Let D0,
D1,...,Dk
be the trapezoids intersected by si, ordered from left to
right.
D0 is the trapezoid containing the left endpoint p
of si. To find it, perform a query on D (the
data structure corresponding to the segments inserted so far) with p.
We have to be careful if p was already present as an endpoint (assume
the new point is slightly to the right).
Dj+1 must be a right neighbor of Dj,
and it is easy to determine which one: If rightp(Dj)
lies above si, then Dj+1
is the lower right neighbor of Dj,
otherwise it is its upper right neighbor.
Update T
and D.
