While simple approximations to the bbox are trivial (such as computing the bounding box of their control points), in this article we deduce the exact bounding box analytically.
M. Müller, J. Bender, N. Chentanez, und M. Macklin. Proceedings of the 9th International Conference on Motion in Games, Seite 55--60. New York, NY, USA, ACM, (2016)