Risanje vozlov s krožnimi loki

diplomsko delo

Žiga Vene (Author), Gašper Fijavž (Mentor)

Abstract

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.

Keywords

vozel;diagram vozla;ravninski graf;risanje grafov;Lombardi risba;risba s krožnimi loki;primarno-dualno pakiranje krožnic;računalništvo;računalništvo in informatika;računalništvo in matematika;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[Ž. Vene]
UDC:	51:004(043.2)
COBISS:	19404803
Views:	565
Downloads:	201
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Drawing knots using circular arcs
Secondary 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.
Secondary keywords:	knot;knot diagram;planar graph;graph drawing;Lombardi drawing;drawing using circular arcs;primal-dual circle packing;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	54 str.
ID:	11824625