  In the paper arXiv:1803.11463, the authors study the arctic curve arising in
random tilings of some planar domains with an arbitrary distribution of defects
on one edge. Using the tangent method they derive a parametric equation for
portions of arctic curve in terms of an arbitrary piecewise differentiable
function that describes the defect distribution. When this distribution
presents "freezing" intervals, other portions of arctic curve appear and
typically have a cusp. These freezing boundaries can be of two types,
respectively with maximal or minimal density of defects. Our purpose here is to
extend the tangent method derivation of arXiv:1803.11463 to include these
portions, hence answering the open question stated in arXiv:1803.11463.
