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Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

Authors Luca Castelli Aleardi, Gaspard Denis, Éric Fusy



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Author Details

Luca Castelli Aleardi
  • LIX - École Polytechnique, Palaiseau, France
Gaspard Denis
  • LIX - École Polytechnique, Palaiseau, France
Éric Fusy
  • LIX - École Polytechnique, Palaiseau, France

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Luca Castelli Aleardi, Gaspard Denis, and Éric Fusy. Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 24:1-24:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.SEA.2018.24

Abstract

We consider the problem of computing a spherical crossing-free geodesic drawing of a planar graph: this problem, as well as the closely related spherical parameterization problem, has attracted a lot of attention in the last two decades both in theory and in practice, motivated by a number of applications ranging from texture mapping to mesh remeshing and morphing. Our main concern is to design and implement a linear time algorithm for the computation of spherical drawings provided with theoretical guarantees. While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders. We provide experimental comparison with initial placers based on planar Tutte parameterization. Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local minima.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • Graph drawing
  • planar triangulations
  • spherical parameterizations

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