Star Shaped Orthogonal Drawing

An orthogonal drawing of a plane graph \(G\) is a planar drawing, denoted by \(D(G)\), of \(G\) such that each vertex of \(G\) is drawn as a point on the plane, and each edge is drawn as a sequence of horizontal and vertical line segments with no crossings. \(D(G)\) is called orthogonally convex if each of its faces is an orthogonally convex polygon \(P\). (Namely, for any horizontal or vertical line \(L\), the intersection of \(L\) and \(P\) is a single line segment or empty). Recently, Chang et al. [1] gave a necessary and sufficient condition for a plane graph to have such a drawing.