Since a new Tron movie is coming out, here's a computational geometry problem about Tron:

Given a bunch of Tron motorcycles, each with an initial position and direction, if they all ride on a straight line, who will crash into who?

Solved it in my PhD in O(n^(4/3 + eps)) time, improving the best previously known time of O(n^(4/3 + eps) * log n).

Images are input/output

The problem has applications to working out a roof layout (imagine a motorcycle starting out from each corner of the roof).

Algorithm in Section 3.5 of my dissertation: nilmamano.com/dissertation/nildissertation.pdf