Risanje vozlov s krožnimi loki

VENE, ŽIGA (author), Fijavž, Gašper (mentor)

Kinderman je s soavtorji razvil sistem za risanje vozlov, kjer za posamezne odseke vozlovega diagrama uporabimo po en krožni lok; tako imenovane Lombardi risbe vozlov. Sistem so podali za diagrame vozlov, v katerih je vsaj eden izmed grafov lic enostaven. V delu opišemo in razdelamo celoten postopek pretvorbe PD zapisa vozlovega diagrama v njegovo risbo. Iz PD zapisa najprej izračunamo graf vozla in grafa lic. Grafa lic s pomočjo Möbiusovih transformacij predstavimo s primarno-dualnim pakiranjem krožnic, na katerem izrišemo diagram vozla, kjer posamezen segment vozlovega diagrama predstavimo s krožnim lokom. Graf vozla po potrebi razširimo z dodatnimi križišči, če ga v primarno-dualno pakiranje ne moremo pretvoriti direktno. Postopek smo v celoti izdelali in delo zaključili z izrisom 664 diagramov vozlov.

• Language: Slovenian
• Keywords: vozel, diagram vozla, ravninski graf, risanje grafov, Lombardi risba, risba s krožnimi loki, primarno-dualno pakiranje krožnic
• Work type: Bachelor thesis/paper
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2020
• PID: 20.500.12556/RUL-116841
• COBISS.SI-ID: 19404803
• Publication date in RUL: 12.06.2020

Secondary language

• Language: English
• Title: Drawing knots using circular arcs

Abstract

Kinderman et al. have introduced a knot layout in which every segment of a knot diagram is a circular arc, also called Lombardi drawings. We describe and discuss the transformation of a knot diagram in PD notation into a knot drawing. We first translate PD notation into a knot graph and it's primal-dual multigraph pair. We calculate a primal-dual circle packing, in which we find the circular arcs representing knot diagram segments. If the primal-dual multigraph pair cannot be transformed into a primal-dual circle packing directly we first extend it. The whole procedure was implemented and using it we generated 664 Lombardi drawings.

• Keywords: knot, knot diagram, planar graph, graph drawing, Lombardi drawing, drawing using circular arcs, primal-dual circle packing