How to morph planar graph drawings

Soroush Alamdari, Patrizio Angelini, Fidel Barrera-Cruz, Timothy M. Chan, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, Penny Haxell, Anna Lubiw, Maurizio Patrignani, Vincenzo Roselli, Sahil Singla, Bryan T. Wilkinso

Research output: Contribution to journalArticle


Given an n-vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous transformation) between the two drawings that preserves straight-line planarity and consists of O(n) steps, which we prove is optimal in the worst case. Each step is a unidirectional linear morph, which means that every vertex moves at constant speed along a straight line, and the lines are parallel although the vertex speeds may differ. Thus we provide an efficient version of Cairns' 1944 proof of the existence of straight-line planarity-preserving morphs for triangulated graphs, which required an exponential number of steps.

Original languageEnglish (US)
Pages (from-to)824-852
Number of pages29
JournalSIAM Journal on Computing
Issue number2
StatePublished - Jan 1 2017
Externally publishedYes


  • Morph
  • Planar graphs
  • Transformation

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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  • Cite this

    Alamdari, S., Angelini, P., Barrera-Cruz, F., Chan, T. M., Da Lozzo, G., Di Battista, G., Frati, F., Haxell, P., Lubiw, A., Patrignani, M., Roselli, V., Singla, S., & Wilkinso, B. T. (2017). How to morph planar graph drawings. SIAM Journal on Computing, 46(2), 824-852.