map Cassini's oval to unit disk

[T-O7]

Okay, so i'm having problems figuring out how exactly i can map the interior of Cassini's oval (|z^2-a^2|<r^2 , 0<a<r) onto the unit disk (|w|<1), so that the axis of symmetry are preserved. Anyone know how to do this? :confused:
(In this case, the cassini oval is a peanut shaped domain, i think)

[ReyChiquito]

Tuff question... Interesting though. Ill do some research and see what i can come up with. Meanwhile ive found some Cassinis ovals here (http://astronomy.swin.edu.au/~pbourke/surfaces/egg/)