latex-pictures

A collection of TikZ drawings and other images 🖌️

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1 file changed, 44 insertions, 0 deletions

diff --git a/upper-stereographic-projection.tikz b/upper-stereographic-projection.tikz
@@ -0,0 +1,44 @@
+% A graphical depiction of the stereographic projection between the upper
+% semi-sphere and the Euclidean plane: we map each point in the upper half of
+% the sphere to the projection of this point in the tangent plane at the north
+% pole by drawing a line between this point and the center of the sphere and
+% then taking the intersection of this line with the plane.
+% Copyright Pablo (C) 2021
+\begin{tikzpicture}[scale=0.8]
+    % The outline of the semi-sphere
+    \begin{scope}
+      \clip (-3, 0) rectangle (3, 3);
+      \draw (0, 0) circle (3);
+    \end{scope}
+            
+    % The equator
+    \begin{scope}
+        \clip (-3, 0) rectangle (3, -1);
+        \draw ellipse (3 and 1);
+    \end{scope}
+            
+    % The equator (on the other side of the sphere)
+    \draw[dotted] ellipse (3 and 1);
+            
+    % The plane
+    \draw[dotted] (-4.5, 1.5) -- 
+                  ( 1.5, 1.5) -- 
+                  ( 4.5, 4.5) -- 
+                  (-1.5, 4.5) -- cycle;
+    
+    % The north pole
+    \filldraw (0, 3) circle (2pt);
+
+    % The center of the sphere
+    \filldraw (0, 0) circle (2pt);
+
+    % A line trhough the center of the sphere
+    \draw (0, 0) -- (1.8, 3);
+
+    % The intersection of the line with the plane
+    \filldraw (1.8, 3) circle (2pt);
+
+    % The intersection of the line and the sphere
+    \filldraw (1.56, 2.57) circle (2pt);
+\end{tikzpicture}
+