TY - GEN

T1 - Optimal morphs of planar orthogonal drawings II

AU - van Goethem, Arthur

AU - Speckmann, Bettina

AU - Verbeek, Kevin

PY - 2019/11/28

Y1 - 2019/11/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85076896754&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-35802-0_3

DO - 10.1007/978-3-030-35802-0_3

M3 - Conference contribution

AN - SCOPUS:85076896754

SN - 978-3-030-35801-3

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 33

EP - 45

BT - Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings

A2 - Archambault, Daniel

A2 - Tóth, Csaba D.

PB - Springer

CY - Cham

T2 - 27th International Symposium on Graph Drawing and Network Visualization, GD 2019

Y2 - 17 September 2019 through 20 September 2019

ER -