% This picture is a comparison between the euclian distance and the Riemannian 
% distance in a three-dimensional sphere
% Copyright Pablo (C) 2021
\begin{tikzpicture}
  % The cirference
  \draw (0, 0) circle (3);

  % The equator
  \begin{scope}
    \clip (-3, 0) rectangle (3, -3);
    \draw ellipse (3 and 1);
  \end{scope}

  % The equator (on the other side of the sphere)
  \begin{scope}
    \clip (-3, 0) rectangle (3, 3);
    \draw[dotted] ellipse (3 and 1);
  \end{scope}

  \draw[thick, dotted] (0, 3) -- (-1, 0);

  % Greenwhich
  \begin{scope}
    \clip (-3, -3) rectangle (0, 3);
    \draw ellipse (1 and 3);
  \end{scope}

  % Greenwhich (on the other side of the sphere)
  \begin{scope}
    \clip (3, -3) rectangle (0, 3);
    \draw[dotted] ellipse (1 and 3);
  \end{scope}

  % Greenwhich (on the other side of the sphere)
  \begin{scope}
    \clip (-3, 0) rectangle (0, 3);
    \draw[very thick, color=violet] ellipse (1 and 3);
  \end{scope}

  % The dots
  \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt);
\end{tikzpicture}

