% This picture represents the stereographic projection
% (C) Thiago Brevidelli
\begin{tikzpicture}[scale=0.4]
  % The outline of the sphere
  \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}

  % The plane
  \draw (-9, -4) -- (-5,  0) 
                 -- (-3,  0) 
        ( 3,  0) -- ( 9,  0) 
                 -- ( 5, -4) 
                 -- (-9, -4);

  % A line trought the sphere and the plane
  \coordinate (N) at (0,  3);
  \coordinate (a) at (2, -1);
  \coordinate (b) at (3, -3);
  \draw[dotted] (N) -- (a);
  \draw         (a) -- (b);

  % The dots
  \filldraw (N) circle (2pt) (a) circle (2pt) (b) circle (2pt);
\end{tikzpicture}
