Plane Sections of the Cylinder – Dandelin Spheres


dandelin-spheres

Edit and compile if you like:

% Plane Sections of the Cylinder - Dandelin Spheres
% Author: Hugues Vermeiren
\documentclass{article}
\usepackage{tikz}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{10pt}%
\tikzset{
MyPersp/.style={scale=1.8,x={(-0.8cm,-0.4cm)},y={(0.8cm,-0.4cm)},
z={(0cm,1cm)}},
% MyPersp/.style={scale=1.5,x={(0cm,0cm)},y={(1cm,0cm)},
% z={(0cm,1cm)}}, % uncomment the two lines to get a lateral view
MyPoints/.style={fill=white,draw=black,thick}
}
\begin{document}
\begin{tikzpicture}[MyPersp,font=\large]
% the base circle is the unit circle in plane Oxy
\def\h{2.5}% Heigth of the ellipse center (on the axis of the cylinder)
\def\a{35}% angle of the section plane with the horizontal
\def\aa{35}% angle that defines position of generatrix PA--PB
\pgfmathparse{\h/tan(\a)}
\let\b\pgfmathresult
\pgfmathparse{sqrt(1/cos(\a)/cos(\a)-1)}
\let\c\pgfmathresult %Center Focus distance of the section ellipse.
\pgfmathparse{\c/sin(\a)}
\let\p\pgfmathresult % Position of Dandelin spheres centers
% on the Oz axis (\h +/- \p)
\coordinate (A) at (2,\b,0);
\coordinate (B) at (-2,\b,0);
\coordinate (C) at (-2,-1.5,{(1.5+\b)*tan(\a)});
\coordinate (D) at (2,-1.5,{(1.5+\b)*tan(\a)});
\coordinate (E) at (2,-1.5,0);
\coordinate (F) at (-2,-1.5,0);
\coordinate (CLS) at (0,0,{\h-\p});
\coordinate (CUS) at (0,0,{\h+\p});
\coordinate (FA) at (0,{\c*cos(\a)},{-\c*sin(\a)+\h});% Focii
\coordinate (FB) at (0,{-\c*cos(\a)},{\c*sin(\a)+\h});
\coordinate (SA) at (0,1,{-tan(\a)+\h}); % Vertices of the
% great axes of the ellipse
\coordinate (SB) at (0,-1,{tan(\a)+\h});
 
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Click to download: dandelin-spheres.texdandelin-spheres.pdf
Open in Overleaf: dandelin-spheres.tex