Morphing Schnyder Drawings of Planar Triangulations

  • Fidel Barrera-Cruz
  • Penny Haxell
  • Anna Lubiw
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

We consider the problem of morphing between two planar drawings of the same triangulated graph, maintaining straight-line planarity. A paper in SODA 2013 gave a morph that consists of O(n2) steps where each step is a linear morph that moves each of the n vertices in a straight line at uniform speed [1]. However, their method imitates edge contractions so the grid size of the intermediate drawings is not bounded and the morphs are not good for visualization purposes. Using Schnyder embeddings, we are able to morph in O(n2) linear morphing steps and improve the grid size to O(nO(n) for a significant class of drawings of triangulations, namely the class of weighted Schnyder drawings. The morphs are visually attractive. Our method involves implementing the basic “flip” operations of Schnyder woods as linear morphs.

Keywords

algorithms computational geometry graph theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Fidel Barrera-Cruz
    • 1
  • Penny Haxell
    • 1
  • Anna Lubiw
    • 1
  1. 1.University of WaterlooWaterlooCanada

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