  We obtain limit shape of perfect matchings on a large class of rail-yard
graphs with right boundary condition given by the empty partition, and left
boundary condition given by either by a staircase partition with constant
density or a piecewise partition with densities either 1 or 0. We prove the
parametric equations for the frozen boundary, and find conditions under which
the frozen boundary is a cloud curve, or a union of disjoint cloud curves.
