  Collisions between nuclei at ultrarelativistic energies produce a
color-deconfined plasma that expands explosively and rapidly reverts to the
color-confined (hadronic) state. In non-central collisions, the zone of hot
matter is transversely anisotropic and may be "tilted" relative to the
direction of the incoming beams. As the matter cools and expands into the
vacuum, the evolution of the system shape depends sensitively on the dynamical
response of the plasma under extreme conditions. Two-pion intensity
interferometry performed relative to the impact parameter can be used to
measure the approximate final shape of the system, when pions decouple from the
system. We use several transport models to illustrate the dependence of the
final shape on the QCD equation of state and late-stage hadronic rescattering.
The dependence of the final shape on collision energy may reveal non-trivial
structures in the QCD phase diagram. Indeed, the few measurements published to
date show a tantalizing behaviour in an energy region under intense
experimental and theoretical scrutiny, as signatures of a first-order phase
transition may appear there. We discuss strong parallels between shape studies
in heavy ion collisions and those in two other strongly-coupled systems.
