Embedding cues about travel time in schematic maps Herman Haverkort Dept. of Mathematics and Computer Science, Eindhoven Univ. of Technology, E-mail:
[email protected] Abstract—On schematic maps of public transport systems, distances on the map are typically not proportional to actual travel times, which may cause surprises for the map user. This study proposes several possible solutions to give a user visual cues about which connections are fast and which connections are slow in terms of distance on the map per minute of travel time.
In a schematic map of a public transport system, different sections of lines often have very different speeds in terms of millimeters on the map per minute of travel time. This study proposes different techniques to give the user visual cues about differences in speeds between different sections, so that a user may take better-informed decisions about which routes to take and how much time to allow for that. Of course, we could consider printing travel times in minutes along the lines, but this is not always feasible. Even if it is, adding up numbers is a tedious task and it would be helpful to give users some visual cues about where to expect faster and slower connections. Our goal is therefore to enable users to get an impression of speed differences at a glance, rather than exact numbers. In this study a schematic map of the major train services in the Netherlands is used as an example, see Fig. 1a. Major waters are added in the background of the map to make it more compelling. One could debate which stations and connections should be considered major enough to include in this map, and how exactly one should determine typical travel times per section, but this is irrelevant for this study. The point is that the map gives no visual cues about the speed differences between different sections. The travel time from ’s Hertogenbosch to Deventer via Arnhem is the same as via Amersfoort, but the latter option looks like a big detour on the map. This may be interpreted as a shortcoming of the schematization; arguably, a quality criterion for schematic transportation maps is how well they maintain that the shortest route on the map is the fastest route in reality [1]. However, violations of the shortestis-fastest principle may not always be avoidable. Another example is the section Den Helder–Alkmaar, which takes about eight times as long as Den Haag C–Den Haag HS, and slightly longer than Utrecht–Amsterdam C. For giving cues about travel times, we may draw inspiration from several types of existing maps. Time-space transformations [2] distort the shape of the network, such that the distance between any pair of points on the map becomes proportional to the travel time between them. Unfortunately, in our case, such distortion would undo the schematization and thus defeat the purpose. Stevens and Goldsberry [3] discuss how speeds can be visualized on motorway traffic maps. Their preferred solution is to place small marks along the roads that cut them into segments of equal travel time. While this enables users to determine fairly exact travel times by counting the marks along any particular route, it does not necessarily give users a strong visual cue about what routes to consider. Buchin et al. [4] replace line sections by wiggly lines with length
proportional to the travel time. From a typical road map users can guess speed differences between, say, motorways and twisting mountain roads from the differences in line style and the number of curves. In some public transport systems, the price of a journey is determined by the number of zones crossed on the map. For a more in-depth discussion of related work, see the more detailed version of this paper [5]. To achieve our goal, we may vary properties of the lines on the map or of the background. Lines may have colour (hue, brightness, saturation), a dash pattern, width, and shape. On typical public transit maps, line colour and pattern are already loaded with meaning, which leaves width and shape to be used for our purposes. In addition, we may introduce colour or structure in the background. Below I will describe four solutions to visualize speed differences; some of these may be combined for greater effect. Four more candidates and full maps are given in a more detailed version of this paper [5]. Width adjustment: (Fig. 1b) The width of each line section is a sublinear function of its speed: the faster the wider. Shape adjustment: (Fig. 1c) The wiggliness of each line section is inversely proportional to its speed: slow lines get many serpentines, medium-fast lines only an occasional bend, and fast lines follow a smooth course. Note that we vary wiggliness as a property in its own right and not as a tool to merely make a line section longer, as with Buchin et al. [4]. Heat map: (Fig. 1b) The brightness of the background is adjusted as follows. A continuous function f from location to inverse speed (minutes per millimeter) is constructed, such that the integral of f over a line section on the map gives the travel time for that section. The function f is displayed on the background as a map with dark shades for high values of f (low speeds) and bright shades for low values (high speeds). Blob collection: (Fig. 1d) The map is divided into zones, such that any single train crosses a zone boundary once every 20 minutes. This causes zones to have small diameter on the map where speeds are low, and large diameter where speeds are high—the pattern of small and large zones may thus give visual cues about speed differences. The zones are drawn as a loosely packed collection of mostly circular blobs. To realize optimal usability and applicability of each of these techniques, we need to establish design rules that govern such issues as the shape of the function that maps speed to line width; the number of wiggles on a typical median-speed line; requirements for the interpolation method underlying the heat map; and the number of zones in a blob collection (for a more elaborate list, see the full paper [5]). After establishing such rules we should compare the techniques on expressive power, usability, affordance, demands on visual resources, production complexity and general appearance. Below I provide some preliminary observations based on my experiences with drawing the proof-of-concept maps, and I mention some questions that require further (theoretical or experimental) investigation.
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Eindhoven Travel time/unit distance: Etten-L. 5 min. Groningen 10 min. 20 min. Den Helder Hoorn Almere C Leeuwarden Almere C Leeuwarden Venlo Venlo Groningen Weert Weert Lelystad Lelystad Roosendaal Roosendaal Change in Utrecht for: Change in Utrecht for: Amsterdam C VlissingenAmsterdam C Vlissingen • Maastricht↔A-Zuid/Schiphol; • Maastricht↔A-Zuid/Schiphol; Heerenveen Heerenveen Alkmaar Alkmaar Roermond Roermond AA• Heerlen↔A-Amstel...Den Helder. • Heerlen↔A-Amstel...Den Helder. AAHeerlen Heerlen Intercities from Maastricht go to Intercities from Maastricht go to Steenwijk Steenwijk Sloterdijk Sloterdijk Assen Assen Sittard Sittard Amstel Amstel Alkmaar but not Den Helder. Alkmaar but not Den Helder. Castricum Castricum Hilversum Hilversum Zwolle c Herman Haverkort,Emmen Zwolle c Herman Haverkort,Emmen 2014. Map is for 2014. Map is for Maastricht Maastricht illustration only, not for travel planning! illustration only, not for travel planning! Beverwijk Beverwijk Zaandam Zaandam Amersfoort Amersfoort Mari¨ enberg Mari¨ enberg Apeldoorn Apeldoorn Haarlem Haarlem Almelo Almelo A-Zuid A-Zuid Hengelo Hengelo Heemstede-A. Heemstede-A. Deventer Deventer Schiphol Schiphol Enschede Enschede Utrecht Utrecht Leiden Leiden Zutphen Zutphen DenH- Ln v NOI DenH- Ln v NOI Dieren Dieren Den Haag C Den Haag C Gouda Gouda Ede-Wag. Ede-Wag. Den Haag HS Den Haag HS A portrait of the Dutch A portrait of the Dutch Arnhem Arnhem R-Alexander R-Alexander Intercity railway network Intercity railway network Delft Delft Schiedam C Schiedam C NS Intercity NS Intercity Nijmegen Nijmegen R-Blaak R-Blaak Rotterdam C Rotterdam C Dordrecht Dordrecht NS Intercity Direct NS Intercity Direct Oss Oss Breda Breda other train services other train services ’s Hertogen bosch ’s Hertogen bosch between IC stations between IC stations Helmond Helmond Eindhoven Eindhoven Travel time/unit distance: #border crossings / 3 = Etten-L. Etten-L. min. 10c) min.With 20 min. travel time (hrs) ±20 min. a) Excerpt of the base map. b) With width adjustmentVenlo and heat 5map. shape adjustment. d) With blob collection. Venlo Weert Weert Roosendaal Roosendaal Change in Utrecht for: Change in Utrecht for: Vlissingen • Maastricht↔A-Zuid/Schiphol; Vlissingen • Maastricht↔A-Zuid/Schiphol; Roermond Roermond • Heerlen↔A-Amstel...Den Helder. • Heerlen↔A-Amstel...Den Helder. Heerlen Intercities from Maastricht go to Heerlen Intercities from Maastricht go to Sittard Sittard Alkmaar but not Den Helder. Alkmaar but not Den Helder. Den Helder
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Theoretical expressive power: how accurately can speed Maastricht differences be visualized? Width adjustment and heat maps arguably have the largest expressive power: they allow a precise mapping from speed to visualization. Shape adjustment cannot be used to distinguish very fast lines from medium-fast lines—both types of lines need to be smooth and straight or otherwise the map will look rather chaotic. Blob collections are meaningful for long journeys (for short rides they are poor, since a trip across one zone boundary may take anything between 0 and 40 minutes). However, a set of zones with the required properties may not always exist. Usability: can a user, after having learnt how to use the map, tell preferable from less preferable routes at a glance? How accurate is the information about travel time which a user can obtain from the map by studying it in detail? It seems that width adjustment and heat maps visually emphasize faster connections, whereas shape adjustment visually emphasizes slower connections. To what extent can users judge differences in line width, background brightness and wiggliness accurately and relate these to differences in speed and travel time? Affordance: can users tell preferable from less preferable routes without training, or is training required? Demands on visual resources: which parameters of the drawing are used to encode speeds and cannot be used to encode other information? How much does the visualization of speeds clutter the map, making connections harder to find or necessitating a larger map? While drawing the maps, I found that blob collections cause some amount of clutter and I felt that I had to remove the waterways to compensate for this.
d
Production complexity: how difficult is it to construct Maastricht the map? Width adjustment seems easiest to implement; the other solutions require further research. Heat maps require non-trivial interpolation, because speeds are given only as average speeds for line sections and no speed values are given for any particular point. Shape adjustment requires careful coordination of global and local shape. Blob collections call for the development of algorithms to find suitable sets of zones. General appearance: do people find the design stylish or ugly, what associations does the design evoke, and how much do people agree on that? What do you think of these designs?
c Herman Haverkort, 2014. Map is for illustration only, not for travel planning!
c Herman Haverkort, 2014. Map is for illustration only, not for travel planning!
Acknowledgements. The author thanks Anne Driemel, Mathijs Miermans, Maxwell Roberts and Alexander Wolff for feedback on the maps presented above. R EFERENCES [1]
[2]
[3]
[4]
[5]
T. Milea, O. Schrijvers, K. Buchin, and H. Haverkort, “Shortest-paths preserving metro maps,” in Proc. 19th Int. Symp. Graph Drawing (GD), ser. Lect. Notes Computer Sc. (LNCS), no. 7034, 2012, pp. 445–446. N. Ahmed and H. J. Miller, “Timespace transformations of geographic space for exploring, analyzing and visualizing transportation systems,” J. of Transport Geography, vol. 15, p. 217, 2007. J. Stevens and K. Goldsberry, “Fixed-interval segmentation for travel time estimations in traffic maps,” 2012, presentation at Ann. Meeting Assoc. of American Geographers (AAG). K. Buchin, A. van Goethem, M. Hoffmann, M. van Kreveld, and B. Speckmann, “Linear cartograms with fixed vertex locations,” 2014, manuscript in preparation. H. Haverkort, “Embedding cues about travel time in schematic maps,” 2014, manuscript available online.
