%0 Journal Article %1 befklow-mpgdt3d-CGT23 %A Buchin, Kevin %A Evans, Will %A Frati, Fabrizio %A Kostitsyna, Irina %A Löffler, Maarten %A Ophelders, Tim %A Wolff, Alexander %D 2023 %J Comput. Geom. Topol. %K %N 1 %P 5:1--5:18 %R 10.57717/cgt.v2i1.33 %T Morphing Planar Graph Drawings Through 3D %V 2 %X In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an $n$-vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with $O(n^2)$ steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.

@article{befklow-mpgdt3d-CGT23, abstract = {In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an $n$-vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with $O(n^2)$ steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.}, added-at = {2023-12-12T21:39:02.000+0100}, author = {Buchin, Kevin and Evans, Will and Frati, Fabrizio and Kostitsyna, Irina and L{\"o}ffler, Maarten and Ophelders, Tim and Wolff, Alexander}, biburl = {https://www.bibsonomy.org/bibtex/2e4b917373ae8da414f13625044eab3c4/admin}, doi = {10.57717/cgt.v2i1.33}, interhash = {415d6d71de3327ccff01cc205b165160}, intrahash = {e4b917373ae8da414f13625044eab3c4}, journal = {Comput. Geom. Topol.}, keywords = {}, number = 1, pages = {5:1--5:18}, slides = {http://www1.pub.informatik.uni-wuerzburg.de/pub/wolff/slides/befklow-mpgdt3d-SOFSEM23-slides.pdf}, timestamp = {2023-12-12T21:39:02.000+0100}, title = {Morphing Planar Graph Drawings Through {3D}}, volume = 2, year = 2023 }