Morphing Rectangular Duals

We consider the problem of morphing between rectangular duals of a plane graph $G$, that is, contact representations of $G$ by axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts. If we require that we have a rectangular dual continuously throughout the morph, then a morph only exists if the source and target rectangular duals realize the same REL. Hence, we are less strict and allow intermediate contact representations of non-rectangular polygons of constant complexity (at most 8-gons). We show how to compute a morph consisting of $O(n^2)$ linear morphs in $O(n^3)$ time. We implement the rotations of RELs as linear morphs to traverse the lattice structure of RELs.