%
% lemnispara.tex -- parametrization of the lemniscate
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math,calc}
\begin{document}
\def\skala{1}

\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\dx{4}
\def\dy{4}
\input{lemnisparadata.tex}

% add image content here
\draw[color=red!20,line width=1.4pt] \lemnispathmore;
\draw[color=red,line width=1.4pt] \lemnispath;

\draw[->] ({-1.6*\dx},0) -- ({1.8*\dx},0) coordinate[label={$X$}];
\draw[->] (0,{-0.7*\dy}) -- (0,{0.7*\dy}) coordinate[label={right:$Y$}];

\draw ({1.5*\dx},-0.05) -- ({1.5*\dx},0.05);
\draw ({\dx},-0.05) -- ({\dx},0.05);
\draw ({0.5*\dx},-0.05) -- ({0.5*\dx},0.05);
\draw ({-0.5*\dx},-0.05) -- ({-0.5*\dx},0.05);
\draw ({-\dx},-0.05) -- ({-\dx},0.05);
\draw ({-1.5*\dx},-0.05) -- ({-1.5*\dx},0.05);
\draw (-0.05,{0.5*\dy}) -- (0.05,{0.5*\dy});
\draw (-0.05,{-0.5*\dy}) -- (0.05,{-0.5*\dy});

\node at ({\dx},0) [above] {$1$};
\node at ({-\dx},0) [above] {$-1$};
\node at ({-0.5*\dx},0) [above] {$-\frac12$};
\node at ({0.5*\dx},0) [above] {$\frac12$};
\node at (0,{0.5*\dy}) [left] {$\frac12$};
\node at (0,{-0.5*\dy}) [left] {$-\frac12$};

\def\s{0.02}

\draw[color=red] ($(LA)-\s*(NA)$) -- ($(LA)+\s*(NA)$);
\draw[color=red] ($(LB)-\s*(NB)$) -- ($(LB)+\s*(NB)$);
\draw[color=red] ($(LC)-\s*(NC)$) -- ($(LC)+\s*(NC)$);
\draw[color=red] ($(LD)-\s*(ND)$) -- ($(LD)+\s*(ND)$);
\draw[color=red] ($(LE)-\s*(NE)$) -- ($(LE)+\s*(NE)$);
\draw[color=red] ($(LF)-\s*(NF)$) -- ($(LF)+\s*(NF)$);
\draw[color=red] ($(LG)-\s*(NG)$) -- ($(LG)+\s*(NG)$);
\draw[color=red] ($(LH)-\s*(NH)$) -- ($(LH)+\s*(NH)$);
\draw[color=red] ($(LI)-\s*(NI)$) -- ($(LI)+\s*(NI)$);
\draw[color=red] ($(LJ)-\s*(NJ)$) -- ($(LJ)+\s*(NJ)$);
\draw[color=red] ($(LK)-\s*(NK)$) -- ($(LK)+\s*(NK)$);
\draw[color=red] ($(LL)-\s*(NL)$) -- ($(LL)+\s*(NL)$);
\draw[color=red] ($(LM)-\s*(NM)$) -- ($(LM)+\s*(NM)$);
\draw[color=red] ($(LN)-\s*(NN)$) -- ($(LN)+\s*(NN)$);
\draw[color=red] ($(LO)-\s*(NO)$) -- ($(LO)+\s*(NO)$);
\draw[color=red] ($(LP)-\s*(NP)$) -- ($(LP)+\s*(NP)$);
\draw[color=red] ($(LQ)-\s*(NQ)$) -- ($(LQ)+\s*(NQ)$);
\draw[color=red] ($(LR)-\s*(NR)$) -- ($(LR)+\s*(NR)$);
\draw[color=red] ($(LS)-\s*(NS)$) -- ($(LS)+\s*(NS)$);
\draw[color=red] ($(LT)-\s*(NT)$) -- ($(LT)+\s*(NT)$);
\draw[color=red] ($(LU)-\s*(NU)$) -- ($(LU)+\s*(NU)$);

\CB
\CC
\CD
\CE
\CF
\CG
\CH
\CI
\CJ
\CK
\CL
\CM
\CN
\CO
\CP
\CQ
\CR
\CS
\CT
\CU

\fill[color=blue] (LA) circle[radius=0.07];
\node[color=blue] at (LA) [above right] {$S$};

\end{tikzpicture}
\end{document}