4 research outputs found
CelticGraph: Drawing Graphs as Celtic Knots and Links
Celtic knots are an ancient art form often attributed to Celtic cultures,
used to decorate monuments and manuscripts, and to symbolise eternity and
interconnectedness. This paper describes the framework CelticGraph to draw
graphs as Celtic knots and links. The drawing process raises interesting
combinatorial concepts in the theory of circuits in planar graphs. Further,
CelticGraph uses a novel algorithm to represent edges as B\'ezier curves,
aiming to show each link as a smooth curve with limited curvature.Comment: Appears in the Proceedings of the 31st International Symposium on
Graph Drawing and Network Visualization (GD 2023
Angles of Arc-Polygons and Lombardi Drawings of Cacti
We characterize the triples of interior angles that are possible in
non-self-crossing triangles with circular-arc sides, and we prove that a given
cyclic sequence of angles can be realized by a non-self-crossing polygon with
circular-arc sides whenever all angles are at most pi. As a consequence of
these results, we prove that every cactus has a planar Lombardi drawing (a
drawing with edges depicted as circular arcs, meeting at equal angles at each
vertex) for its natural embedding in which every cycle of the cactus is a face
of the drawing. However, there exist planar embeddings of cacti that do not
have planar Lombardi drawings.Comment: 12 pages, 8 figures. To be published in Proc. 33rd Canadian
Conference on Computational Geometry, 202
Lombardi drawings of knots and links
In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings
Lombardi drawings of knots and links
In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings