Morphing Planar Graph Drawings with a Polynomial Number of Steps
نویسندگان
چکیده
In 1944, Cairns proved the following theorem: given any two straight-line planar drawings of a triangulation with the same outer face, there exists a morph (i.e., a continuous transformation) between the two drawings so that the drawing remains straight-line planar at all times. Cairns’s original proof required exponentially many morphing steps. We prove that there is a morph that consists ofO(n) steps, where each step is a linear morph that moves each vertex at constant speed along a straight line. Using a known result on compatible triangulations this implies that for a general planar graph G and any two straight-line planar drawings ofGwith the same embedding, there is a morph between the two drawings that preserves straight-line planarity and consists ofO(n) steps.
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Morphing Planar Graphs Drawings Efficiently
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