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Dr. techn. Ing. Jan Legerský

Publikace

Computing Animations of Linkages with Rotational Symmetry

Autoři
Dewar, S.; Grasegger, G.; Legerský, J.
Rok
2020
Publikováno
36th International Symposium on Computational Geometry (SoCG 2020). Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2020. Leibniz International Proceedings in Informatics (LIPIcs). vol. 164. ISSN 1868-8969. ISBN 978-3-95977-143-6.
Typ
Stať ve sborníku
Anotace
We present a piece of software for computing animations of linkages with rotational symmetry in the plane. We construct these linkages from an algorithm that utilises a special type of edge colouring to embed graphs with rotational symmetry.

FlexRiLoG—A SageMath Package for Motions of Graphs

Autoři
Grasegger, G.; Legerský, J.
Rok
2020
Publikováno
Mathematical Software – ICMS 2020. Springer, Cham, 2020. p. 442-450. Lecture Notes in Computer Science. vol. 12097. ISSN 0302-9743. ISBN 978-3-030-52199-8.
Typ
Stať ve sborníku
Anotace
In this paper we present the SageMath package FlexRiLoG (short for flexible and rigid labelings of graphs). Based on recent results the software generates motions of graphs using special edge colorings. The package computes and illustrates the colorings and the motions. We present the structure and usage of the package.

On the Classification of Motions of Paradoxically Movable Graphs

Autoři
Grasegger, G.; Legerský, J.; Schicho, J.
Rok
2020
Publikováno
Journal of Computational Geometry. 2020, 11(1), 548-575. ISSN 1920-180X.
Typ
Článek
Anotace
Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown recently that a graph has flexible edge lengths if and only if the graph has a special type of edge coloring called NAC-coloring. We address the question how to determine paradoxical motions of a generically rigid graph, namely, proper flexible edge lengths of the graph. We do so using the set of all NAC-colorings of the graph and restrictions to 4-cycle subgraphs.