Embodied Navigation in Immersive Abstract Data Visualization:
Is Overview+Detail or Zooming Better for 3D Scatterplots?
Yalong Yang, Maxime Cordeil, Johanna Beyer, Tim Dwyer, Kim Marriott and Hanspeter PfisterFig. 1. Conditions tested in our user study: a) Room-sized interface (or Rm). b) Room-sized interface with an overview (or RmO). c)
Zooming interface (or Zm): users zoom in and out with a “pinch” gesture. d) Zooming interface with an overview (or ZmO).
Abstract— Abstract data has no natural scale and so interactive data visualizations must provide techniques to allow the user to choose
their viewpoint and scale. Such techniques are well established in desktop visualization tools. The two most common techniques arezoom+pan and overview+detail. However, how best to enable the analyst to navigate and view abstract data at different levels of scale
in immersive environments has not previously been studied. We report the findings of the first systematic study of immersive navigation
techniques for 3D scatterplots. We tested four conditions that represent our best attempt to adapt standard 2D navigation techniques
to data visualization in an immersive environment while still providing standard immersive navigation techniques through physicalmovement and teleportation. We compared room-sized visualization versus a zooming interface, each with and without an overview.
We find significant differences in participants’ response times and accuracy for a number of standard visual analysis tasks. Both zoom
and overview provide benefits over standard locomotion support alone (i.e., physical movement and pointer teleportation). However,which variation is superior, depends on the task. We obtain a more nuanced understanding of the results by analyzing them in terms ofa time-cost model for the different components of navigation: way-finding, travel, number of travel steps, and context switching.
Index Terms—Immersive Analytics, Information Visualization, Virtual Reality, Navigation, Overview+Detail, Zooming, Scatterplot

1

I NTRODUCTION

Abstract data has no natural scale. That is, data that is not based in aphysical reference space can be freely re-scaled and viewed from any
angle that best supports the analysis task. However, this freedom also
represents a challenge to the design of interactive navigation methods:
how do we allow people to move freely through an abstract information
space without confusing them? Designers of desktop visualization
tools have grappled with this problem for decades and have evolved
sophisticated techniques for navigation. For example, it is common indata visualizations, such as scatterplots, time-series, and so on, to allow
users to zoom in, making a specific region larger to access more detail.
They can then pan around at the new zoom level or zoom out again
to reorient themselves in the full dataset. Another common approachis to provide a minimap window to provide an overview of the wholedataset at all times. As discussed in Section 2.1, these methods are wellstudied and widely accepted in desktop data visualization.
Recent developments in technology has seen renewed interest in using immersive environments for data visualization, but this requires us
to reconsider and possibly adapt navigation methods that have become• Yalong Yang, Johanna Beyer and Hanspeter Pfister are with the School ofEngineering and Applied Sciences, Harvard University, Cambridge, MA,
USA. E-mail: {yalongyang, jbeyer, pfister}@g.harvard.edu• Maxime Cordeil, Tim Dwyer and Kim Marriott are with the Department of
Human-Centred Computing, Faculty of Information Technology, Monash
University, Melbourne, Australia. E-mail: {max.cordeil, tim.dwyer,
kim.marriott}@monash.edu
Manuscript received xx xxx. 201x; accepted xx xxx. 201x. Date of Publication
xx xxx. 201x; date of current version xx xxx. 201x. For information on
obtaining reprints of this article, please send e-mail to: reprints@ieee.org.
Digital Object Identifier: xx.xxxx/TVCG.201x.xxxxxxx

standard on the desktop. As virtual and augmented reality headsets
continue to improve — e.g., in resolution, field-of-view, tracking stability, and interaction capabilities — they present a viable alternative
to traditional screens for the purposes of data visualization. A recent
study has found a clear benefit to an immersive display of 3D clusteredpoint clouds over more traditional 2D displays [32]. However, in thatstudy the only way for participants to change their point of view was
through physical movement. There are questions about how one mightnavigate in situations where the participant cannot move around (e.g.,they are seated), or where the ideal zoom-level for close inspection of
the data is too large to fit in the physically navigable space.
In Virtual Reality (VR) gaming “teleporting” is a standard way tonavigate a space that is too large to fully explore through one-to-one
scale physical movement. The equivalent of the desktop minimap
overview+detail in VR is World In Miniature (WIM) navigation. Zooming is also possible in immersive environments through a latched gesture
to scale the information space around the user. However, the effectiveness of such immersive navigation techniques for point cloud datavisualization applications in VR has not previously been tested. The inherent differences between such abstract data visualizations and typical
VR worlds, namely, the freedom to move between different scales andviewpoints, makes it unclear whether standard VR navigation methods
are sufficient to support analysis tasks.
Our overarching research question, therefore, is: how can we bestenable the analyst to navigate and view abstract data at different
levels of scale in immersive environments? To address this question
we first thoroughly review standard data visualization navigation techniques from desktop environments and the initial work that has begun
to provide navigable data spaces in immersive environments (Sec. 2).
We find that existing literature in immersive data visualization has not
fully explored how to adapt navigation techniques for data visualization from the desktop and/or to adapt VR navigation techniques to theapplication of data visualization. Therefore, in Section 3, we look at
the space of possible ways in which users can navigate immersive datavisualizations and from this, in Sec. 4.1, we choose and study four basic
navigation possibilities: room-sized data at fixed-scale with physicalnavigation versus a smaller data display with zooming (dynamic scale),each with and without an overview WIM display.
Specifically, we compare zooming to overview+detail. We are particularly interested in how to ensure that navigation remains embodied
through physical movements and gestures that are as natural as possible [22]. The contributions of this paper are:
1. The first systematic exploration of overview and detail interaction
paradigms in immersive scatterplot visualization, Sec. 3.
2. A study comparing four navigation conditions (as above), Sec. 4
and Sec. 5. This finds that: Participants significantly preferred
either zoom or overview over standard locomotion support alone.
Adding an overview also improved accuracy in some tasks. Roomsized egocentric views were generally faster in our study.
3. A more nuanced interpretation of our study results using a navigation time-cost model, Sec. 6.
4. Recommendations for use of zoom and overview in combination
with physical navigation for immersive data visualization, Sec. 7.
2 R ELATED W ORK
2.1 Navigation in 2D Visualizations
A foundation of visual data exploration is the Shneiderman Information Seeking Mantra of “Overview first, filtering and details on demand” [60]. Several paradigms have emerged to support navigation
following this mantra, such as overview+detail, focus+context [41] andzooming [17]. Many 2D visualization techniques provide such interactions, such as Google Map (zooming), PowerPoint (overview+detail),and fish-eye views (focus+context). In an extensive literature review,
Cockburn et al. [19] conclude that each technique has issues — zooming impacts memory [20]; focus+context distorts the information space;and overview + detail views also make it difficult for users to relate
information between the overview and the detailed view [9, 29].
Navigation has also been studied on mobile displays. Burigat etal. [14] found that interactive overviews were particularly advantageous
on small-screen mobile devices for map navigation tasks [14, 15]. However, in the context of information visualization, adding an overview
to a zoomable scatterplot on a PDA was found to be ineffective anddetrimental compared to a zoomable user interface only [16].
With screens and projectors becoming cheaper, larger and easier totile, researchers have explored the benefits of large display sizes for navigating visualizations. Ball and North [4] studied the effect of display
size on 2D navigation of abstract data spaces and found that larger displays and physical navigation outperformed smaller displays. They also
found that virtual navigation (i.e., pan and zoom) was more frustrating
than physically navigating a large tiled-display. Ball and North [5] also
investigated the reason for improved performance of information space
navigation on large displays and found that physical movements werethe main factor, compared to field of view. Another study by Ronneand Hornbaek [55] investigated focus+context, overview+detail andzooming on varying display sizes. They found that small size display
was least efficient, but found no differences between medium and large
screens and that overview+detail performed the best.
In our study, we investigate the use of overview+detail and continuous zoom, as they are most suited to our tasks. We do not consider
focus+context as it is not well suited to our tasks (i.e., counting points
and evaluating distances between pairs of points), and spatial distortion
would introduce misinterpretation of distances.
2.2 Navigation in VR Environments
Research in 3D User Interfaces (3DUI) and Virtual Reality has exploreddifferent ways for users to navigate 3D immersive scenes. Laviola etal. [37, Ch. 8] provide a taxonomy of these techniques. They describe
four navigation metaphors — walking, steering, selection-based traveland manipulation based travel.
Walking in VR can be either real walking (i.e., the user walks witha VR headset in the real world) or an assisted form of walking (e.g.,using a treadmill [26] or more dedicated devices to emulate walking inplace [31]). While those walking devices provide a realistic sensationof walking in the virtual world, they are bulky and not affordable fora wide audience. Abtahi et al [1] recently investigated mechanisms toincrease users’ perceived walking speed for moving in a large virtualenvironment. However, it is not trivial on how to apply their techniquesfor visualization navigation. In our research, we focus on physicalwalking available through HMD VR devices, however restricted to acommon office size area. Walking has been found to be more efficientthan using a joystick for orientation in VR [18], and has generally beenfound to be beneficial for perception and navigation tasks compared tocontroller-based interactions [35, 56, 57]. Walking has also been provento be more efficient than standing at a desk for tasks involving visual
search and recalling item locations in space [53].
In contrast to walking, steering metaphors allow the user to navigate
the space without physically movement. They are usually gaze- and/or
controller-based. Teleportation is a very common locomotion techniquewhich consists of casting a ray from a tracked controller to the desired
location [44] and a button push to travel there. Bowman et al. [12] foundthat hand-based steering was more efficient than gaze-based travel,
but that instant teleportation (with no transition between initial andfinal location) was detrimental for orientation compared to continuous
viewpoint change. Laviola et al. [37] argue that continuous uncontrolled
movements of the viewpoint induce cybersickness, but that it can be
mitigated if the transition is very fast. Modern teleportation techniques
use fade or blinking metaphors where the screen transitions to black
before the move and is restored at the destination position. In all theconditions of our experiment we allow this type of teleportation toallow the user to fast track travel in the virtual environment if needed.
An alternative VR navigation technique is WIM [43, 63], which
introduces a “minimap” to allow the user to teleport by selecting atarget position in the miniature. Recent refinements offer scalable,
scrollable WIMs (SSWIMs) [71], or support for selecting the optimal
viewpoint in dense occluded scenes [65]. We designed an embodied
placement for WIM, and two different teleportation methods with WIM.
In summary the effects of spatial memory, cybersickness and overallusability of such techniques have been studied in general purpose
VR applications. In the context of abstract visualization their relative
drawbacks and benefits are unclear.
2.3

Immersive Analytics and Space Navigation

3D scatterplots have received significant attention in Immersive Analytics research [2, 21, 25, 32, 52]. Raja et al. [54] found that using body
motion and head-tracking in a CAVE-like environment was beneficial
compared to non-immersive environments for low-level scatterplot
tasks (i.e., cluster detection, distance estimation, point value estimation and outlier detection). Kraus et al. [32] explored the effect of
immersion for identifying clusters with scatterplots. They explored a
2D scatterplot matrix and 3D on-screen, and immersive table-size androom-size spaces. Overall their found that the VR conditions were well
suited to the task. However they also pointed out that their room-size
condition may not have been optimal due to the lack of an overview.
Body movements have been observed in Immersive Analytics studies involving 3D scatterplots, which may indicate potential benefits fordata exploration and presentation. For example, Prouzeau et al. [52]observed that some participants tended to put their heads inside 3D
scatterplots to explore hidden features; Batch et al. [7] observed participants organize their visualizations in a gallery-style setup and walkthrough them to report their findings. Simpson et al. [61] informallystudied walking versus rotating in place for navigating a 3D scatterplot,
and their preliminary result indicated that participants with low spatial
memory were more efficient in the walking condition.
Other alternatives to walking in a room-size environment have also
been explored. Filhio et al. [66] found that a seated VR setup for 3D
scatterplots performed better than on a desktop screen. Satriadi etal. [59] tested different hand gesture interactions (user standing still) to
pan and zoom 2.5D maps in Augmented Reality, but the visualizations
were within a fixed 2D viewport in the 3D space.
Flying is a steering metaphor that has been used as an alternative to
walking to obtain a detailed view of an immersive visualization. Withflying, benefits of immersion were found compared to a 2D view forFig. 2. Our study compares two main effects, leading to four conditions.

distance evaluation tasks in scatterplots [67]. Sorger et al. [62] designed
an overview+detail immersive 3D graph navigation metaphor that uses
flying to gain an overview, and a tracked controller-based teleport to aselected node position to obtain details from a node-centric perspective.
The main takeaway of their informal expert-study is that overviews
were perceived as important to keep the user oriented in the graph.
To our knowledge, WIMs have been underexplored in immersive
data visualization. Nam et al. [46] introduced the Worlds-in-Wedges
technique that combines multiple virtual environments simultaneously
to support context switching for forest visualization. The study of
Drogemuller et al. [23] was the first to formally evaluate one andtwo-handed flying vs. teleportation and WIM in the context of large
immersive 3D node-link diagrams [23]. They found that the flying
methods were faster and preferred compared to teleportation and WIMs,
for node finding and navigation tasks in the 3D graph. However, they
did not test the condition where the user only walks around the room
without instrumented metaphors for overview+detail.
Finally, scaling the visualization as a 3D object in VR via bimanualinteraction has been used in Immersive Analytics systems [30, 68] but
not formally studied against other VR navigation techniques. In summary, there is evidence that overview+detail and zooming are beneficial
for navigating 2D visualizations. However, their relative benefit in thecontext of immersive 3D scatterplots is still underexplored.
3 S TUDY R ATIONALE AND D ESIGNSOur study is intended to address the gaps in the literature describedabove in terms of how to carry over well understood 2D navigation
techniques to immersive visualizations (see Fig. 2). We decided to
not include 2D interfaces for 3D scatterplots as testing conditions, as
the 2D alternatives (i.e., scatterplot matrix and 3D scatterplot on a 2D
screen) have been tested to be less effective than representing them as
3D scatterplots in an immersive environment [32].
We focus on adapting zoom and overview+detail techniques. We
did not include focus+context in our study, as it has been shown thatsuch spatial distortion techniques are not effective for large 2D display
spaces [55], and we expect similar results in the immersive environments. However, formal confirmation of this is worthwhile future work.
Adapting overview+detail and zooming techniques to immersive environments from 2D interfaces requires many design decisions. In thefollowing, we describe our design considerations and choices.
3.1 Overview+Detail
The idea of the overview+detail is to provide two separate display
spaces representing the same information but at different scales. The
basic design of our overview is straightforward: the whole information
space in which the user is standing is represented in a cube – with alldata glyphs scaled down appropriately. However, three essential design
choices remain unanswered: placement of the overview; Point of View
(PoV) indicator in the overview; and overview teleportation.
Placement of the overview: In 2D display environments, the overview
is commonly placed at a global fixed position relative to the display:either at a corner of the detail view (e.g., some on-line maps) or outside
the detail view (e.g., some text editors, PowerPoint). When using theoverview on a 2D display, the user’s Field of View (FoV) is consistentand can cover the full display space at all times. Thus, the user caneasily access the overview at any time in this placement. Unlike 2D
displays, in an immersive environment, the user is expected to perform
more body movement. As a result, the user’s FoV is constantly changing. If the overview is placed at a fixed global position in immersive
environments, the user may forget its location or it may not be reachable
when required. In general, the overview needs to be easily accessible
so it can be brought into focus for close inspection, but by default it
should not occlude the users’ view of the main scene. A logical design
choice is to place the overview somewhere at the periphery of the users’view by default, but allow the user to grab it with the controller to bring

Fig. 3. Enlarging and shrinking the overview with arm movement.

Fig. 4. Demonstration of point-and-click teleportation. pcurrent (the greendot) is the current position of the user; pAoI (the blue dot) is the positionof Area of Interest (AoI) and the clicked position; and pteleport (the yellowdot) is the position the user will teleport to.

it up for close inspection. But there remains the question of what is thebest default location relative to the user.
Our first idea was to place the overview at a fixed position relative to
the FoV, i.e., the overview follows the user’s movement, e.g., to always
appear at the bottom right corner of the user’s FoV. We tested it withtwo participants; both of them reported the overview to be distracting
and cluttered. They also found it difficult to access (grab) the overview.
We then attached the overview to the user’s off-hand controller. Thiswas inspired by WIM where the miniature is associated with a tracked
physical board [43, 63], and Mine et al. [45] who attached widgets tovirtual hands in VR. To further reduce visual clutter, we shrink theoverview by default and allow the user to enlarge the overview by
touching it with the other controller. This embodied design allows
users to enlarge or shrink the overview by simple hand movements (seeFig. 3). We tested it with another participant, and explicitly asked if
she felt the overview caused visual clutter, was distracting, or difficult
to access. The participant was highly positive about the new design.
PoV indicator in the overview: In 2D overview+detail interfaces, a
FoV box is used to indicate which portion of the overview is presented
in the detail view. Similarly, in WIM, it is also important to indicate
the view position, but in addition the direction the user is facing [63].
Following their designs, we use a cube to represent the tracked headset.
The position and rotation of the cube are synchronized with the headset
in real-time. We also use a semi-transparent cone attached to the cube
to represent the user’s view direction (see Fig. 3).
Overview teleportation: Tight coupling between the overview anddetail views is standard in 2D interfaces (e.g., [29, 72]). The aim is
to allow the user to change the portion of the scene presented in thedetail view by interacting with the overview. There are two widelyused implementations: drag-and-drop and point-and-click interactions.
Changing the detail view in 2D interfaces is equivalent to changing theviewing point and direction in immersive environments. We adapted
the 2D interactions for immersive environments:
Drag-and-drop teleportation: On 2D interfaces, the user can selectthe FoV box in the overview then drag-and-drop it at a new position in
the overview. The detail view will then switch to the new position. In
immersive environments, WIM allows participants “pick themselvesup”, i.e., the user can pick up the PoV indicator and drag it to a newposition in the overview to teleport to the dropped location in the detailview. We implemented the same mechanism in our visualizations.
Point-and-click teleportation: The user can also directly choose
the destination and explicitly trigger a command to change the detailview. On 2D interfaces, the operation involves pointing a cursor at thedestination position in the overview and then clicking to translate thedetail view. In immersive environments, in addition to changing theposition of the user, we also need to adjust the user’s orientation. We
implemented a mechanism that will determine the user’s position andorientation (see Fig. 4). Basically, the teleport target position is on thestraight line connecting the current position and the Area of Interest

FactorOverview+Detail
Zooming
Visualization
Number of views

Fig. 5. The gesture to zoom and rotate simultaneously. From left to right:
scale up the object and rotate clockwise; from right to left: scale down
the object and rotate anti-clockwise.

(AoI), but slightly away from the AoI to ensure it is within the user’s
FoV. The orientation is the direction of this straight line.
Drag-and-drop teleportation is expected to give users more control of
their position and orientation and possibly give them a better estimationof their position and orientation after the teleportation. However, thismulti-step operation is not welcomed by all users [33]. Point-and-click
teleportation requires less steps, but may increase the gap between the
expected and actual teleported position and rotation. Like many other
2D interfaces, we include both mechanisms in our visualizations, to let
users choose their preferred option.
3.2 Zooming
Although 2D desktop interfaces usually use the scroll-to-zoom
metaphor, pinch-to-zoom is the standard zooming gesture on most
multi-touch devices. The idea of pinch-to-zoom is to re-scale according
to the distance between two touch points [28]. Immersive systems
can naturally be considered as multi-touch systems as they are capableof tracking at least two hand-held controllers. Therefore, we use thepinch-to-zoom gesture in our visualizations.
The naive implementation of pinch-to-zoom in immersive environments (i.e., only scaling the size of the object) shifts the positions of
the controllers relative to the object. As a result, inconsistency is introduced between the interaction and the displayed information, which
confuses the user. To address this issue, we integrate rotation into thesame gesture, i.e., the rotation of the manipulated object is based on the
direction between the two touch points while zooming. Additionally,
we apply adjusted 3D translation to the object to ensure the positionsof the controllers relative to the zoomable object are preserved in theinteraction (i.e., latching). The simultaneous zoom and rotate gesturein the 3D immersive environment is demonstrated in Fig. 5. A similar
concept is also widely used on 2D multi-touch zooming interfaces, e.g.,
photo editing interfaces on mobile phones.
4 U SER S TUDY
We pre-registered our user study at https://osf.io/ycz5x. We also
include results of statistical tests as supplementary materials. Test
conditions are also demonstrated in the supplemental video.
4.1 Experimental Conditions
In addition to the two main effects discussed in Sec. 3, we summarize
the characteristics and parameters of test conditions in Tab. 1.
Rm: To allow the user to explore finely-detailed data, we take advantageof the large display space in immersive environments and create a roomsized visualization, see Fig. 1(a). Room-sized design in immersive
environments is considered to be more immersive than table-sizedvisualizations [32, 73]. A few types of room-sized visualizations havebeen explored, e.g., node-link diagrams [34], egocentric globes [73],and scatterplots [32, 52]. Room-sized visualizations are expected toscale better for representing finely detailed data. However, only subparts of the visualization can be seen by the viewer at one time, so thatthe user may lose context during exploration.
We use a 3D cube of 2×2×2 meters as the display space of the roomsized visualization. Manipulating a large display space in an immersive
environment is likely to introduce strong motion sickness [73]. We
therefore keep the position and rotation of the display space fixed.
Participants can freely move by walking (a few steps) within the space
as well as use pointer teleportation, i.e., the user can use a pointer tochoose the destination on the floor and then click the controller button toteleport to the destination in the immersive environment. Such pointerteleportation is now a standard locomotion mechanism in major VR
platforms (like Oculus, SteamVR and Windows Mixed Reality). We

Rm
✘
✘

RmO
✔
✘

1

2
Overview : 40 cm
Detail view : 2 m
Overview : ✘Detail view : ✘Overview : ✔
Detail view : ✘

Size

2m

Resize✘Grab✘

Locomotion
Physical movement
Pointer teleportation
Overview teleportation

✔
✔
✘

✔
✔
✔

Zm
✘
✔

ZmO
✔
✔

1

2
Overview : 40 cm
Detail view : 60 cm
Overview : ✘Detail view : ✔
Overview : ✔
Detail view : ✔

60 cm
✔
✔
✔
✔
✘

✔
✔
✔

Table 1. Characteristics and parameters of test visualizations.

enable this standard functionality in all our tested conditions. This is
the only support for navigation in this condition.
RmO: In this condition, in addition to Rm, we provide an overview ofthe display space, see Fig. 1(b). The detail view of RmO is the same as
Rm. The overview is a 3D cube of 40×40×40 centimeters when it isenlarged (see Fig. 3). The default size of the overview is 10×10×10
centimeters. Participants can grab the overview by moving a hand-heldcontroller inside and hold the trigger button. The overview will thenattach to this controller. Moving and rotating the controller will also
move and rotate the overview. We did not allow participants to resize
the overview, as it would increase the complexity of the interactions.
Participants can teleport using the overview as discussed in Sec. 3.1.
Zm: The visualization is initially table-sized (60×60×60 centimeters),
and participants can use the pinch-to-zoom gesture (described in Sec.
3.2) for resizing, see Fig. 1(c). The small initial size allows participants
to have an overview of the information first, which is recognized as
the standard analytic work flow. We also allow participants to grab theview and manipulate it with a hand-held controller.
ZmO: In this condition, in addition to Zm, we provide an overview of thezooming view, see Fig. 1(d). The detail view of ZmO is the same as Zm(with an initial size of 60×60×60 centimeters), and the overview is thesame as it is in RmO (with an enlarged size of 40×40×40 centimetersand default size of 10×10×10 centimeters).
4.2

Experimental Setup

We used a Samsung Odyssey virtual reality headset with a 110° fieldof view, 2160×1200 pixels resolution and 90 Hz refresh rate. The PC
was equipped with an Intel i7-9750H 2.6 GHz processor and NVIDIA
GeForce RTX 2060 graphics card. The study took place in a space withapproximate 2.5×2.5 meters (6.25 m2 ).
Following feedback from our pilot user study and as a common
practice for reducing motion sickness in VR [42, 73], we created an
external reference frame, which is a 4×4 meters virtual floor.
Rm and the detail view of RmO shared the same center of the physicalroom. Their orientations were identical in the whole study. Zm and thedetail view of ZmO were placed 50 centimeters in front of the user’s
head position and 50 centimeters below it. This setup allows users toeasily reach the visualization and keep the full visualization within their
FoV at the beginning of each trial. We repositioned and resized thevisualization at the beginning of every trial. We also asked participants
to move back to the center before the start of every trial.
4.3

Data

We used MNIST [38], a real-world handwritten digits database to generate point cloud data. For each data set, we first randomly sampled
5,000 images as data points , and then used t-SNE [40] to calculate theirprojected 3D positions (i.e., 5,000 points per scatterplot). The t-SNE
technique projects high-dimensional data into two or three dimensions.
In our case, we used TensorFlow’s projection tool [64] as the implementation of t-SNE to project 784 dimensions (28 × 28 pixels) per image
to three dimensions. We kept the default parameters and executed 800
iterations per data set, which has been tested to be sufficient for gettingFig. 6. Example stimuli for three task conditions. The labels are only for demonstration purposes. (a,b) Distance: participants had to estimate whichpair of colored points (yellow or red) has the larger spatial distance. The distance within each pair varies in (a) and (b) to be relatively close and far
respectively. (c) Count: participants had to find which group of colored points (yellow, red or blue) has the largest number of points.

a stable layout. We used different data sets for all trials. In total, we
generated 60 data sets (4 for visualization training trials, 16 for task
training trials, and 40 for study trials). All points are colored gray,except the red-, yellow-, and blue-colored targets in tasks. Points inthe scatterplot were rendered as spheres with 3 cm diameter in Rm andthe detail view of RmO. The size of the points was proportional in otherrepresentations. Sample data is shown in Fig. 6.
4.4

Tasks

Sarikaya and Gleicher proposed a task taxonomy for scatterplots. This
identified three types of high-level tasks: object-centric, browsing, andaggregate-level [58]. Instead of investigating fine detailed information, browsing and aggregate-level tasks are looking at general patterns,
trends or correlations. These types of tasks require relatively less navigation effort, and participants preferred small-sized display spaces forsome of these tasks [32]. To better understand the navigation performance, we intended to select tasks that require relatively significant
navigation efforts. For our user study, we chose two object-centric tasks
that require the participant to navigate to the fine detailed data.
Distance: Which of the point pairs are further away from each other:
the red pair or the yellow pair? Comparing distance is representativeof a variety of low-level visualization tasks, e.g., identifying outliersand clusters. These tasks are also essential parts of high-level analysis processes, e.g., identifying misclassified cases and understanding
their spatial correlation with different nearby classes in the embedding
representation of a machine-learning system. Variations of this task
have been studied in most of the studies we reviewed [2, 32, 52, 67, 70].
Among them, we directly adopted this task from Bach et al [2]. Similar
to their study, we had two target pairs: one pair was colored red, andthe other pair was colored yellow (see Fig. 6 (a,b)). The point cloud
was dense yet sparse enough that the target points could be identified
without the need for interactions other than changing the viewing direction. In all conditions, the participants had to first search for the targets
and then compare their 3D distance by moving/teleporting around thespace and/or rotating the visualization when available (see Tab. 1).
Participants needed to choose from two choices: red or yellow.
Whether the two points in a pair can be both presented in the FoV
can be a key factor affecting the performance in immersive visualizations [73]. We investigated this factor by creating two categories of
distance: Close and Far. In Close, the larger distance of the pair wascontrolled to be 25% of side length of the view (e.g., 0.5 meters in Rm).
In Far, we controlled this parameter to be 75% (e.g., 1.5 meters in Rm).
We also controlled the difference between the distances of the two pairs
to be 10%. We expect a small difference can potentially encourage
participants to verify their answers from different viewing positions anddirections and thus increase the number of navigations. For the same
reason, we placed each pair far away from the other pair (i.e., they had adistance of 75% of the side length of the view, for example, 1.5 metersin Rm). We developed an automatic strategy to select the points to meetall controlling requirements. We first repeatedly randomly select a pairof points from the 5000 points in a data set until the pair meets the
distance requirement for Close or Far and then keep randomly selecting
the other pair until all other requirements are met.

Count: Which group has the largest number of points: the red group,
the yellow group, or the blue group? This task is essential for processes that require the understanding of numerosity, e.g., counting thenumber of misclassified cases or cases with specific properties for aclassification system. Again, variations of this task have been studiedin some of the studies we reviewed [2, 67, 70]. We created three groupsof points, which were colored in red, yellow, and blue (see Fig. 6 (c)).
The points in a group were close to each other to form a small cluster.
Points could partially overlap with each other, but we made sure thatthe number of points is unambiguous. The participant has to first search
for the groups and then sequentially get close to each group to countthe number of points within that group. In all conditions, participants
can move or teleport around the space. In Zm and ZmO, participants alsoneed to enlarge the view to count the points. Participants are not able
to count the points in the overview in RmO and ZmO due to its small size.
Participants need to choose from three choices: red, yellow, or blue.
The number of points in a group varied from 5 to 10. Again, toincrease the potential number of navigation steps needed to complete
this task, we placed groups far apart from each other (approximate 50%of the side length of the view, that is, e.g., one meter in Rm). Unlike in
the Distance tasks where we used an automatic process to select targets,in the Count task, such method may produce ambiguous overlappingcases. Instead, we manually selected groups of points for each trial.
4.5

Participants

We recruited 20 participants (14 females and six males) from Harvard
University. All had a normal or corrected-to-normal vision, were righthanded, and all were college students. All participants were within
the age range of 20−30. VR experience varied: three participants
had no experience before this user study; ten participants had 0−5
hours experience; four participants had 5−20 hours experience, andthree participants had more than 20 hours of experience. Most of
our participants do not play computer/video/mobile games frequently:
17 participants reported they played less than 2 hours of games per
week, and the other three participants played 2−5 hours per week. We
provided a $20 gift card as compensation for each participant.
4.6

Design and Procedures

The experiment followed a full-factorial within-subject design. We
used a Latin square (4 groups) to balance the visualizations, but kept
the ordering of tasks consistent: Distance then Count. The experimentlasted 1.5 hours on average. Each participant completed 40 study trials:
4 VR conditions × (3 Distance-Close + 3 Distance-Far + 4 Count)
Participants were first given a brief introduction to the experiment
and VR headset. After putting on the VR headset, we asked themto adjust it to see the sample text in front of them clearly. We thenconducted a general VR training session to teach participants how tomove in VR space and how to manipulate a virtual object. First, we
asked participants to move for a certain distance physically. Then
we told them to touch the touchpad to enable the pointer and click
the touchpad to teleport. We asked participants to get familiar withthe pointer teleportation with a few more teleportations. At the final
stage of the pointer teleportation training, we asked them to teleportto a place marked with a green circle on the floor. We then asked
the participants to grab a green cube by putting the controller inside
the cube and holding the trigger button. The participants finished thetraining session by placing the green cube at a new indicated position
with a specific rotation. All participants completed the training andreported that they were familiar with the instructed interactions. The
training session took around 5 minutes.
We conducted a visualization training session every time a participant encountered a visualization condition for the first time. In the
training session, we introduced the available interactions and asked
participants to get familiar with them with no time limit. Each condition (visualization×task) started with 2 training trials followed by
timed study trials. Before each trial, we re-positioned participants to
the room’s center and faced them in a consistent direction. In the training trials, participants were not informed about specific strategies forcompleting the task but were encouraged to explore their own strategies.
The correct answer was presented to them after they had selected ananswer in the training trials. If a participant answered incorrectly, we
asked the them to review the training trial and verify their strategies.
After each task, participants were asked to fill in a questionnaire
regarding their strategies in each visualization, their subjective ratingsof confidence, mental and physical demands of each visualization, andto rank the visualizations based on their preference. We had a 5-minutebreak between two tasks. After completing two tasks, participants wereasked to fill another survey rating the overall usability and discussing
the pros and cons of each visualization. The demographic information
was collected at the end of the user study. The questionnaire listed
visualizations in the same order as presented in the experiment.
4.7

MeasuresWe measured time from the first rendering of the visualization to adouble-click of the controller trigger. After the double-click, the visualization was replaced by a multiple-choice panel with task description
and options. Participants’ choice was compared to the correct answer
for their accuracy. We recorded the position and rotation of the headset,
controllers, and visualizations every 0.2 seconds. We also recorded
the number of different interactions participants conducted in eachstudy trial, including teleportation and zooming. We also collected
the overview usage percentage, which is the percentage of time theparticipant was looking at the overview of each study trial. The sizeof both Zm and ZmO were also collected every 0.2 seconds. In the pilot
study, we also asked participants to report the level of motion sickness
they experienced in each condition. All participants reported the minimal level of motion sickness for all conditions. This could be becausethat the participant’s FoV was not fully occupied at any time, and theparticipant could easily access the visual reference (the floor). Thus,
we decided to not record the motion sickness level in the formal study.
4.8

Statistical Analysis

For dependent variables or their transformed values that can meetthe normality assumption, we used linear mixed modeling to evaluate
the effect of independent variables on the dependent variables [8].
Compared to repeated measure ANOVA, linear mixed modeling iscapable of modeling more than two levels of independent variables anddoes not have the constraint of sphericity [24, Ch. 13]. We modeled all
independent variables and their interactions as fixed effects. A withinsubject design with random intercepts was used for all models. We
evaluated the significance of the inclusion of an independent variable
or interaction terms using log-likelihood ratio. We then performed
Tukey’s HSD post-hoc tests for pair-wise comparisons using the leastsquare means [39]. We used predicted vs. residual and Q — Q plots tographically evaluate the homoscedasticity and normality of the Pearson
residuals respectively. For other dependent variables that cannot meetthe normality assumption, we used a Friedman test to evaluate theeffect of the independent variable, as well as a Wilcoxon-NemenyiMcDonald-Thompson test for pair-wise comparisons. Significancevalues are reported for p < .05(∗), p < .01(∗∗), and p < .001(∗ ∗ ∗),respectively, abbreviated by the number of stars in parenthesis.

Fig. 7. Results for time (seconds) and accuracy by task. Confidence intervals indicate 95% confidence for mean values. A dashed line indicatesstatistical significance for p < .05.

Fig. 8. Camera movement distance per task trial. A dashed line indicatesstatistical significance for p < .05.

5 R ESULTS
In this section, we first summarize self-reported strategies, then provide
a pairwise comparison of performance (task time and accuracy) withthe different visualization conditions. Finally we discuss interactions,user preference, and qualitative feedback.
5.1 How did participants complete the tasks?
We asked participants to describe their strategies after each task. We
found participants’ strategies were relatively consistent.
The distance task: In Rm, most participants (14 out of 20) stayed
within the visualization space, within which, four participants explicitly
mentioned that they used the pointer to “jump” to the center of a pairof points as well as the center of two pairs. Six other participants statedthey teleported outside the visualization space to have a better overview
first, and then teleported back to the visualization space.
In RmO, most participants (13 out of 20) mentioned they mainly used
the overview to find points. Eight participants used the overview toestimate the distance first, and then confirmed the answer in the detailview. 11 participants reported that they used the overview to teleport.
Four participants used the same strategy they used in Rm to teleport tothe center of a pair of points as well as the center of two pairs.
In Zm, most participants (17 out of 20) tried to find points in thesmall-sized view, and then compared the distance with an enlarged
view. Other participants completed tasks with only small-sized views.
In ZmO, most participants (18 out of 20) used the most popular
strategy in Zm, i.e., using the small-sized view to find points, andcomparing distances with an enlarged view. In which, seven participants
mentioned that they sometimes used the overview to teleport when thevisualization was enlarged. Two other participants kept the visualization
small all the time to answer the questions.
The count task: In Rm, most participants (14 out of 20) mainly physically walked to the place of interest in the space while the other six
participants reported they mainly used pointer teleportation.
In RmO, most participants (17 out of 20) mainly used the overview toteleport. Two other participants mainly used pointer teleportation, andone participant mainly walked.

Fig. 9. Number of interactions per task trial. The number of interactions is considered to be the sum of number of teleportations and number ofzoomings. A dashed line indicates statistical significance for p < .05.

having no significant gaming experience (17 out of 20 play less than
2 hours of games per week). However, due to the limited number ofparticipants with gaming experience in our user study, we are unable todraw statistical conclusions about this effect.

Fig. 10. Average usage of the overview per trial. A dashed line indicatesstatistical significance for p < .05.

In Zm, most participants (16 out of 20) zoomed in and out to reachdifferent groups. Three other participants first enlarged the visualization, then grabbed and moved the view to get to groups. One participant
first zoomed in and then used the pointer to teleport to groups.
In ZmO, most participants (14 out of 20) zoomed in and out to complete the task and stated that they did not use the overview much. Six
other participants first enlarged the visualization, and then used theoverview to teleport to groups.
5.2 Is having an overview beneficial?
Rm vs. RmO: We found Rm was faster in the Count task (∗∗). Rm alsotended to be faster in the other tasks, but the differences were notstatistically significant. We also found RmO was more accurate in the
Distance-Close task (∗), see Fig. 7. We believe the improved accuracy
may come from the fact that the overview provided a different perspective as well as a different scale for the participants to confirm theiranswers. Eight participants explicitly reported using the overview for
the distance comparison (see Sec. 5.1). We also found participants felt
more confident with RmO than Rm in the Distance task (∗∗, see Fig. 14)
which aligned with their higher accuracy in RmO.
Zm vs. ZmO: We found similar performance between Zm and ZmO, exceptthat ZmO was slower than Zm in the Distance-Far task condition (∗, seeFig. 7). The very similar performance may because participants only
use the overview occasionally in ZmO. Apart from the overview, Zm
and ZmO share the same view and interactions. The limited use of
the overview in ZmO can be confirmed from both the users’ strategy(see Sec. 5.1), and the fact that participants only spent around 10% on
average of their time looking at the overview (see Fig. 10). This findingaligned with the results from Nekrasovski et al. [47] where they foundthat presence of an overview did not affect the performance of a 2D
zoomable hierarchical visualization (rubber sheet).
Summary: Overall, adding an overview can increase task accuracy insome tasks, but may also introduce extra time cost. We also found an
overview seems to be unnecessary in Zm, and adding one may even be
distracting or disturbing for difficult tasks (e.g., the Distance-Far task).
Due to the very similar performance between Zm and ZmO, we did notinclude ZmO in the following pair-wise comparisons explicitly.
5.3 Visualization manipulation vs. Move (Zm vs. Rm)
We found Zm was slower than Rm in the Count task (∗∗∗). It tended to be
slower in the Distance-Close task but not significantly. Zm and Rm had
similar time performance in the Distance-Far task. Our results partiallyalign with the results from Lages and Bowman [35]. They found that theperformance of walking and object manipulation in VR was affectedby the gaming experience of participants. In essence, participants
without significant gaming experience performed better with physicalmovement, while 3D manipulation enabled higher performance forparticipants with gaming experience. Most of our participants reported

5.4 Zooming vs. Overview+Detail (Zm vs. RmO)
We found Zm and RmO had similar time performance in the easier tasks(i.e., the Distance-Close and Count tasks), and Zm was faster than RmO
in the difficult task (i.e., the Distance-Far tasks, ∗, see Fig. 7). Previous
user studies on 2D displays also found a similar time performance between these two types of interfaces (e.g., [51, 55]) in simple navigation
tasks. We also found RmO was more accurate in the Distance-Close task(∗). This finding is partially aligned with the study by Plumlee andWare [51] where they also found overview+detail increased the accuracy compared to a zooming interface on a 2D display. They suggested
that the benefit may be due to reduced visual working memory load byhaving an extra view in the overview+detail interface.
5.5 How did participants move and interact?
We found that participants had significantly more camera movementin Rm and RmO than in Zm and ZmO (all ∗ ∗ ∗). Rm also required morecamera movement than RmO in the Distance-Far task (∗ ∗ ∗) (see Fig. 8).
Motion parallax is a likely explanation. It is key to depth perception
in immersive environments: a stronger cue than stereopsis, as well as
being key to resolving occlusion. As the size of visualization increases,
you have to move further to get the same motion parallax benefits.
We also found participants
teleported significantly more in
Rm and RmO than in Zm and ZmO(all ∗ ∗ ∗). Rm also required
more camera movement than
RmO in the Distance-Close andDistance-Far tasks (∗ ∗ ∗). Participants also performed significantly more zooming interac- Fig. 11. Size of the zoomable visualtions in Zm than ZmO in the ization per trial.
Count task (∗ ∗ ∗). The size ofthe zooming interface was shown in Fig. 11.
We also added up the number of teleportation and zooming steps
as the number of interactions. We found participants performed moreinteractions in Rm than in RmO (∗) and Zm (∗ ∗ ∗) in the Distance-Far
task. We also found Zm and ZmO required more interactions than Rm and
RmO in the Count task (all ∗ ∗ ∗).
In summary, we found that overview or zoom reduced the number ofrequired movements and teleportation compared to standard locomotion
support alone. We also found Zm and ZmO needed a significant amountof pinch-to-zoom interactions in the Count tasks.
5.6 Which condition did participants prefer?
We asked participants to rank visualizations according to their preference for each task (see Fig. 12). For both the Distance and Count tasks,
we found participants preferred Zm (∗ ∗ ∗) and RmO (∗) over Rm. We also
found Zm was preferred over RmO (∗). Participants also rated the overallusability (see Fig. 13). We found the Rm was considered to have lower
usability than RmO (∗∗), Zm (∗ ∗ ∗) and ZmO (∗).
Zm tended to be the most preferred visualization in our user study
with more than 50% of participants ranking it best in both tasks (seeFig. 12). Zm was also reported to be less demanding (see Fig. 14).
Rm was not preferred by our participants, even though it generallyFig. 12. User preference ranking of each condition for two tasks (Distanceand Count). Dashed lines indicate p < .05.

Fig. 13. Overall usability ratings. Dashed lines indicate p < .05. Percentage of negative and positive rankings is shown next to the bars.

performed well (see Fig. 7). There could be two possible reasons: First,
participants felt Rm was more physical demanding (see Fig. 14) andthe recorded movement data confirmed their subjective feeling (seeFig. 8). Second, with a fixed large scale single-view visualization,
Rm was expected to have a high visual working memory load. The
higher number of interactions and movements in Rm partially supports
this assumption. Subjectively, participants also rated Rm to be morementally demanding than Zm (∗) and ZmO (∗) in the Count task.
5.7 Qualitative user feedback
We asked participants to give feedback on the pros and cons of each
design. We clustered comments into groups for each visualization.
In this subsection, we demonstrate representative ones along with thenumber of participants mentioned these similar comments.
Rm was mentioned to be “close to real life” by 11 participants.
Among them, four participants explicitly reported it to be “immersive”,
three participants felt “more engaged”, and three participants liked its
fixed view: “it is easier to remember the points, whether in front or
behind me.” However, ten participants also reported “it is difficult tofind the points sometimes.”
RmO was considered an improvement over Rm. 15 participants reported that “the minimap was really useful for finding the points andmoving around.” Three participants also stated that “it is really good tohave two scales [of views] at the same time.” However, two participants
felt “overwhelmed” by the interactions. Another two complained that“it breaks spatial continuity [when teleporting with the overview].”
Zm was found to be “intuitive” and “easy to use” by 11 participants.
Among them, three participants mentioned that they like the “flexibility” of the interaction and feel they have “more control”. One alsocommented that “it solves the problem of distance in a continuous way.
Without losing the reference.” However, three commented it to be “notfeeling real [comparing to Rm and RmO].” Two others mentioned: “I
may lose perspective after I move or zoom the view multiple times.”ZmO was mainly compared to Zm. Six participants found “the minimap was good to jump around.” However, 12 participants commented
that “I did not use the minimap much.” Five participants also complained that “it can be confusing as you have too many choices.”
5.8 Summary
Of the four navigation methods that we tested, we found some significant differences in participant performance across the different tasks.
However, there was no one navigation method that was best for every task. The overview increased accuracy for the Rm condition in the
Distance-Close task, however, the overview seemed to be an unnecessary distraction in the other tasks, and provided no benefit to the Zm
condition. Zm was faster in the most difficult task (i.e., the Distance-Fartask). Participants also clearly did not like the Rm condition.
6 D ISCUSSION AND N AVIGATION T IME -C OST M ODELOur study did not find a single best navigation method. In particular,
analysis of the time data did not reveal a clear winner: for instance,
Zm was faster in the Distance-Far task but slower in the Count task.
Furthermore, we found that Rm performed generally well in terms of

Fig. 14. Confidence, mental demand, and physical demand ratings ina five-point-Likert scale for two tasks. Dashed lines indicate p < .05.
Percentage of negative and positive rankings is shown next to the bars.

time, but participants, for instance, complained about the difficulty offinding targets. This should have introduced extra time costs, but thiswas not reflected in the overall time.
To provide a more nuanced understanding of these mixed results,
we now provide an initial exploratory analysis of the timing results based on previously suggested models of time cost for navigation [13, 48, 50, 51] and interactive visualization [36, 69]. Navigation
is a complex process with multiple components and the relevance of
these components will vary in different tasks. By considering the costof each component separately, we hope to better explain our results.
For example, while participants might spend more time identifying
the targets with Rm, they may spend less time on other components,
thereby compensating for this loss. Based on the literature, the fourmost essential components in models of navigation time-cost are:Wayfinding (term from [13, 48]): This is the process of finding thedestination. Similar to decision costs to form goals in [36].
Travel (term from [13, 48]): This is the process of “moving” to thedestination. It can be walking, teleportation or manipulating the visualization to the desired form. Similar to physical-motion costs to execute
sequences in [36] and transit between visits in [50, 51]
Number-of-travels (term from [50,51]): Due to limited visual working
memory [69], completing a task can involve more than one travel toaccess information or to confirm the answer.
Context-switching (term from [69]): When the perceived view
changes (either through physical movement or manipulating the visualization), the user must re-interpret it based on expectation. Similar
to view-change costs to interpret perception in [36].
In the rest of this section, we first analyze our visualization conditions with our navigation time-cost model. We then discuss the relative
importance of the components in our two tasks. Finally, we summarize
our discussion by demonstrating how we can use our model to suggest
visualization techniques for different tasks. We also demonstrate how
we can use this model to identify the specific performance bottleneckof a visualization, and then propose potential strategies to improve it.
6.1 Visualization Analysis
In this subsection, we analyze the time cost (or performance) of ourvisualization conditions in terms of the above components. The resultsof our analysis are demonstrated in Fig. 15.
Wayfinding: The overview in RmO could better facilitate the processof identifying targets compared to Rm. Participants’ comments confirmed this, where 12 out of 20 mentioned “it is much easier to findthe points [in RmO] with the minimap [, rather than in Rm].” For thesame reason, we believe that the overview in ZmO can better support
identifying targets compared to Zm, especially when the visualizationis enlarged. Zm supports searching targets in its small-sized state well.
This is confirmed by the users’ strategy where most participants locatedtargets with size-reduced (or zoomed-out) Zm (see Sec. 5.1). However,participants lose the overview once they enlarge the visualization. Participants clearly had difficulties in finding the targets in Rm(see Sec. 5.7).
In summary, we suggest that the time-cost of our tested visualizations
in wayfinding is ordered as: RmO < ZmO < Zm < Rm.

Task
Distance-Close
Distance-Far
Count

Wayfinding
MediumHigh
Low

Travel
High
High
High

# of Travels
MediumHigh
Low

Context-switching
MediumHigh
Low

Table 2. Relative importance of time-cost components for tasks.

Fig. 15. Navigation time-cost of our tested conditions broken down into
four navigation components. Positions are relative and qualitative, notbased on precise metrics.

Travel: We believe, in our relatively small-sized testing environment,
physical movement in Rm might take less time than Zm. Familiarity
with natural walking could make Rm outperform the relatively unnatural pinch-to-zoom gesture of Zm (i.e., people are unable to rescale aphysical object in real life). This assumption was partially confirmed
by previous studies (e.g., the ones reviewed by Ball et al. [6]) where
physical movement gives better time performance using visualizations
on large tiled displays. In Rm, apart from physical movement, we also
provide pointer teleportation. However, pointer teleportation can only
ease transit if the destination is within the users’ FoV. In RmO, the users
can teleport to a place outside their FoV using the overview. Comparing
to Rm, RmO has a more flexible teleportation mechanism, which should
result in a faster transit. For the same reason, we believe ZmO could
outperform Zm in travel. In summary, we suggest that the time-cost of
our tested visualizations in travel is ordered as: RmO < Rm < ZmO < Zm.
Number-of-travels: We use recorded interaction data as a proxy measure of the number-of-travels. Overall, Rm clearly required significantly
more physical movement and teleportations than other visualizations(see Sec. 5.5). RmO also required more physical movement and teleportation than Zm (see Sec. 5.5). Although Zm required a large number ofzooming in the Count task, we believe RmO required an overall larger
number of travels. We found that the camera movement was similarin Zm and ZmO. Meanwhile, ZmO required more teleportation, while
the number of performed zooming interactions was more in Zm. In
summary, we suggest that our tested visualizations in number-of-travels
is ordered as: Zm ≈ ZmO < RmO < Rm.
Context-switching: Physical movement is a spatial-continuous activity, which we consider to induce minimal context-switching costs. We
also consider the “pinch-to-zoom” gesture a spatial-continuous traveling method which has similar performance compared to physicalmovement. Instant movement by teleportation introduces spatial disorientation and discontinuity [3, 11]. Furthermore, compared to themore predictable pointer teleportation where the destination is usually
within the FoV, teleportation with the overview is expected to have ahigher cost. Apart from teleportation, a user can also move based on theinformation in the overview (e.g., a user can identify the target is rightof the current viewing direction in the overview and then turn right tofind the target). This operation is also expected to be high-cost, as theuser needs to visually link two separate display spaces. In Rm, participants performed more teleportations than in Zm (see Fig. 9), which we
consider inducing greater context-switching costs. Participants also
spent more time with the overview in RmO than in ZmO (see Fig. 10).
In summary, we suggest the time-cost of our tested visualizations incontext-switching is ordered as: Zm < Rm < ZmO < RmO.
6.2

Task Analysis

Based on the quantitative interaction data, qualitative feedback, and ourobservations in the user study, we infer the relative importance of thetime-cost model components for our tested tasks (see Tab. 2).
In the Count task, the targets are groups of points, so they are easy
to find. Therefore, we believe that participants required minimal effort
in wayfinding, and the number of travels is near identical across tested
conditions. The context-switching effort should also be relatively low,
as points in one group were all within the FoV. Thus, participants did
not require frequent switching of views. Participants still needed toswitch views when moving to the next target group, but the number ofsuch switches is relatively low.

For the Distance task, there are only four colored targets, so thetarget points were more difficult to locate. Participants had to keepchanging their viewing position and direction to find them. Moreover,
the targets were mostly not within the participant’s FoV at the sametime, so participants had to switch views frequently to perform thecomparison. The recorded interaction data shows that the DistanceFar task required more physical movement than the other two task
conditions in Rm (∗ ∗ ∗), RmO (∗ ∗ ∗), and ZmO (∗).
In summary, we suggest that the effort required for wayfinding,number-of-travels, and context-switching was higher in the Distancetask than in the Count task. Within the Distance task, the Far condition
requires more effort in these three components than the Close condition.
Travel is an essential part in all navigation tasks, and we consider it tohave a high weight in all conditions.
6.3 Suggesting visualizations for tasks
We demonstrate the potential of our navigation time-cost model torecommend visualization techniques for different tasks. We do this byexplaining the overall time performance using the analysis results fromSec. 6.1 and 6.2.
For tasks that are less demanding on wayfinding and number-oftravels (e.g., the Distance-Close and Count tasks in our study), Rm is
expected to have a good performance. This is because although Rm
is not good at these two components, they have a limited amount ofinfluence. On the other hand, Rm shows an overall good performanceon the more important component (i.e., travel). For tasks that requirea significant effort in number-of-travels and context-switch (e.g., theDistance-Far task in our study), Zm is a good choice, as it outperforms
other conditions on these two components.
RmO has its advantages for wayfinding and travel, but the high cost incontext-switching significantly influences its performance. For futurestudies, we should consider techniques that reduce the effort for contextswitching in RmO, e.g., animated teleportation [10, 63], or instead ofalways teleporting forwards, allowing users to interactively choose theirviewing direction of the teleportation destination [27]. We also propose
a preliminary idea that when the user selects a target in the overview,a visual indicator will appear in the detail view to guide the user tothe target. This is inspired by the work from Petford et al. [49], which
reviewed guiding techniques for out-of-view objects.
7 C ONCLUSION AND F UTURE W ORK
We would recommend that developers of immersive visualization systems provide a variety of navigation methods to suit different tasks andenvironments. For example, if the user has the capability to operate
in a large open space, then there are definitely tasks (such as Distance
Close) that will benefit from room-size navigation. However, in seatedVR, the zoom is going to be essential. Our adaptation of the traditional
overview technique may be useful in room-size navigation for tasks
that require operation at different scales, but such an overview shouldbe easy to hide until required, to prevent distraction.
For future studies, a larger tracking space would support greater
physical navigation but may also cause significant fatigue. Larger,
more complex data may benefit the overview more. We also suggestthat designs that can reduce context-switching cost in overview+detailinterfaces are likely to improve its performance. We also would like todesign studies to verify our navigation time-cost model systematically.
ACKNOWLEDGMENTS
This research was supported in part under KAUST Office of SponsoredResearch (OSR) award OSR-2015-CCF-2533-01 and Australian Research Council’s Discovery Projects funding scheme DP180100755.
Yalong Yang was supported by a Harvard Physical Sciences and Engineering Accelerator Award. We also wish to thank all our participants
for their time and our reviewers for their comments and feedback.

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