Travel-Time Maps: Linear Cartograms with Fixed Vertex Locations

Abstract

Abstract. Linear cartograms visualize travel times between locations, usually by deforming the underlying map such that Euclidean distance corresponds to travel time. We introduce an alternative model, where the map and the locations remain fixed, but edges are drawn as sinusoid curves. Now the travel time over a road corresponds to the length of the curve. Of course the curves might intersect if not placed carefully. We study the corresponding algorithmic problem and show that suitable placements can be computed efficiently. However, the problem of placing as many curves as possible in an ideal, centered position is NP-hard. We introduce three heuristics to optimize the number of centered curves and show how to create animated visualizations.

Assessing the Graphical Perception of Time and Speed on 2D+Time Trajectories

“…We used the visual variable length by creating time ticks orthogonal to the path (similar to Figure 7). These ticks resemble Linear Cartograms with Fixed Vertex Positions [16], but they do not distort the path.…”

“…As a result, Linear Cartograms do not remain faithful to the spatial position -or 2D attributes -of data points. To solve this issue, Linear Cartograms with Fixed Vertex Positions [16] maintain the position of points, and instead, create sinusoidal links whose length represents time between points. Visits [70] uses a similar approach: position along the horizontal axis represents time, while sizes of the circles encode duration.…”

Information from imagery: ISPRS scientific vision and research agenda

“…Usability is another issue in visualisation (Joshi et al 2014), which includes the effectiveness and efficiency of visualisation techniques. With effectiveness in mind, map-alike representations such as schematic maps and cartograms (Buchin et al 2014) are emerging. In particular, a number of methods for the automated generation of schematic maps (Ti and Li 2014) have been developed.…”

Interaction Geography in a Museum

“…We draw from space-time visualization research concerning time geography [15] and the use and advancement of the space-time cube and space-time cube operations such as space flattening [5,21]. Moreover, we also draw from the visualization and analysis of movement [3,4,6], the use of flow maps by expert and non-expert audiences [27,28,31] and early attempts to visualize movement and interaction in interior environments [14,17,38].…”