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%
% polargleichung.tex -- Kegelschnitte in Polardarstellung
%
% (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{2}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\p{1}
\begin{scope}
\clip (-4,-3) rectangle (1.1,3);
\fill[color=blue!20]
(0,1)
--
plot[domain=90:-90,samples=100] ({\x}:{\p/(1+cos(\x))})
--
(0,-1) arc (-90:90:1)
--
cycle;
\fill[color=blue!20]
(0,1) arc (90:270:1)
--
plot[domain=-90:-145,samples=20] ({\x}:{\p/(1+cos(\x))})
--
plot[domain=145:90,samples=20] ({\x}:{\p/(1+cos(\x))})
--
cycle;
\fill[color=darkgreen!20]
plot[domain=90:-90,samples=100] ({\x}:{\p/(1+cos(\x))})
-- cycle;
\fill[color=darkgreen!20]
(0,1)
--
(0,3)
--
plot[domain=145:90,samples=20] ({\x}:{\p/(1+cos(\x))})
--
cycle;
\fill[color=darkgreen!20]
(0,-1)
--
(0,-3)
--
plot[domain=-145:-90,samples=20] ({\x}:{\p/(1+cos(\x))})
--
cycle;
\end{scope}
\draw[->] (-4.1,0) -- (1.3,0) coordinate[label={$\varphi=0$}];
\draw (0,-3.1) -- (0,3.1);
\begin{scope}
\clip (-4,-3) rectangle (1.1,3);
\draw[color=red,line width=1.4pt] (0,0) circle[radius=1];
\foreach \e in {10,20,...,90}{
\draw[color=blue!\e!red,line width=1.4pt]
plot[domain=0:360,samples=100]
(\x:{\p/(1+(\e/100)*cos(\x))});
}
\draw[color=blue,line width=1.4pt]
plot[domain=-145:145,samples=100] ({\x}:{\p/(1+cos(\x))});
\foreach \e in {10,30,50,70,90}{
\draw[color=darkgreen!\e!blue,line width=1.4pt]
plot[domain={-138+\e/5}:{138-\e/5},samples=100]
(\x:{\p/(1+((\e+100)/100)*cos(\x))});
}
\end{scope}
\fill[color=white] (0,1) circle[radius=0.04];
\draw (0,1) circle[radius=0.04];
\fill[color=white] (0,-1) circle[radius=0.04];
\draw (0,-1) circle[radius=0.04];
\node at (0,0.6) [left] {$p$};
\node at (0,0) [below left] {$O$};
\fill[color=white] (0,0) circle[radius=0.04];
\draw (0,0) circle[radius=0.04];
\node[color=red] at (45:1) [above right] {$\varepsilon=0$};
\node[color=red] at ($(45:1)+(0,0.2)$) [above right] {Kreis:};
\node[color=blue!70!red] at (-3.5,0.7) {$\varepsilon=0.7$};
\node[color=blue!70!red] at (-3.5,0.9) {Ellipse:};
\node[color=blue] at (-3.4,2.65) [rotate=-18] {Parabel: $\varepsilon=1$};
\node[color=darkgreen!90!blue] at (-1,2.8) [right] {Hyperbel: $\varepsilon=1.9$};
%\draw[color=yellow]
% plot[domain=90:-90,samples=100] ({\x}:{\p/(1+cos(\x))});
\end{tikzpicture}
\end{document}
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