latex-pictures

A collection of TikZ drawings and other images 🖌️
sphere-quotient.tikz (898B)

 1 % This picture represents the isomorphism between the n-dimensional sphere and
 2 % the quotient of the (n + 1)-dimensional simple orthogonal group by the
 3 % n-dimensional simple orthogonal group
 4 % Copyright Pablo (C) 2023
 5 \begin{tikzpicture}[scale=0.5]
 6   % The sphere
 7   \begin{scope}
 8     \clip (-3, -3) rectangle (3, 2.625);
 9     \draw (0, 0) circle (3);
10   \end{scope}
11 
12   % The equator
13   \begin{scope}
14     \clip (-3, 0) rectangle (3, -3);
15     \draw ellipse (3 and 1);
16   \end{scope}
17 
18   % Greenwhich
19   \begin{scope}
20     \clip (-3, -3) rectangle (0, 2.625);
21     \draw ellipse (1 and 3);
22   \end{scope}
23 
24   \draw (-3, 2.625) -- ( 1.5, 2.625)
25                     -- (   3, 3.375) node[right]{$T_p \mathbb{S}^n$}
26                     -- (-1.5, 3.375)
27                     -- cycle;
28   \filldraw[black] (0, 3) circle (2pt) node[right]{$p$};
29   \draw (0, 3.375) node[above]{$\operatorname{SO}_n$};
30 \end{tikzpicture}