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arXiv · 1808.10826

Upward Planar Morphs

Giordano Da Lozzo·Giuseppe Di Battista·Fabrizio Frati·Maurizio Patrignani·Vincenzo Roselli
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Abstract

We prove that, given two topologically-equivalent upward planar straight-line drawings of an $n$-vertex directed graph $G$, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of $O(1)$ morphing steps if $G$ is a reduced planar $st$-graph, $O(n)$ morphing steps if $G$ is a planar $st$-graph, $O(n)$ morphing steps if $G$ is a reduced upward planar graph, and $O(n^2)$ morphing steps if $G$ is a general upward planar graph. Further, we show that $\Omega(n)$ morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an $n$-vertex path.

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Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, Maurizio Patrignani, Vincenzo Roselli. 2018-08-31. Upward Planar Morphs. https://arxiv.org/abs/1808.10826

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