Kinetic data structures: animating proofs through time

Kinetic Data Structures (KDS for short) are a new class of data structures aimed at keeping track of attributes of interest in systems of moving objects [1, 2]. ln this video we illustrate the principies of KDS design in the context of some classical geometric problems, such as the calculation of the convex hull or closest pair of moving points in the plane. ln an ordinary simulation the positions of the points are advanced by a fixed time step, and then the attribute of interest in incrementally recomputed. Since the combii:J.atorial structure of the attribute changes irregularly, it is quite difficult to select a time-step size that avoids both oversampling and undersampling the system. Unlike such fixed step methods, a kinetic data structure performs an event-driven simulation where only events relevant to the attribute of interest are generated and processed. The result is a simulation that is always accurate and with a computation cost dose to the minimum possible. This video presents animations for and contains the description of a few two-dimensional kinetic geometric algorithms: