TY - GEN
T1 - Smooth orthogonal layouts
AU - Bekos, Michael A.
AU - Kaufmann, Michael
AU - Kobourov, Stephen G.
AU - Symvonis, Antonios
N1 - Funding Information:
The work of M.A. Bekos is implemented within the framework of the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State. The work of S. G. Kobourov is supported in part by NSF grant CCF-1115971 and a grant from the Humboldt Foundation.
PY - 2013
Y1 - 2013
N2 - We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axis-aligned line segments, in smooth orthogonal layouts every edge is made of axis-aligned segments and circular arcs with common tangents. Our goal is to create such layouts with low edge complexity, measured by the number of line and circular arc segments. We show that every biconnected 4-planar graph has a smooth orthogonal layout with edge complexity 3. If the input graph has a complexity-2 traditional orthogonal layout, we can transform it into a smooth complexity-2 layout. Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout.
AB - We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axis-aligned line segments, in smooth orthogonal layouts every edge is made of axis-aligned segments and circular arcs with common tangents. Our goal is to create such layouts with low edge complexity, measured by the number of line and circular arc segments. We show that every biconnected 4-planar graph has a smooth orthogonal layout with edge complexity 3. If the input graph has a complexity-2 traditional orthogonal layout, we can transform it into a smooth complexity-2 layout. Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout.
UR - http://www.scopus.com/inward/record.url?scp=84874131540&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874131540&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-36763-2_14
DO - 10.1007/978-3-642-36763-2_14
M3 - Conference contribution
AN - SCOPUS:84874131540
SN - 9783642367625
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 150
EP - 161
BT - Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers
T2 - 20th International Symposium on Graph Drawing, GD 2012
Y2 - 19 September 2012 through 21 September 2012
ER -