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Solis Catherine 202006 MAS Thesis.Pdf An Investigation of Display Shapes and Projections for Supporting Spatial Visualization Using a Virtual Overhead Map by Catherine Solis A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical & Industrial Engineering University of Toronto c Copyright 2020 by Catherine Solis Abstract An Investigation of Display Shapes and Projections for Supporting Spatial Visualization Using a Virtual Overhead Map Catherine Solis Master of Applied Science Graduate Department of Mechanical & Industrial Engineering University of Toronto 2020 A novel map display paradigm named \SkyMap" has been introduced to reduce the cognitive effort associated with using map displays for wayfinding and navigation activities. Proposed benefits include its overhead position, large scale, and alignment with the mapped environment below. This thesis investigates the substantiation of these benefits by comparing a conventional heads-down display to flat and domed SkyMap implementations through a spatial visualization task. A within-subjects study was conducted in a virtual reality simulation of an urban environment, in which participants indicated on a map display the perceived location of a landmark seen in their environment. The results showed that accuracy at this task was greater with a flat SkyMap, and domes with stereographic and equidistant projections, than with a heads-down map. These findings confirm the proposed benefits of SkyMap, yield important design implications, and inform future research. ii Acknowledgements Firstly, I'd like to thank my supervisor Paul Milgram for his patience and guidance over these past two and a half years. I genuinely marvel at his capacity to consistently challenge me to improve as a scholar and yet simultaneously show nothing but the utmost confidence in my abilities. He often said that I remind him of himself; one can only hope to live up to such a standard. I would also like to thank the other members of my committee, Greg Jamieson and Justin Hollands, with whom I was privileged to collaborate throughout the entire process of this thesis. Their support and feedback undoubtedly elevated the quality of my work. I was also very fortunate to work with a group of talented and thoughtful graduate students and post-docs, and I'm grateful for the time and energy they spent with me in discussion about the research. I would also like to send my gratitude to Mindy Thuna at the Engineering Library, who let me pick her brain on multiple occasions about effective research strategies. Though graduate school can be a challenging and often isolating experience, my colleagues in the lab were a source of support, empathy, and friendship that I hope to carry with me well into the future. Joey, Adam, and Fahimeh: I can't thank you enough for allowing me to bring my whole self into the office every day. I would like to thank my family, both from birth and chosen, for supporting me throughout this degree. My mother not only provided me the opportunity to pursue further studies, through her sacrifice and perseverance, but also modelled for me the strength and confidence I needed to face the difficulties set before me. Finally, I must thank my loving partner and best friend Charlie White, unwavering source of kindness and support. Having them by my side throughout this whole journey inspired me to grow as a person, and take so much more from this experience than I could have possibly imagined. It is a joy and a blessing to share my days with you, and my life is enormously, authentically better with you here. iii Contents 1 Introduction and Motivation 1 1.1 Map-aided Wayfinding and Navigation . 1 1.2 SkyMap: A New Display Paradigm . 2 2 Background & Problem Scoping 4 2.1 Defining the Research Space . 4 2.2 Investigating a Dome-shaped SkyMap . 5 2.2.1 Task-optimized distorted displays . 7 2.3 Traditional Cartographic Projections . 8 2.3.1 Classification of projections . 8 2.3.2 Azimuthal cartographic projections . 9 2.4 Review of Literature Addressing Spatial Cognition and Map Use . 11 2.4.1 Cognitive processes associated with map-aided wayfinding . 12 2.5 Research Questions . 13 3 Experimental Method 14 3.1 Experimental Design . 14 3.1.1 The experimental task . 14 3.1.2 Map conditions . 17 3.1.3 Measurement of potentially mediating factors . 18 3.1.4 Non-performance measures . 20 3.2 VR Implementation of Experimental Environment . 20 3.2.1 Software . 20 3.2.2 Trial configurations and counterbalancing . 21 3.2.3 Hardware & physical setup . 22 3.3 Experimental Procedure . 23 3.3.1 Participant recruitment & screening . 23 3.3.2 Introduction and presentation of experimental task . 23 3.3.3 Experiment debrief . 25 3.4 Experimental Variables . 26 3.5 Experimental Hypotheses . 28 3.5.1 Hypothesis 1: SkyMap vs. heads-down display . 28 3.5.2 Hypothesis 2: Relative performance of dome projections . 28 3.5.3 Hypotheses about influence of trial configuration . 29 iv 4 Results 30 4.1 Overview . 30 4.2 Results by Trial Block . 32 4.2.1 Effect of map condition on Mean Absolute Error . 32 4.2.2 Effect of map condition on mean visual angle error . 35 4.2.3 Effect of map condition on mean response time . 37 4.2.4 Effect of map condition on mean trial confidence . 38 4.2.5 Effect of map condition on mental workload . 39 4.3 Analysis of Performance by Trial Configuration . 40 4.3.1 Significance testing of AE & VAE data . 43 4.3.2 Directional error . 44 4.4 Individual Differences . 45 4.5 Feedback & Qualitative Observations . 46 5 Discussion 47 5.1 Substantiation of SkyMap Advantages . 47 5.2 Effects of Trial Configuration on Map Condition Differentiation . 48 5.2.1 Interpreting the meaning of visual angle error . 48 5.3 Study Limitations . 51 5.3.1 Limitations & potential extensions of data analysis . 51 5.4 Considerations for SkyMap Implementation . 52 6 Conclusion 53 6.1 Summary of Key Findings . 53 6.2 Implications for SkyMap Design and Future Research . 54 References 55 Appendices Appendix A: Details of Implementation of Inverse Polar Azimuthal Projections . 60 Appendix B: Experiment Forms and Questionnaires . 64 Appendix C: Supplementary Information & R Output from Data Analyses . 75 v List of Tables 2.1 Initial SkyMap shape considerations . 6 2.2 The five principal azimuthal projections and their preserved spatial properties . 10 3.1 Screenshots of all map conditions . 18 3.2 The 16 layouts defining the relative position of the green tower to the two reference towers . 22 3.3 Independent & predictor variables (by trial, trial block, and individual) . 26 3.4 Dependent variables (by trial, trial block, and individual) . 27 4.1 Tukey's HSD values from post hoc analysis of MAE model . 33 4.2 Tukey's HSD values from post hoc analysis of MVE model . 36 4.3 Correlation table comparing individual differences to overall task performance . 45 vi List of Figures 2.1 Three common developable map surfaces and their corresponding projection types . 8 2.2 Illustration of lines of longitude & circles of latitude for different azimuthal projections . 9 3.1 Screenshot of example experimental task with the flat SkyMap condition . 14 3.2 Photograph of fun-house mirror . 15 3.3 Screenshots of the dome mesh and map texture . 21 3.4 Finite State Machine diagram of the experimental task procedure . 25 4.1 Histogram of Absolute Error data for all trials (excluding outliers) . 31 4.2 Distribution of Mean Absolute Error values by map condition . 32 4.3 Distribution of Mean Visual Angle Error values by map condition . 35 4.4 Distribution of mean response times by map condition . 37 4.5 Distribution of mean confidence ratings by map condition . 38 4.6 Distribution of mental workload ratings by map condition . 39 4.7 Absolute Error distribution by trial layout and distance . 40 4.8 Visual Angle Error distribution by trial layout and distance . 41 4.9 Absolute Error means by trial layout, distance and map condition . 42 4.10 Visual Angle Error means by trial layout, distance and map condition . 42 4.11 Density contours showing horizontal and vertical visual angle deviations by trial layout, dis- tance and map condition . 44 vii Chapter 1 Introduction and Motivation 1.1 Map-aided Wayfinding and Navigation Visual representations of environments have been used for millennia for the description and understanding of spatial information. Maps, more specifically, have existed in different forms throughout many civilizations (Tufte, 1983). Though the display technology has since become more sophisticated, its aims have remained largely unchanged: to retain and share knowledge about an environment, specifically the locations of the elements it contains. One task facilitated by maps that is of particular interest in this thesis is that of wayfinding. Wayfinding can be described as the activity of moving through an environment towards a specific target or location (destination). I make a distinction here between wayfinding and navigation, which both fit the above description, by further specifying that wayfinding involves some sort of cognitive representation of a space that is accessed in order to make decisions about what route to take to arrive at the intended destination (Taylor, Bruny´e,& Taylor, 2008). This is distinct from navigation in that navigation does not rely on an existing representation of a space, but instead involves the use of cues, in the environment and/or provided by an aid, that indicate what route to follow. As the technology around maps and other wayfinding aids has advanced remarkably over recent decades, maps have become a tool for everyday use. The modern road map, whose visual style persists today, proliferated in the U.S.
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