latex-pictures

A collection of TikZ drawings and other images 🖌️
upper-central-projection.tikz (1376B)

 1 % A graphical depiction of the central projection between the upper
 2 % semi-sphere and the Euclidean plane: we map each point in the upper half of
 3 % the sphere to the projection of this point in the tangent plane at the north
 4 % pole by drawing a line between this point and the center of the sphere and
 5 % then taking the intersection of this line with the plane.
 6 % Copyright Pablo (C) 2021
 7 \begin{tikzpicture}[scale=0.8]
 8     % The outline of the semi-sphere
 9     \begin{scope}
10       \clip (-3, 0) rectangle (3, 3);
11       \draw (0, 0) circle (3);
12     \end{scope}
13             
14     % The equator
15     \begin{scope}
16         \clip (-3, 0) rectangle (3, -1);
17         \draw ellipse (3 and 1);
18     \end{scope}
19             
20     % The equator (on the other side of the sphere)
21     \draw[dotted] ellipse (3 and 1);
22             
23     % The plane
24     \draw[dotted] (-4.5, 1.5) -- 
25                   ( 1.5, 1.5) -- 
26                   ( 4.5, 4.5) -- 
27                   (-1.5, 4.5) -- cycle;
28     
29     % The north pole
30     \filldraw (0, 3) circle (2pt);
31 
32     % The center of the sphere
33     \filldraw (0, 0) circle (2pt);
34 
35     % A line trhough the center of the sphere
36     \draw (0, 0) -- (1.8, 3);
37 
38     % The intersection of the line with the plane
39     \filldraw (1.8, 3) circle (2pt);
40 
41     % The intersection of the line and the sphere
42     \filldraw (1.56, 2.57) circle (2pt);
43 \end{tikzpicture}
44