Three-Dimensional Visualization of Activity-Travel Patterns
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1 C. Rinner 231 Three-Dimensional Visualization of Activity-Travel Patterns Claus Rinner Department of Geography University of Toronto, Canada ABSTRACT Geographers have long been interested in spatio-temporal patterns of human activity, and in the consequences of these patterns on urban development and transportation networks. Typically, data about individuals behaviour in space and time has been collected using activity-travel diaries. Today, automatic tracking by GPS receivers gains importance, e.g. in real-time fleet management, and people can also be traced indirectly when using credit or customer cards, and passing toll stations or border control. Potentially huge amounts of spatio-temporal data will be collected for different purposes, and existing analytical tools in GIS may prove to be insufficient to handle these data. The purpose of this paper is to develop a tool to model and visualize mobile objects. We propose to combine three-dimensional (3D) data representation with interactive manipulation to support the exploration of activity-travel patterns. This concept is based on a geometrical formulation of time geography, and extends previous work on 3D geovisualization of spatio-temporal activity patterns by an enhanced level of interactivity. A prototype was implemented using the Virtual Reality Modeling Language (VRML) to analyze sample, GPS-recorded travel data in downtown Toronto. TIME GEOGRAPHY,THEN AND NOW Time geography was suggested by Hägerstrand (1970) as an integrating concept for studying human activity in space and time. A space-time path combines the two-dimensional spatial component of a person s actual movement with time, graphically represented by the third, vertical dimension. A space-time prism represents locations that can be reached by a person starting from, or ending at a known location. Hägerstrand s theory focuses on space-time constraints that limit human activities. Kwan (2000) suggests using interactive geovisualization methods to explore the vast amounts of high-dimensional data on activity-travel behaviour. In particular, Kwan models space-time paths in a 3D GIS to analyse the day-time activity patterns of individuals by ethnic groups. The software
2 232 C. Rinner used in her work is the ArcView 3D Analyst which allows for interactive manipulation of the viewpoint of a 3D scene. Dykes & Mountain (2003) discuss digital representations of spatiotemporal phenomena that support exploratory data analysis. Their twodimensional, combined map view and time view of discrete measurement points allows for interactive exploration of spatio-temporal patterns in individual activity logs. The Location Trends Explorer software also offers simple indexing of point data to generate summary surfaces of spatiotemporal activity. Mountain (2004) further focuses on the visual inspection of mobile trajectories with respect to their space, time, and attribute dimensions. Precise visualization tools and advanced operational methods for measuring spatio-temporal accessibility in GIS have to be based on a mathematicalgeometrical framework for time geography such as the one proposed by Miller (under review). Until today, only partial attempts have been made to provide exact geometrical descriptions of the time geographic concepts of space-time path and space-time prism. Miller defines a space-time path as a sequence of 2D control points with a time stamp together with a set of straight-line path segments. Control points represent measured locations in space and time while path segments are interpolated between adjacent control points. Travel velocity can be estimated for any point on the space-time path. A space-time prism for a time interval is defined by Miller as an upwards open cone starting at the beginning of the interval and intersecting a downwards open cone starting at the end of the interval. If the prism is to include activity participation during the unobserved time interval, a cylinder fragment of the length of the activity duration has to be added between the two cones. Hornsby & Egenhofer (2002) discuss the handling of spatio-temporal data on different levels of detail using different terminology: lifeline thread for space-time path, and lifeline bead for space-time prism. These authors present generic questions that should be answered by appropriate information systems at different granularities (Hornsby & Egenhofer 2002, pp ): Who else has visited this location? How many times? To what other locations has individual X travelled? How did the speed of movement vary? Do individuals X and Y have similar travel patterns? What is the overall trend of movement?
3 C. Rinner 233 This paper proposes interactive visualization tools to address such tasks by exploratory data analysis. REPRESENTING ACTIVITY-TRAVEL DATA USING 3D GEOMETRIES Measured locations of a person over time can be represented as a spacetime path consisting of points and straight line segments with (x, y, z) coordinates. To account for location error in measurements such as GPS recordings we further propose to use space-time pipes consisting of spheres around measured locations and oblique cylinders connecting the spheres. The radius of these 3D buffer geometries represents the maximum location error. Space-time prism can be represented by vertical 3D cones pointing upward or downward. Any activity that does not involve movement given the scale of analysis (Raubal et al. 2004) is called a space-time station. Stations can be represented by vertical cylinders with the length indicating the duration of stationarity (activity participation). Fig. 1: 3D geometries to represent time geographic concepts, a) spacetime path, b) space-time pipe, c) space-time stations, d) spacetime prism The Web standard for describing interactive 3D objects and worlds (Web3D Consortium 2004) is the Virtual Reality Modeling Language (VRML). Table 1 lists the VRML nodes used to implement the 3D geometries identified above.
4 234 C. Rinner A one-pixel thick representation of a space-time path is created using the IndexedLineSet node in VRML. This geometry contains a series of points (x, t, y) with spatial coordinates x and y and temporal coordinate t for the vertical direction in the VRML scene. A series of indices is referring to these points to draw them on screen and connect them with straight lines. Tab. 1: Implementation of time geographic concepts as VRML nodes Concept Space-time path Space-time pipe Space-time prism Space-time station VRML node IndexedLineSet Sphere and Cylinders, or Extrusion with circular cross-section Cone, or Extrusion with growing/ shrinking cross-section Cylinder, or Extrusion The space-time pipe around each space-time path is implemented as an Extrusion in VRML. Extrusions consist of a cross section, in this instance an approximated circle, and a spine, that is an orthogonal path for the cross section. The VRML browser will display a 3D pipe resulting from the conceptual movement of the cross section through the spine path. Space-time prisms are modelled using the Cone geometric primitive while space-time stations are represented by simple Cylinders. Both of these time geography concepts could also be defined as extrusions, where prisms would have a growing or shrinking cross section. a) b) c) Fig. 2: 3D Visualization of space-time constraints in VRML: a) extrusions to show individuals activities as a space-time path/pipe, and cone (bottom) to represent a space-time prism, b) zoom on cylinders which encompass space-time stations, c) bird s view on sample paths and stations in downtown Toronto Sample travel data has been recorded in the city of Toronto, Canada, using a handheld computer that was equipped with a GPS receiver card. The data
5 C. Rinner 235 simulate the travel of several individuals through the western downtown area ending at a university building. The VRML objects generated from the GPS recordings have been combined with a geo-referenced, 1997 orthophoto from the University of Toronto s Map Library. Figure 2 shows three screenshots of angular and vertical views of the VRML scene. This demo is available at (requires VRMLenabled Web browser; orthophoto is 3 MB large). ADDING INTERACTIVITY TO SUPPORT VISUAL ANALYSIS OF SPACE-TIME CONSTRAINTS The CosmoPlayer 2.1 VRML browser used in the case study provides navigation tools to move freely the viewer s position with respect to the 3D scene. In addition to visually exploring the GPS data, we support analysis through the interactive capabilities of VRML. The base map (orthophoto) can be moved through time by either activating a pre-defined animation, or dragging the map in the vertical direction using the mouse pointer. In this way, the projection of a path on the 2D surface becomes readily apparent where the path/pipe intersects the moving map following a path on the street level. We plan to implement additional functions allowing users to switch individual paths/pipes on or off, highlight paths/pipes, interactively modify pipe widths, and interactively position cylinders and cones representing stations and space-time prisms, respectively. These functions are under development and will be realized by a combination of VRML with a Java applet on the same HTML page. The Java applet will provide the user with controls such as buttons and checkboxes to activate the functions. Through the VRML 2.0 External Authoring Interface, the Java code can manipulate the contents of the VRML scene. DISCUSSION AND FURTHER WORK This paper presents a three-dimensional visualization modelling approach for spatio-temporal travel patterns. The use of VRML offers analysts a highly interactive visualization environment to explore data of interest. This approach extends work by Kwan (2000) and Dykes & Mountain (2003) by its comprehensive implementation of time geographic concepts, and the level of interactivity offered to the user. While Dykes & Mountain
6 236 C. Rinner support the exploration of spatio-temporal data through conventional 2D techniques, Kwan makes a case for 3D displays to reduce the complexity of working with multi-variate data sets such as activity-travel data. However, it remains unclear how interactive Kwan s tools really are. Inferring from the software she used, her approach would be limited to changing the viewpoint on the data, while this paper propagates user interaction with data elements such as moving the background map through time, switching space-time paths on and off, or interactively positioning space-time stations in the 3D scene. Possible extensions of this prototype include improvements to the display and interactivity functions, as well as the addition of spatial analysis methods. For example, cylinders encompassing spatially clustered paths of different individuals over limited time periods could be generated automatically, or the road network could be intersected geometrically with 3D prisms to verify potential locations of an individual. We anticipate that the proposed visualization tools will help researchers and professionals analysing individual data (e.g. in crime analysis, epidemiology, life-path pattern analysis, animal tracking & tracing) in order to improve urban planning, health-care, or for a better understanding of our natural environment. The collection, storage, and use of people s locations is creating ethical and legal problems relating to personal privacy. But instead of posing an additional threat, we suggest that the proposed tools might rather be useful to evaluate spatio-temporal privacy issues. Geographic visualization might help decision-makers to understand the level of detail of data acquisition that is technically feasible, and to suggest legal limitations on the accuracy and use of such data. ACKNOWLEDGEMENTS I am grateful to Han Min Park for helping with the VRML programming. Thanks to Ann Zimmerman (Department of Zoology, U of T, and the Koffler Scientific Reserve at Jokers Hill) and Don Boyes (Department of Geography, U of T) for providing a GPS recording unit for data acquisition. Two anonymous reviews helped to improve the quality of this paper.
7 C. Rinner 237 REFERENCES Dykes, J.A., Mountain, D.M. (2003): Seeking structure in records of spatio-temporal behaviour: visualization issues, efforts and applications. Computational Statistics and Data Analysis 43: Hägerstrand, T. (1970): What about People in Regional Science? Papers of the Regional Science Association 24: Hornsby, K., Egenhofer, M.J. (2002): Modeling moving objects over multiple granularities. Annals of Mathematics and Artificial Intelligence 36: Kwan, M.-P. (2000): Interactive geovisualization of activity-travel patterns using three-dimensional geographical information systems: A methodological exploration with a large data set. Transportation Research C 8: Miller, H.J. (under review): A measurement theory for time geography. Draft available at [ ]. Mountain, D.M. (2004): Exploring Mobile Trajectories. Poster presented at the EURESCO Geovisualisation EuroConference on Methods to Support Interaction in Geovisualisation Environments, , Kolymbari, Crete, Greece. Raubal, M., Miller, H., Bridwell, S. (forthcoming 2004): User Centered Time Geography for Location-Based Services. Geografiska Annaler B. Web3D Consortium (2004): Creating Open Standards for Communicating 3D, Introduction to the VRML97 International Standard. [ ].
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