I used to work at Disney Research. This is a great example of the kinds of problems that get explored there. The constraints are totally different than the normal consumer-focused engineering you find elsewhere, because the creative conceits are simultaneously a challenge and a get-out-of-jail-free card.

The impossible parts of problems could be solved by visual sleight of hand or some artistic trick, leaving you open to explore and solve some really interesting application specific problems with technology. The much, much harder part is making any of this research work robust and compelling enough to actually show in the parks.