Time-Space Maps from Triangulations

Bies, Sandra; Kreveld, Marc van

doi:10.1007/978-3-642-36763-2_45

Cited by 18 publications

(31 citation statements)

References 15 publications

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“…travel times from one source only (e.g. [3]). In the single source case another variant are so-called isochrones which deform maps such that the Euclidean distance corresponds to travel time (e.g.…”

Section: Related Workmentioning

confidence: 99%

Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation

Bouts

Dwyer

Dykes

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract-We present an efficient technique for topology-preserving map deformation and apply it to the visualization of dissimilarity data in a geographic context. Map deformation techniques such as value-by-area cartograms are well studied. However, using deformation to highlight (dis)similarity between locations on a map in terms of their underlying data attributes is novel. We also identify an alternative way to represent dissimilarities on a map through the use of visual overlays. These overlays are complementary to deformation techniques and enable us to assess the quality of the deformation as well as to explore the design space of blending the two methods. Finally, we demonstrate how these techniques can be useful in several-quite different-applied contexts: travel-time visualization, social demographics research and understanding energy flowing in a wide-area power-grid. Permanent repository link

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Section: Related Workmentioning

confidence: 99%

Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation

Bouts

Dwyer

Dykes

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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“…In addition to the results on linear cartograms [3,5,12,18], several other papers are also related. Weights of edges (but for very different applications) can also be visualized by the width [2].…”

Section: Related Workmentioning

confidence: 99%

“…"Relative lengths" of stretches are immediately quantified, whereas "relative colors" do not have a clear interpretation. These observations have led to the development of linear cartograms [3,5,12,18]. Linear cartograms try to display time more clearly by distorting the base map.…”

Section: Introductionmentioning

confidence: 99%

Travel-Time Maps: Linear Cartograms with Fixed Vertex Locations

Buchin

Goethem

Hoffmann

et al. 2014

Lecture Notes in Computer Science

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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.

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“…In the previous studies (e.g. Ahmed & Miller, 2007;Axhausen, Dolci, Fröhlich, Scherer, & Carosio, 2008;Bies & Kreveld, 2013;Campbell, 2001;Campenhout, 2010;Goedvolk, 1988;Spiekermann & Wegener, 1994;Tyner, 1992;Shimizu & Inoue, 2009;Kaiser, Walsh, Farmer, & Pozdnoukhov, 2010;Ramaer, 2011;Wu & Hung, 2012), line and/or point cartograms are often used to visualize travelling-times and are referred to as distance cartograms, distance-by-time cartograms, time-space maps or travel-time maps. However, some of these studies only describe how to deform the network according to travelling-times (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Shimizu & Inoue, 2009), while others only explain how to deform the map's boundaries based on travelling-times (e.g. Bies & Kreveld, 2013). Some methods produce maps that are not easily recognizable (e.g.…”

Section: Introductionmentioning

confidence: 99%

An alternative method to constructing time cartograms for the visual representation of scheduled movement data

Ullah

Kraak

2014

Journal of Maps

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In a cartogram, the map elements are purposely modified with respect to an attribute. A time cartogram is a type of cartogram in which the geographic-distance between locations is replaced by a time-related attribute such as travelling-time, deforming the geography accordingly. This study concentrates on centred time cartograms that visualize travellingtimes from a fixed starting location to other locations in the region. Several methods to construct time cartograms have been proposed, however these methods are not entirely satisfactory. In particular, none of them describes how to deform both the network and the map's boundaries based on travelling-times, which is necessary to maintain recognizability. In many cases, homeomorphism and topology are not maintained. The resultant maps from such methods are highly deformed and are difficult to read. Some of these methods are computationally demanding, while the procedures of others are not fully described. We present a method to construct time cartograms for the visual representation of scheduled movement data using the Dutch railways network as a case study. The method was developed by approaching the construction of time cartograms as a two-step process. In the first step, vector calculus is used to displace the train stations according to travelling-times from a fixed starting station. In the second step, moving-least-squares based affine deformation is applied to deform the railroads and the map's boundaries accordingly. To enhance understanding, concentric circles are drawn from the starting station to depict travelling-times. The method maintains homeomorphism and topology and yields time cartograms that are easily recognizable.

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Time-Space Maps from Triangulations

Cited by 18 publications

References 15 publications

Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation

Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation

Travel-Time Maps: Linear Cartograms with Fixed Vertex Locations

An alternative method to constructing time cartograms for the visual representation of scheduled movement data

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