2016/06/01 by Soroush Alamdari, Patrizio Angelini, Alamdari, Soroush +23
Computer Science · Engineering · #68R10 #Advanced Image and Video Retrieval Techniques #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Robotics and Sensor-Based Localization
paper · pdf · doi:10.48550/arxiv.1606.00425
openalex publication_date 2016/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.