  Van Goethem and Verbeek recently showed how to morph between two planar
orthogonal drawings $\Gamma_I$ and $\Gamma_O$ of a connected graph $G$ while
preserving planarity, orthogonality, and the complexity of the drawing during
the morph. Necessarily drawings $\Gamma_I$ and $\Gamma_O$ must be equivalent,
that is, there exists a homeomorphism of the plane that transforms $\Gamma_I$
into $\Gamma_O$. Van Goethem and Verbeek use $O(n)$ linear morphs, where $n$ is
the maximum complexity of the input drawings. However, if the graph is
disconnected their method requires $O(n^{1.5})$ linear morphs. In this paper we
present a refined version of their approach that allows us to also morph
between two planar orthogonal drawings of a disconnected graph with $O(n)$
linear morphs while preserving planarity, orthogonality, and linear complexity
of the intermediate drawings.
  Van Goethem and Verbeek measure the structural difference between the two
drawings in terms of the so-called spirality $s = O(n)$ of $\Gamma_I$ relative
to $\Gamma_O$ and describe a morph from $\Gamma_I$ to $\Gamma_O$ using $O(s)$
linear morphs. We prove that $s+1$ linear morphs are always sufficient to morph
between two planar orthogonal drawings, even for disconnected graphs. The
resulting morphs are quite natural and visually pleasing.

Computational Geometry