcommand\TikzRLMinusA[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRABPlain
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.5,\Tikzn*0.5)}
\newcommand \TikzLowerPointerRight{(\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.5,\Tikzn)} \newcommand\TikzUpperPointerRight{(\Tikzn*0.5,\Tikzn)}
\newcommand\TikzLowerPointA{(-1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-\Tikzn,1.8*\Tikzn)}
%\newcommand\TikzLowerPointB{(1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(\Tikzn,1.8*\Tikzn)}
\draw [LiftedPathStyle, PathArrowAtPosStyleOne,PathArrowAtPosStyleFour,rounded corners=15pt]
(P) -- (0.1,0.1)
(0.1,0.1) .. controls \TikzLowerPointerRight and \TikzUpperPointerRight .. (0,\Tikzn*1.5)
node[pos=0.7,right=3pt] {$\ell_-$}
.. controls \TikzUpperPointerLeft and \TikzLowerPointerLeft .. (-0.3,0.2);
\draw [LiftedPathStyle, PathArrowAtPosStyleNine,rounded corners=15pt]
(-0.3,0.2) .. controls \TikzLowerPointA and \TikzUpperPointA .. (y) node[pos=0.4,left] {$\a$};
\draw [LiftedPathStyle, PathArrowAtPosStyleEnd,rounded corners=15pt]
(y) -- (-0.4*\Tikzn,2.2*\Tikzn) -- (-1*\Tikzn,1.5*\Tikzn);
\draw[LiftedPathStyle] (0.08*\Tikzn,0.4*\Tikzn) node {$r$};
\end{tikzpicture}
}
\newcommand\TikzRLPlusB[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRABPlain
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.5,\Tikzn*0.5)}
\newcommand \TikzLowerPointerRight{(\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.5,\Tikzn)} \newcommand\TikzUpperPointerRight{(\Tikzn*0.5,\Tikzn)}
\newcommand\TikzLowerPointA{(-1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-\Tikzn,1.8*\Tikzn)}
\newcommand\TikzLowerPointB{(1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(\Tikzn,1.8*\Tikzn)}
\draw [LiftedPathStyle, PathArrowAtPosStyleOne, PathArrowAtPosStyleSeven, rounded corners=15pt]
(P) -- (0,0.3)
(0,0.3) .. controls \TikzLowerPointerLeft and \TikzUpperPointerLeft .. (0,\Tikzn*1.5)
.. controls \TikzUpperPointerRight and \TikzLowerPointerRight .. (0.2,0) node[pos=0.3,right=3pt] {$\ell_+$};
\draw [LiftedPathStyle, PathArrowAtPosStyleNine, rounded corners=15pt]
(0.2,0) .. controls \TikzLowerPointB and \TikzUpperPointB .. (y) node[pos=0.6,right] {$\b$};
\draw [LiftedPathStyle, PathArrowAtPosStyleNine]
(y) .. controls \TikzUpperPointA and \TikzLowerPointA .. (-0.8,0.3) node[pos=0.6,left] {$\a$};
\draw[LiftedPathStyle] (0.08*\Tikzn,0.4*\Tikzn) node {$r$};
\end{tikzpicture}
}
\newcommand\TikzRLPlusLMinusA[1]{
\begin{tikzpicture}[scale={#1}]
\newcommand\Tikzn{2}
\MacroCrossingLRABPlain
\newcommand\TikzLowerPointerLeft{(-\Tikzn*0.5,\Tikzn*0.5)}
\newcommand \TikzLowerPointerRight{(\Tikzn*0.5,\Tikzn*0.5)}
\newcommand\TikzUpperPointerLeft{(-\Tikzn*0.5,\Tikzn)} \newcommand\TikzUpperPointerRight{(\Tikzn*0.5,\Tikzn)}
\newcommand\TikzLowerPointA{(-1.2*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointA{(-\Tikzn,1.8*\Tikzn)}
%\newcommand\TikzLowerPointB{(1.3*\Tikzn,0.3*\Tikzn)} \newcommand\TikzUpperPointB{(\Tikzn,1.8*\Tikzn)}
\draw [LiftedPathStyle, PathArrowAtPosStyleOne, PathArrowAtPosStyleFour, rounded corners=15pt]
(P) -- (0,0.3)
(0,0.3) .. controls \TikzLowerPointerLeft and \TikzUpperPointerLeft .. (0,\Tikzn*1.4)
.. controls \TikzUpperPointerRight and \TikzLowerPointerRight .. (0.3,0.2); %node[pos=0.3,right=3pt] {$\ell_+$};
\renewcommand\TikzLowerPointerLeft{(-\Tikzn*0.7,\Tikzn*0.5)}
\renewcommand\TikzLowerPointerRight{(\Tikzn*0.7,\Tikzn*0.5)}
\renewcommand\TikzUpperPointerLeft{(-\Tikzn*0.8,\Tikzn)}
\renewcommand\TikzUpperPointerRight{(\Tikzn*0.8,\Tikzn)}
\draw [LiftedPathStyle,PathArrowAtPosStyleFour,rounded corners=15pt]
(0.3,0.2) .. controls \TikzLowerPointerRight and \TikzUpperPointerRight .. (0,\Tikzn*1.6)
node[pos=0.7,right=3pt] {$\ell$}
.. controls \TikzUpperPointerLeft and \TikzLowerPointerLeft .. (-0.5,0.3);
\draw [LiftedPathStyle, PathArrowAtPosStyleNine,rounded corners=15pt]
(-0.5,0.3) .. controls \TikzLowerPointA and \TikzUpperPointA .. (y) node[pos=0.6,left] {$\a$};
\draw[LiftedPathStyle] (0.08*\Tikzn,0.4*\Tikzn) node {$r$};
\end{tikzpicture}
}
%%%%% begin of double lifted triangles %%%%%%%%
\tikzstyle{DoubleTriangleStyle}=[thick]
\tikzstyle{DoubleTriangleLightStyle}=[gray!90]
\newcommand\MacroDoubleTriangle{
\newcommand\Tikzn{2}
\coordinate (P) at (0,\Tikzn);
\draw (0,0) -- (P) node[pos=0.3, left] {$r$};
\draw (-\Tikzn,0) -- (-\Tikzn,\Tikzn) node[pos=0.6,left]{$\b$}; %left
\draw (0,0) -- (-\Tikzn,0) node[pos=0.5,below]{$\a$}; %left
\draw (\Tikzn,0) -- (\Tikzn,\Tikzn) node[pos=0.6,right]{$\a$}; %right
\draw (0,0) -- (2,0) node[pos=0.5,below]{$\b$}; %right
\draw [fill=violet] (P) circle (\TikzPunctureSize*\Tikzn);
\foreach \pos in {(0,0),(-\Tikzn,\Tikzn) ,(\Tikzn,\Tikzn), (-\Tikzn,0) ,(\Tikzn,0)}
{\draw [fill=olive] \pos circle (\TikzPointSize*\Tikzn);}
}
\newcommand\MacroDoubleTriangleWithArrow{
\MacroDoubleTriangle
\draw[NooseArrowAtPosStyleSeven] (0,0) -- (-\Tikzn,\Tikzn) node[pos=0.3,left] {$\ell$}; % left
\draw[NooseArrowAtPosStyleFour] (\Tikzn,\Tikzn) -- (0,0) node[pos=0.7,right] {$\ell$}; % right
}
\newcommand\MacroDoubleTriangleNoArrow{
\MacroDoubleTriangle
\draw (0,0) -- (-\Tikzn,\Tikzn) node[pos=0.3,left] {$\ell$}; % left
\draw (\Tikzn,\Tikzn) -- (0,0) node[pos=0.7,right] {$\ell$}; % right
}
\newcommand\TikzDoubleTriangleCounterclockwise[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleStyle]
\MacroDoubleTriangleWithArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw [RedGammaStyle, ->] (-\Tikzn *0.65, \Tikzn *0.5) -- (\Tikzn *0.8, \Tikzn *0.5);
\begin{scope}[gray]
\draw (-\Tikzn * 0.35,\Tikzn * 0.72) node {$\tilblacktri{k}$};
\draw (\Tikzn * 0.35,\Tikzn *0.72) node {$\tilblacktri{k+1}$};
\end{scope}
\end{tikzpicture}
}
\newcommand\TikzDoubleTriangleClockwise[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleStyle]
\MacroDoubleTriangleWithArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\draw [RedGammaStyle, <-] (-\Tikzn *0.8, \Tikzn *0.5) -- (\Tikzn *0.7, \Tikzn *0.5);
\begin{scope}[gray]
\draw (-\Tikzn * 0.35,\Tikzn * 0.72) node {$\tilblacktri{k+1}$};
\draw (\Tikzn * 0.35,\Tikzn *0.72) node {$\tilblacktri{k}$};
\end{scope}
\end{tikzpicture}
}
\newcommand\TikzDoubleTriangleKPlusPlus[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\MacroDoubleTriangleNoArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\coordinate (pk) at (-0.6*\Tikzn,0.6*\Tikzn);
\coordinate (pk1) at (0.2,0.3*\Tikzn);
\draw [LiftedPathStyle, PathArrowAtPosStyleTwo, PathArrowAtPosStyleEnd, rounded corners=5pt] (pk) -- (-0.1,0) -- ($(P)+(-0.1,0)$) -- (pk1);
%\foreach \pos in {(pk),(pk1)}
% {\draw [black,fill=blue] \pos circle (\TikzIntersectionSize*\Tikzn);}
\end{tikzpicture}
}
\newcommand\TikzEllMinusRR[1]{ %
\begin{tikzpicture}[scale={#1}]
\MacroChubbySelfFoldedTriangle
\MacroEllMinusRRLong
\end{tikzpicture}
}
\newcommand\TikzDoubleTriangleKKPlus[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\MacroDoubleTriangleNoArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\coordinate (pk) at (-0.2+-0.5*\Tikzn,0.4*\Tikzn);
\coordinate (pk1) at (0,0.9*\Tikzn);
\draw [LiftedPathStyle, PathArrowAtPosStyleSix, PathArrowAtPosStyleEnd, rounded corners=5pt] (pk) -- (-\Tikzn+0.2,\Tikzn) -- (0,0) -- (pk1);
%\foreach \pos in {(pk),(pk1)}
% {\draw [black,fill=blue] \pos circle (\TikzIntersectionSize*\Tikzn);}
\end{tikzpicture}
}
\newcommand\TikzEllPlusEllMinusR[1]{ %
\begin{tikzpicture}[scale={#1}]
\MacroChubbySelfFoldedTriangle
\MacroEllPlusEllMinusR
\end{tikzpicture}
}
\newcommand\TikzDoubleTriangleKThirdEdgePlus[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\MacroDoubleTriangleNoArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\coordinate (pk) at (-0.3*\Tikzn,0.3*\Tikzn);
\coordinate (pk1) at (0,0.1*\Tikzn);
\draw [LiftedPathStyle, PathArrowAtPosStyleTwo, PathArrowAtPosStyleSix, PathArrowAtPosStyleEnd, rounded corners=5pt] (pk) -- (-\Tikzn,\Tikzn) -- (P) -- (pk1);
%\foreach \pos in {(pk),(pk1)}
% {\draw [black,fill=blue] \pos circle (\TikzIntersectionSize*\Tikzn);}
\end{tikzpicture}
}
%%%%%%% from om_2k+2 to om_2k+4
\newcommand\TikzDoubleTriangleRRL[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\MacroDoubleTriangleNoArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\coordinate (pk2) at (0.6*\Tikzn,0.6*\Tikzn);
\draw [LiftedPathStyle, PathArrowAtPosStyleSix, PathArrowAtPosStyleEnd, rounded corners=5pt] (-0.2,0.3) -- ($(P)+(-0.1,-0.2)$) -- (0.2,0.1) -- (pk2);
\end{tikzpicture}
}
\newcommand\TikzDoubleTriangleRLL[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\MacroDoubleTriangleNoArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\draw [LiftedPathStyle, PathArrowAtPosStyleTwo, PathArrowAtPosStyleEnd, rounded corners=15pt]
(0,0.9*\Tikzn) -- (0,0.2) -- (\Tikzn-0.2,\Tikzn) -- (0.7,0.5) ;
\end{tikzpicture}
}
\newcommand\TikzRREllMinus[1]{ %
\begin{tikzpicture}[scale={#1}]
\MacroChubbySelfFoldedTriangle
\MacroRREllMinus
\end{tikzpicture}
}
\newcommand\TikzDoubleTriangleRddotRL[1]{
\begin{tikzpicture}[scale=#1, DoubleTriangleLightStyle]
\MacroDoubleTriangleNoArrow
\draw (-\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\ddot{r}$};
\draw (\Tikzn,\Tikzn) -- (P) node[pos=0.5,above]{$\dot{r}$};
\draw [LiftedPathStyle, PathArrowAtPosStyleTwo, PathArrowAtPosStyleEnd, rounded corners=5pt] (0,0) -- (0,\Tikzn) -- (\Tikzn,\Tikzn) -- (0.3,0.3) ;
\end{tikzpicture}
}
\newcommand\TikzRREllPlusnonBT[1]{ %
\begin{tikzpicture}[scale={#1}]
\MacroChubbySelfFoldedTriangle
\MacroRREllPlusnonBT
\end{tikzpicture}
}
\newcommand\TikzRLMinLPlus[1]{ %
\begin{tikzpicture}[scale={#1}]
\MacroChubbySelfFoldedTriangle
\MacroRLMinLPlus
\end{tikzpicture}
}
%%%%% end of double lifted triangles %%%%%%%%
\newcommand\WheelLocalTriangulation[1]{ % USED
\begin{tikzpicture}[scale=#1]
\path (0:0) coordinate (origin);
\path (1*50:2) coordinate (1);
\path (2*50:2) coordinate (2);
\path (3*50:2) coordinate (3);
\path (4*50:2) coordinate (4);
\path (5*50:2) coordinate (5);
\path (6*50:2) coordinate (6);
\path (7*50:2) coordinate (7);
\draw [fill=gray!20, style=dashed] (origin) circle (2);
\begin{scope}[NonOrientedTriangulationStyle]
\draw [fill=white] (1) -- (2) -- (3) -- (4) -- (5) -- (6) -- (7) -- cycle;
\draw [postaction={decorate}] (1) -- (origin);
\draw [postaction={decorate}] (2) -- (origin);
\draw [postaction={decorate}] (3) -- (origin);
\draw [postaction={decorate}] (4) -- (origin);
\draw [postaction={decorate}] (5) -- (origin);
\draw [postaction={decorate}] (6) -- (origin);
\draw [postaction={decorate}] (7) -- (origin);
\draw [fill=violet] (origin) circle (1.2*\TikzPunctureActualSize);
\draw (origin) node[above=4pt, right=2pt, violet] {\tiny{$P$}};
\node at (0:3) {}; \node at (180:3) {};
\end{scope}
\end{tikzpicture}
}
\newcommand \SelfFoldedLocalTriangulation[1] { % USED
\begin{tikzpicture}[scale={#1}]
\node at (-4,1) {}; \node at (4,1) {};
\coordinate (v1L) at (-2.5,1);
\coordinate (v1R) at (2.5,1);
\coordinate (v2L) at (-2.5,3.5);
\coordinate (v2R) at (2.5,3);
\begin{scope}[NonOrientedTriangulationStyle]
\draw [style = dashed, fill=gray!20] % left gray area
(0,0) .. controls (-3,2) and (-2,3.5) .. (0,4) -- (v2L) -- (v1L) -- (0,0);
\draw [style = dashed, fill=gray!20] % right gray area
(0,0) .. controls (3,2) and (2,3.5) .. (0,4) -- (v2R) -- (v1R) -- (0,0);
\draw[style = thick, postaction={decorate}, fill=white] (0,0) -- (0,2.2);
\draw (0.2,1) node {$r$};
\draw[style = thick, postaction={decorate}] (0,0) .. controls (-3,4) and (3,4) .. (0,0)
node[pos = 0.7, above]{$\ell$};
\draw[style = thick, postaction={decorate}] (0,0) .. controls (-3,2) and (-2,3.5) .. (0,4);
%node[pos = 0.5,right=0.02pt]{$\a$};
\draw (-2.1,2.7) node {$\a$};
\draw[style = thick, postaction={decorate}] (0,0) .. controls (3,2) and (2,3.5) .. (0,4);
%node[pos = 0.4, right]{$\b$};
\draw (2.05,2) node {\tiny $\b$};
\end{scope}
\coordinate (Ps) at (0,2.2); \coordinate (xs) at (0,0); \coordinate (ys) at (0,4);
\foreach \pos in {(0,0),(0,4)}
{\draw[fill=olive] \pos circle (1.2*\TikzPointActualSize);}
\draw [fill=violet] (Ps) circle (1.2*\TikzPunctureActualSize); \draw[violet] (0,2.2) node[above] {\tiny{$P$}}; %Puncture
\end{tikzpicture}
}
\newcommand\MacroTtwoTpathChubby{
\begin{scope}[thick, gray!60]
\newcommand\localfontsize{\small}
\draw[rounded corners = 20pt] (-4,4) -- (0,7) node[pos=0.8,above,black]{\localfontsize $1$} -- (4,4);
\draw[rounded corners = 15pt] (0,0) --
(-2.5,4) %-- (-3,4)
-- (0,6) node[pos=0.8,black]{\localfontsize $2$} -- (4,4);
\draw[thick] (0,0) -- (0,2.9) node[pos=0.8, right,black]{\localfontsize $r$};
\draw[style = thick, rounded corners = 20pt]
(0,0) .. controls (-1.5,2) and (-2,3) .. (0,5) ..
controls (2,3) and (2,2) .. (0,0) node[pos=0.4, above=2pt,black] {\localfontsize $\ell$};
\draw
(0,0) -- (4,4) -- (0,8) -- node[pos=0.5, left] {} (-4,4) -- (0,0);
\end{scope}
\draw [fill=violet] (0,2.9) circle (.3ex);
}
\newcommand\MacroCounterClockRadius[4]{
\draw[TPathStyle, %blue,style = dashed, thick, %line width = 1pt,
rounded corners = 5pt,
decoration={ markings, mark=at position .3 with {\arrow[line width=1pt]{to};},
mark=at position .8 with {\arrow[line width=1pt]{to};}}, postaction={decorate}]
({#1},{#2}) .. controls (0.2,3) and (0.4,3) .. (0,3.5) %node[pos = 0.4, right]{$w_{j+1}$}
.. controls (-0.4,3) and (-0.2,3) .. ({#3},{#4});% node[pos = 0.6, left]{$w_{j}$};
}
\newcommand\MacroClockLoop[4]{
\draw[TPathStyle, %line width = 1.5pt,
rounded corners = 20pt
,decoration={ markings, mark=at position .73 with {\arrow[blue, line width=1pt]{to};}},
postaction={decorate}]
({#1},{#2}) .. controls (-1.5,2) and (-2,3) .. (0,5) ..
controls (2,3) and (2,2) .. ({#3},{#4}); %node[pos=0.5, right] {$\ell$};
}
\newcommand\MacroClockRadius[4]{
\draw[TPathStyle, %blue,style = dashed, thick, %line width = 1pt,
rounded corners = 5pt,
decoration={ markings, mark=at position .3 with {\arrow[line width=1pt]{to};},
mark=at position .8 with {\arrow[line width=1pt]{to};}}, postaction={decorate}]
({#1},{#2}) .. controls (-0.2,3) and (-0.4,3) .. (0,3.5)
.. controls (0.4,3) and (0.2,3) .. ({#3},{#4});
}
\newcommand\MacroCounterClockLoop[4]{
\draw[TPathStyle, %blue, thick, %line width = 1.5pt,
rounded corners = 20pt
,decoration={ markings, mark=at position .73 with {\arrow[blue, line width=1pt]{to};}},
postaction={decorate}]
({#1},{#2}) .. controls (2,2) and (2,3) .. (0,5) ..
controls (-2,3) and (-1.5,2) .. ({#3},{#4}); %node[pos=0.5, right] {$\ell$};
}
\newcommand\TikzPosterTpathSixNineFontSize{\small}
\newcommand\TikzPosterTpathSixNineCaptionSize{\small}
\newcommand\TikzPosterTpathSixNineCaptionLocation{(-3,-2.6)}
\newcommand\TikzTpathSix[2]{
\begin{tikzpicture} [scale = {#1}]
\begin{scope}[rotate=45]
\MacroTtwoTpathChubby
\begin{scope}[TPathStyle]
\draw[rounded corners = 20pt] (0,8) -- (3,5) -- (0,7) -- (-4,4);
\draw (-4,4) -- (0.2*0,-0.1*0);
\MacroCounterClockRadius{0.2*0}{-0.1*0}{-0.5}{1}
\MacroClockLoop{-0.5}{1}{1}{1}
\draw[->] (1,1) -- (3.8,3.8);
\end{scope}
\end{scope}
%\draw (-3,7) node {($6$)};
\node at (-4,6.3) {\TikzPosterTpathSixNineFontSize $b_4$};
\node at (-3,-0.5) {\TikzPosterTpathSixNineFontSize $b_2$};
\node at (0.5,3) {\TikzPosterTpathSixNineFontSize $b_3$};
\node at \TikzPosterTpathSixNineCaptionLocation {\TikzPosterTpathSixNineCaptionSize #2};
\end{tikzpicture}
}
\newcommand\TikzTpathSixBad[2]{
\begin{tikzpicture} [scale = {#1}]
\begin{scope}[rotate=45]
\MacroTtwoTpathChubby
\begin{scope}[TPathStyle]
\draw[rounded corners = 20pt] (0,8) -- (3,5) -- (0,7) -- (-4,4) ;
\draw (-4,4) -- (-0.2,0);
\MacroClockRadius{-0.2}{0}{0.5}{1.5}
\MacroCounterClockLoop{0.5}{1.5}{0.3}{0.3}%{0.5}{0}
%\draw[->] (0.5,0) -- (3.8,3.8);
\draw[->] (0.3,0.3) -- (3.8,3.8);
\end{scope}
\end{scope}
%\draw (-3,7) node {($6'$)};
\node at (-4,6.3) {\TikzPosterTpathSixNineFontSize $b_4$};
\node at (-3,-0.5) {\TikzPosterTpathSixNineFontSize $b_2$};
\node at (0.5,3) {\TikzPosterTpathSixNineFontSize $b_3$};
%\node[white] at (-6.2,3) {$b_1$};
%\node[] at (-8,3){}; \node[] at (2,3){};
\node at \TikzPosterTpathSixNineCaptionLocation {\TikzPosterTpathSixNineCaptionSize #2};
\end{tikzpicture}
}
\newcommand\TikzTpathSeven[2]{
\begin{tikzpicture} [scale = {#1}]
\begin{scope}[rotate=45]
\MacroTtwoTpathChubby
\begin{scope}[TPathStyle]
\draw[rounded corners = 20pt] (0,8) -- (3,5) -- (0,7) -- (-4,4);
\draw (-4,4) -- (-0.6,0.6);
\MacroClockLoop{-0.6}{0.6}{0.6}{1.3}
\MacroCounterClockRadius{0.6}{1.3}{-0.2*0}{0}
\draw[->] (0,0) -- (3.8,3.8);
\end{scope}
\end{scope}
%\draw (-3,7) node {($7$)};
\node at (-4,6.3) {\TikzPosterTpathSixNineFontSize $b_4$};
\node at (-3,-0.5) {\TikzPosterTpathSixNineFontSize $b_2$};
\node at (0.5,3) {\TikzPosterTpathSixNineFontSize $b_3$};
\node at \TikzPosterTpathSixNineCaptionLocation {\TikzPosterTpathSixNineCaptionSize #2};
\end{tikzpicture}
}
\newcommand\MacroTikzTpathEight[1]{
\begin{scope} [scale = {#1}]
\begin{scope}[rotate=45]
\MacroTtwoTpathChubby
\begin{scope}[TPathStyle]
\draw[rounded corners = 20pt] (0,8) -- (-3,5) -- (0,7) -- (3,5) --
(0,6) -- (-3,4) -- (0.1*0,-0.1*0);
\MacroCounterClockRadius{0.1*0}{-0.1*0}{-0.5}{1.5}
\MacroClockLoop{-0.5}{1.5}{1}{1}
\draw[->] (1,1) -- (3.8,3.8);
\end{scope}
\end{scope}
%\draw (-3,7) node {($8$)};
\end{scope}
}
\newcommand\TikzTpathEight[2]{
\begin{tikzpicture} [scale = {#1}]
\MacroTikzTpathEight{1}
\node at (-6.2,3) {\TikzPosterTpathSixNineFontSize $b_1$};
\node at (0.5,3) {\TikzPosterTpathSixNineFontSize $b_3$};
\node at (-4,6.3) {};
\node at (-3,-0.5) {};
\node at \TikzPosterTpathSixNineCaptionLocation {\TikzPosterTpathSixNineCaptionSize #2};
\end{tikzpicture}
}
\newcommand\TikzTpathNine[2]{
\begin{tikzpicture} [scale = {#1}]
\begin{scope}[rotate=45]
\MacroTtwoTpathChubby
\begin{scope}[TPathStyle]
\draw[rounded corners = 20pt] (0,8) -- (-3,5) -- (0,7) -- (3,5) --
(0,6) -- (-3,4) -- (-1,1);
\MacroClockLoop{-1}{1}{0.3}{1}
\MacroCounterClockRadius{0.3}{1}{0}{0}
\draw[->] (0,0) -- (3.8,3.8);
\end{scope}
\end{scope}
%\draw (-3,7) node {($9$)};