Optimal morphs of planar orthogonal drawings II

Van Goethem and Verbeek [12] recently showed how to morph between two planar orthogonal drawings (Forumala Presented). of a connected graph G while preserving planarity, orthogonality, and the complexity of the drawing during the morph. Necessarily drawings (Forumala Presented). must be equivalent, that is, there exists a homeomorphism of the plane that transforms (Forumala Presented). 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 (Forumala Presented). 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 (Forumala Presented). and describe a morph from (Forumala Presented). using O(s) linear morphs. We prove that 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.