  An ab initio analytical model for Fano resonances in two-channel systems is
presented. We find that the lineshape parameter q factors into a background
contribution q_b that depends only on the uncoupled channels and an interaction
contribution q_i that is affected by the coupling between the channels,
revealing how the overall lineshape parameter q may be controlled. In
particular, we show how conical intersections of the background phase shifts
have an important role in the interplay between q_b and q_i. Finally, control
of Fano transmission profiles through q_b and q_i is demonstrated for quantum
billiards.
