Convexity-Increasing Morphs of Planar Graphs

@inproceedings{Kleist2018ConvexityIncreasingMO,
  title={Convexity-Increasing Morphs of Planar Graphs},
  author={Linda Kleist and Boris Klemz and Anna Lubiw and Lena Schlipf and Frank Staals and Darren Strash},
  booktitle={International Workshop on Graph-Theoretic Concepts in Computer Science},
  year={2018}
}
We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of a 3-connected graph, we show how to morph the drawing to one with convex faces while maintaining planarity at all times. Furthermore, the morph is convexity increasing, meaning that angles of inner faces never change from convex to reflex. We give a polynomial time algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along… 
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