I volunteered to make an applet that has 2 graphs. On one you can click stuff and on the other one the lorentz transformation of the point that you clicked is shown. You should be able to see the cosmic lines and hyperboles. I tried to do this in java for a start but java is really not plug & play with these and we need this to be short and sweet, so JavaScript.
To use this, download the .js file and the .html. Place them in a folder bythemselves and open the .html file. I've tested it Chrome and Firefox. It works, most of the time. If not give some other browsers a try.
I'll try to use CanvasJS and/or Jquery, if the need arises. EDIT: It didn't, thank God.
People i need to thank for helping me with learning Java, HTML, JavaScript and making the thing work: Dimitris Stamatiou, Panagiotis Kinnas, Leonidas Arsenopoulos, Thanasis Ermidis, Mixalis Kalogris