latex-pictures

A collection of TikZ drawings and other images 🖌️
quaternion-rotation.tikz (1422B)

 1 % This drawing represents the correspondance between conjugation by pure
 2 % unitary quaternions and rotations in the 3-dimensional euclidian space: the
 3 % coordinates of a unitary quaternion p number with zero real cofficient induce
 4 % a line through the origin in the 3-dimensional enclidian space, and
 5 % conjugation by cos t + p sin t acts as rotation by 2 t around this axis.
 6 % Copyright Pablo (C) 2021
 7 \begin{tikzpicture}
 8   % The rotation axis
 9   \begin{scope}[rotate=-60]
10     % The axis
11     \draw[->] (0, 0) -- (0, 2.5) node[right]{$p$};
12 
13     % The rotation
14     \draw[->] (0.43, 2) node[right]{$2 \theta$} arc (30:360:0.5 and 0.25);
15 
16     % The origin and the intersection of ratation axis with the unit sphere
17     \filldraw (0, 0) circle (1pt) (0, 1) circle (1pt);
18   \end{scope}
19 
20   % The circunference
21   \draw (0, 0) circle (1.5);
22 
23   % The equator
24   \begin{scope}
25     \clip (-1.5, 0) rectangle (1.5, -1.5);
26     \draw ellipse (1.5 and 0.5);
27   \end{scope}
28 
29   % The equator (on the other side of the sphere)
30   \begin{scope}
31     \clip (-1.5, 0) rectangle (1.5, 1.5);
32     \draw[dotted] ellipse (1.5 and 0.5);
33   \end{scope}
34 
35   % Greenwhich
36   \begin{scope}
37     \clip (-1.5, -1.5) rectangle (0, 1.5);
38     \draw ellipse (0.5 and 1.5);
39   \end{scope}
40 
41   % Greenwhich (on the other side of the sphere)
42   \begin{scope}
43     \clip (1.5, -1.5) rectangle (0, 1.5);
44     \draw[dotted] ellipse (0.5 and 1.5);
45   \end{scope}
46 \end{tikzpicture}