You need to visualise the mapping from coordinate (s,t) to (t1,t2) (or reverse)
with t1=st and t2=s(1-t) (or s=t1+t2 and t=t1/(t1+t2)).
In this mapping you have to check how the boundaries are transformed,
and to check if there is no tear in the domain.
In case there is a tear curve, you need to divide your domain along the tear.