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

L. C. Aleardi, Gaspard Denis, Éric Fusy
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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.
快速球面三角形绘图:图形绘图工具的实验研究
我们考虑了计算一个平面图形的球面无交叉测地线图的问题:这个问题,以及密切相关的球面参数化问题,在过去的二十年中在理论和实践中都引起了很多关注,受到许多应用的推动,从纹理映射到网格重划分和变形。我们主要关注的是设计和实现一个线性时间算法,为球面图的计算提供理论保证。虽然不美观,但我们的方法非常快,可以用作球面迭代方法和弹簧嵌入器的初始砂矿。在平面图特参数化的基础上,与初始砂矿进行了实验比较。最后,我们探讨了球形图作为(欧几里得)弹簧嵌入器的初始布局的使用:实验证据表明,这极大地有助于理清布局并达到更好的局部最小值。
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