Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools
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.
Graph drawing
planar triangulations
spherical parameterizations
Mathematics of computing~Graph theory
24:1-24:14
Regular Paper
This work was partially supported by the French ANR GATO (ANR-16-CE40-0009-01).
Luca Castelli
Aleardi
Luca Castelli Aleardi
LIX - École Polytechnique, Palaiseau, France
Gaspard
Denis
Gaspard Denis
LIX - École Polytechnique, Palaiseau, France
Éric
Fusy
Éric Fusy
LIX - École Polytechnique, Palaiseau, France
10.4230/LIPIcs.SEA.2018.24
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Luca C. Aleardi, Gaspard Denis, and Éric Fusy
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