title: determine trajectory for object followers - curve of pursuit
body: <p>I have started to develop unit trajectories for a game server and for now I'm trying to retrieve the position of a unit at a given time. It is easy when the trajectory is just a straight line, but it is far more complicated when unit chases another unit.</p>
  
  <p>I've done <a href="http://evonline.org/splines/SplinesWeb.html" rel="nofollow noreferrer">flash app</a> to illustrate the problem. Black trajectory is for unit which travels in a single direction. Blue chases black and red chases blue. What I want is to precalculate whole trajectory for blue and red to be able to retrieve their position in a constant time.</p>
  
  <p>Is it possible? Thanks for any help!!</p>
  
  <p><img src="https://i.stack.imgur.com/QvZQd.jpg" alt="enter image description here"></p>