title: Vector on upper half of hemisphere
body: <p>I have a normal vector <code>N</code>, which defines the upper half of an hemisphere and an function, which creates random points <code>P</code> on the hemisphere.</p>
  
  <p>Now I want to know, if the randomly choosen point is on the upper half. Is it save to assume, if the length of <code>N+P</code> is greater or equal 1, <code>P</code> is on the upper half, or is there a better way to calculate this in <code>glm</code>?</p>