Fast Layout Methods for Timetable Graphs

Abstract

Abstract.Timetable graphs are used to analyze transportation networks. In their visualization, vertex coordinates are fixed to preserve the underlying geography, but due to small angles and overlaps, not all edges should be represented by geodesics (straight lines or great circles). A previously introduced algorithm represents a subset of the edges by Bézier curves, and places control points of these curves using a forcedirected approach [5]. While the results are of very good quality, the running times make the approach impractical for interactive systems. In this paper, we present a fast layout algorithm using an entirely different approach to edge routing, based on directions of control segments rather than positions of control points. We reveal an interesting theoretical connection with Tutte's barycentric layout method [18], and our computational studies show that this new approach yields satisfactory layouts even for huge timetable graphs within seconds.

Curvilinear Graph Drawing Using the Force-Directed Method

“…Brandes and Wagner show how to use Bézier curves to draw graphs with vertices at fixed locations [6], with applications to the display of geographic networks. Related work on 3D curvilinear drawings of geographic networks is presented in [4,5,21].…”