@inproceedings{05b3e7cc5a28423c8c72dc9f8ae22817,

title = "Lombardi drawings of knots and links",

abstract = "Knot and link diagrams are projections of one or more 3-dimensional simple closed curves into IR2 such that no more than two points project to the same point in IR2 These diagrams are drawings of 4-regular plane multigraphs. Knots are typically smooth curves in IR2 so their projections should be smooth curves in IR2 with good continuity and large crossing angles: exactly the properties of Lombardi graph drawings (defined by circular-arc edges and perfect angular resolution). We show that several knots do not allow plane Lombardi drawings. On the other hand, we identify a large class of 4-regular plane multigraphs that do have Lombardi drawings. We then study two relaxations of Lombardi drawings and show that every knot admits a plane 2-Lombardi drawing (where edges are composed of two circular arcs). Further, every knot is near-Lombardi, that is, it can be drawn as Lombardi drawing when relaxing the angular resolution requirement by an arbitrary small angular offset ε while maintaining a 180° angle between opposite edges.",

author = "Philipp Kindermann and Stephen Kobourov and Maarten L{\"o}ffler and Martin N{\"o}llenburg and Andr{\'e} Schulz and Birgit Vogtenhuber",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2018.; 25th International Symposium on Graph Drawing and Network Visualization, GD 2017 ; Conference date: 25-09-2017 Through 27-09-2017",

year = "2018",

doi = "10.1007/978-3-319-73915-1_10",

language = "English (US)",

isbn = "9783319739144",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "113--126",

editor = "Kwan-Liu Ma and Fabrizio Frati",

booktitle = "Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers",

}