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Origin-Destination Flow Maps in Immersive Environments

Yalong Yang, Tim Dwyer, Bernhard Jenny, Kim Marriott, Maxime Cordeil and Haohui Chen

Fig. 1. 3D Globe (left) was the fastest and most accurate of our tested visualisations. Flat maps with curves of height proportional to

distance (right) were more accurate but slower than 2D straight lines. Experiments were conducted individually in virtual reality but our

motivation for this work is to support future mixed-reality collaborative scenarios like those envisaged in these ﬁgures.

Abstract

— Immersive virtual- and augmented-reality headsets can overlay a ﬂat image against any surface or hang virtual objects in

the space around the user. The technology is rapidly improving and may, in the long term, replace traditional ﬂat panel displays in many

situations. When displays are no longer intrinsically ﬂat, how should we use the space around the user for abstract data visualisation?

In this paper, we ask this question with respect to origin-destination ﬂow data in a global geographic context. We report on the ﬁndings

of three studies exploring different spatial encodings for ﬂow maps. The ﬁrst experiment focuses on different 2D and 3D encodings for

ﬂows on ﬂat maps. We ﬁnd that participants are signiﬁcantly more accurate with raised ﬂow paths whose height is proportional to ﬂow

distance but fastest with traditional straight line 2D ﬂows. In our second and third experiment we compared ﬂat maps, 3D globes and a

novel interactive design we call MapsLink, involving a pair of linked ﬂat maps. We ﬁnd that participants took signiﬁcantly more time with

MapsLink than other ﬂow maps while the 3D globe with raised ﬂows was the fastest, most accurate, and most preferred method. Our

work suggests that careful use of the third spatial dimension can resolve visual clutter in complex ﬂow maps.

Index Terms—Origin-destination, Flow Map, Virtual Reality, Cartographic Information Visualisation, Immersive Analytics

1 INTRODUCTION

In many applications it is important to visualise the ﬂows between

different geographic locations. Such ﬂows include, for example, mi-

gration patterns [56], movement of goods or knowledge [45], disease

or animals [23, 24]. Here we restrict attention to ﬂows that start and

end at ﬁxed geographic locations but whose exact trajectory is either

unknown or irrelevant. Visualisation of such origin-destination ﬂows

is a difﬁcult information visualisation challenge, because both the lo-

cations of origins and destinations and the connections between them

need to be represented. The most common visualisation is the OD

(origin-destination) ﬂow map, where each ﬂow is represented as a line

connecting the origin and destination on a map. A disadvantage of

OD ﬂow maps is that they become cluttered and difﬁcult to read as the

number of ﬂows increases. Nonetheless, ﬂow maps remain popular as

they are intuitive and well-suited to showing a small number of ﬂows.

With the arrival of commodity head-mounted displays (HMDs) for

virtual-reality (VR), e.g. HTC Vive, and augmented-reality (AR), e.g.

Microsoft Hololens, Meta2 and Magic Leap, we can expect to see

geographic visualisations such as OD ﬂow maps used in mixed-reality

(MR) applications. Such applications include situated analytics [20]

• Yalong Yang is with Monash University and Data61, CSIRO, Australia.

E-mail: yalong.yang@monash.edu.

• Tim Dwyer, Bernhard Jenny, Kim Marriott and Maxime Cordeil are with

Monash University. E-mail: {tim.dwyer, bernie.jenny, kim.marriott,

max.cordeil}@monash.edu.

• Haohui Chen is with Data61, CSIRO, Australia. E-mail:

caronhaohui.chen@data61.csiro.au.

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

where visualisations can be made available in almost any environment

such as in the ﬁeld, surgery or factory ﬂoor, and collaborative visualisa-

tion scenarios, where two or more people wearing HMDs can each see

and interact with visualisations while still seeing each other [12].

The key question we address is whether traditional 2D OD ﬂow

maps are the best way to show origin-destination ﬂow in such immer-

sive environments or whether some variant that makes use of a third

dimension may be better. While current guidelines for information

visualisation design caution against the use of 3D spatial encodings of

abstract data [42, Ch. 6], in the case of global ﬂow data visualised in

immersive environments the third dimension offers an extended design

space that is appealing for a number of reasons:

•

The height dimension offers the possibility of an additional spatial

encoding for data attributes.

•

Lifting ﬂow curves off the map may reduce clutter and provide better

visibility of the underlying map.

•

In immersive environments, occlusions can be resolved by natural

head movements or gesture manipulations to change the view angle.

•

In 2D ﬂow maps the ﬂows may be perceived as trajectories (high-

ways, shipping routes, etc.), lifting them into the third dimension

may resolve this ambiguity.

We investigate this design space through three controlled user studies.

To the best of our knowledge we are the ﬁrst to do so. Our paper has

three main contributions.

The ﬁrst contribution is to chart the design space for 3D ﬂow maps

(Sec. 3). Following D

¨

ubel et al. [17] we separate the design space into

two orthogonal components: the representation of ﬂow, e.g. straight

or curved lines in 2 or 3D, and the representation of the geographic

reference space, e.g. 3D globe or ﬂat map. Furthermore, origins and

destinations can either be shown on the same or separate globes or

maps. This leads to a rich multi-dimensional design space.

The second contribution is evaluation of different ﬂow maps in VR

arXiv:1908.02089v1 [cs.HC] 6 Aug 2019

differing in the representation of ﬂow (Study 1, Sec. 4). We compared

2D ﬂow representations with (a) straight and (b) curved ﬂow lines, and

3D ﬂow tubes with (c) constant height, height varying with (d) quantity

and (e) distance between start and end points. We measured time and

accuracy to ﬁnd and compare the magnitude of ﬂow between two pairs

of locations. We found that participants were most accurate using 3D

ﬂows on ﬂat maps when ﬂow height was proportional to ﬂow distance

and that this was the preferred representation. Participants were less

accurate with straight 2D ﬂows than with 3D ﬂows, but faster.

The third contribution is evaluation of different ﬂow map visuali-

sations primarily varying in the representation of the reference space

(Studies 2 and 3). For the same task as above, we ﬁrst compared a ﬂat

map with 2D ﬂow lines, a ﬂat map with 3D ﬂow tubes, a 3D globe with

3D tubes, and a novel design called MapsLink involving a pair of ﬂat

maps linked with 3D tubes. We found (Sec. 5) that participants were

much slower with the linked map pair than all other representations.

What surprised us was that participants were more accurate with the

3D globe than with 2D ﬂows on a ﬂat map and linked map pairs. Par-

ticipants were also faster with the 3D globe than with 3D ﬂows on a

ﬂat map. The ﬁnal experiment (Sec. 6) was similar but with higher

densities of ﬂows. This found the 3D globe to be the fastest and most

accurate ﬂow visualisation. It was also the preferred representation.

The performance of the 3D globe is unexpected. While we assumed

that 3D ﬂows might reduce the problem of clutter, we did not expect that

the 3D globe with its potential shortcomings of occlusion and distortion

would be more effective than 2D or 3D ﬂows on a ﬂat map. However,

this result accords with [65], who found that in VR environments 3D

globes were better than maps for a variety of map reading tasks.

2 RE LATED WORK

2.1 Immersive Analytics

With the commodiﬁcation of VR and AR HMDs there is growing

interest in how to visualise abstract data in immersive environments [2,

8, 18, 34]. While there is considerable caution about the use of 3D in

abstract data visualisation, e.g. [42, Chap. 6], there is also a realisation

that data visualisation in immersive environments will be increasingly

common because of the growing ﬂexibility that MR HMDs offer over

traditional desktop environments including ability to associate data with

objects in physical environments [20] and to support collaboration [12].

Particular use cases include 3D graph layout e.g. [12, 33, 41, 59] and

multivariate data visualisation, e.g. [7,11].

There seems considerable potential to use the third dimension for

visualisation of spatially embedded data [17]. This is because the geo-

graphic reference space typically takes up two-dimensions, adding a

third dimension offers the possibility of an additional spatial encoding

for data attributes. Indeed common geographic representations such as

space-time cubes or prism maps routinely use a third dimension even

though they are to be displayed on standard desktop displays. Evalu-

ations of such 3D geographic visualisation (e.g. [38]) on ﬂat displays

has not yielded positive results. However, there has been little research

into the effectiveness of such visualisation using modern head-tracked

binocular HMDs. The most relevant study by Yang et al. [65] compared

task performance for three standard map reading tasks—distance com-

parison, area comparison and direction estimation—using different 2D

and 3D representations for the Earth. They compared a 3D exocentric

globe placed in front of the viewer, an egocentric 3D globe placed

around the viewer, a ﬂat map (rendered to a plane in VR) and a curved

map, created by projecting the map onto a section of a sphere curved

around the user. In almost all cases the egocentric globe was found to

be the least effective visualization and the curved map was generally

better than the ﬂat map. Overall the exocentric globe was the best

choice. It was slightly preferred by participants, was more accurate and

faster than the other visual presentations for direction estimation and

more accurate than the egocentric globe and the ﬂat map for distance

comparison, though more time was required for comparison of areas

than with ﬂat and curved maps.

2.2 2D Flow Visualisation

Shortly after Henry Drury Harness created the ﬁrst known ﬂow map in

1837 [50], they were popularised by Minard’s work [51]. Early digital

cartographers extended and improved techniques to map quantitative

origin-destination ﬂows and networks using straight lines with width

proportionately varying with quantitative attributes [9,37,39, 55, 56, 61].

Visual clutter is a major concern for maps with a few dozens, hun-

dreds or even thousands of ﬂows. Tobler [56] identiﬁes ﬁltering meth-

ods and guidelines for simplifying ﬂow data to increase the readability

of maps, such as sub-setting (to only show ﬂows of a selected area),

thresholding (to only display the largest ﬂows), or merging (to aggre-

gate ﬂows with spatially close origins and destinations). Interaction, as

for example described by van den Elzen and van Wijk [57], can provide

interactive ﬁltering and aggregation that restricts the set of origins and

destinations to a manageable amount.

Research in cartography [36, 40, 53] and network visualisation [27,

28] has identiﬁed design principles and aesthetic criteria that can reduce

clutter in ﬂow maps. Jenny et al. [36] compiled the following design

principles to declutter 2D maps: curving ﬂows, minimising overlap

among ﬂows [47] and between ﬂows and nodes [62], avoiding acute-

angle crossings [32], radially distributing ﬂows [31], and stacking

small ﬂows on top of large ﬂows [16]. Among techniques that employ

curvature to improve the readability of ﬂows, bundling of ﬂows into

tree-like structures rooted at ﬂow origins has been in use for a long

time and several algorithms for their automatic generation have been

proposed [5, 15, 44,46, 54]. While these techniques offer aesthetically

appealing results for one-to-many ﬂow maps, it is unclear how to best

adapt them to many-to-many ﬂows. For example, so-called conﬂuent

bundling techniques can merge ﬂows without ambiguity but can be

challenging to interpret [3]. Another problem with such bundling is

that it obscures individual ﬂow lines where they share common end

points. An alternative use of curvature is to fan out (maximise the space

between) ﬂows incident to origins or destinations [49]. Such a technique

was recently found to offer improved readability in a controlled study

[36] and is one of the conditions included in our Study 1 (Sec. 4).

Alternatives to ﬂow maps include density ﬁelds to show the spatial

concentrations of ﬂows [48,52], or OD (origin-destination) maps [63]

that spatially order ﬂows in columns and rows of connectivity matrices

embedded on a geographic map. Flowstrates [4] and MapTrix [64]

are two related approaches combining non-geographic OD matrix with

two geographic maps for showing the locations of origins and destina-

tions. In Flowstrates ﬂows connect a temporal heatmap with the two

geographic maps, and in MapTrix each ﬂow line links one OD matrix

cell with its geographic location on the two connected maps.

2.3 3D Flow Maps

Lifting origin-destination ﬂows into the third dimension is not a new

idea. Early examples of ﬂow maps drawn with three-dimensional arcs

elevated above 2D reference maps and 3D globes were introduced more

than 20 years ago [13, 14, 43]. The explicit goal of these early maps

was to increase readability by disentangling ﬂows.

The height of ﬂows above the reference map or globe can vary with

the total volume of ﬂows [19], the distance between endpoints [13],

the inverse of the distance [58], time [25] or any other attribute [58].

Discussion of such 3D “geovirtual” environments typically focuses on

interactive ﬁltering to deal with clutter (e.g. [6]). We are not aware of

any study evaluating the effectiveness of these different 3D encodings.

3 DESIGN SPACE

Visualisations of OD ﬂow data can present geographic locations of

origins and destinations, the direction of ﬂow and ﬂow weight (mag-

nitude or other quantitative attribute). OD ﬂow maps achieve this by

showing each ﬂow as a line or arrow on a map connecting the origin

and destination. In this section we explore the design space of 3D

OD ﬂow maps. D

¨

ubel et al. [17] categorize geospatial visualizations

based on whether the reference space (i. e. the map or surface) is shown

in 2D or 3D and whether the abstract attribute is shown in 2D or 3D.

In the case of ﬂow maps, this categorization implies the design space

Fig. 2. Study 1: Tested 2D and 3D ﬂow maps.

has two orthogonal components: the representation of ﬂow and the

representation of geographic region.

3.1 Representation of Flow

Flow on 2D OD ﬂow maps is commonly shown by a straight line from

origin to destination with line width encoding magnitude of ﬂow and an

arrowhead showing direction. However, as discussed above, with this

encoding visual clutter and line crossings are inevitable, even in small

datasets. One way to overcome this is to use curved instead of straight

lines, such that the paths are carefully chosen to “fan out” or maximise

the separation between ﬂows at their origins and destinations [49].

Such curved ﬂow maps have shown to be more effective in “degree

counting” tasks [36]where the curvature reduced overlaps. Conversely,

edge bundling has also been suggested as a way of overcoming clutter.

In this approach curved paths are chosen so as to visually combine

ﬂows from adjacent regions [64]. While bundling can greatly reduce

clutter, its disadvantage is that it can make individual ﬂows difﬁcult to

follow. Thus, it is probably best suited to overview tasks.

In the case of 3D ﬂow representations, height can be used to encode

ﬂow magnitude or some other quantitative property or to reduce the

visual clutter caused by crossings or overlapping. Not only does the

use of a third dimension allow ﬂows to be spaced apart, in modern

immersive MR environments it also allows the viewer to use motion

perspective to better distinguish between ﬂows by either moving their

head or by rotating the presentation. Based on our literature review

(Sec. 2), possible 3D representations include:

•

Constant maximum height: in which each ﬂow is shown as a curved

line connecting the origin and destination and all ﬂows have the same

maximum height above the surface of the reference space. This is

arguably the simplest way to use height to help address the problem

of overlapping ﬂows.

•

Height encodes quantity: height is either proportional or inversely

proportional to ﬂow magnitude [19]. This allows double-coding the

ﬂow magnitude with both thickness and height.

•

Height is proportional to distance: height is proportional to the

distance between origin and destination, short ﬂows will be close to

the reference space surface while longer ﬂows will be lifted above

it [13]. This will tend to vertically separate crossings.

•

Height is inversely proportional to distance: this was suggested

in [58]. The advantage is that it increases the visual salience of

ﬂows between geographically close locations but at the expense of

increasing overlap.

3.2 Representation of Reference Space

In 2D ﬂow maps the reference space is always a ﬂat map, which can

of course also be used in an immersive environment. However, in

the case of global ﬂows it also makes sense to use a 3D exocentric

globe representation in which the ﬂow is shown on a sphere positioned

in front of the viewer. The disadvantage of a globe representation is

that the curved surface of the globe causes foreshortening and only

half of the globe can be seen at one time. An alternative is to use a

3D egocentric representation for the globe in which the user is placed

inside a large sphere [65

–

67]. This suffers from similar drawbacks

to the exocentric globe: foreshortening and inability to see more than

half of the Earth’s surface. Furthermore, because of the position of the

user it is difﬁcult to see the height of ﬂows. In [65] we found that the

egocentric globe led to worse performance than the exocentric globe

for standard map reading tasks and also led to motion sickness.

Typically the same reference space (map or globe) is used to show

both origins and destinations. However, in 2D representations such

as MapTrix or Flowstrates [4,64] origins and destinations are shown

on different maps. Potential beneﬁts are reduction of clutter in the

reference space representations and clearer depiction of ﬂow direction.

In a 3D environment probably the simplest representation using two

reference space representations is to show two 2D maps on ﬂat planes

with ﬂow shown by connecting tubes. Such a representation is akin

to Collins and Carpendale’s VisLink technique [10], where multiple

2D abstract data representations are viewed in a 3D environment, with

lines linking related points across views. This was the inspiration for

our MapLink technique evaluated in Study 2, Sec. 5.

4 ST UDY 1: 2D AN D 3D F L OWS O N FLAT MAPS

The ﬁrst user study focuses on representation of ﬂow in VR. It compares

readability of ﬁve ﬂow representations (two 2D and three 3D) using the

same reference space representation: a ﬂat map.

4.1 Visualisations and interactions

The two 2D representations were:

2D straight:

Connecting origins and destinations with straight lines is

the most common way to create a 2D ﬂow map (Fig. 2(a)).

2D curve:

Using curved ﬂow lines that increase separation and acute

angle crossings has been shown to increase readability for dense ﬂows

in 2D ﬂow maps [36]. The routing technique in [35] was used to created

2D curved ﬂows (Fig. 2(b)).

The three 3D ﬂow representations used 3D tubes to connect origins

and destinations. We used a cubic B

´

ezier curve to create the tubes using

Equation (1), where

P

0

and

P

3

are the origin and destination of a ﬂow,

0≤t≤1

is the interpolation factor, and

P

1

and

P

2

are the two control

points to decide the shape of the tube.

B(t) = (1−t)3P

0+3(1−t)2tP

1+3(1−t)t2P

2+t3P

3(1)

For

P

1

and

P

2

, we make their projected po-

sitions on 2D map plane the same as

P

0

(the

origin) and

P

3

(the destination) respectively,

so the projected trajectory on the 2D map

plane of the 3D tube is a straight line. This

allows users to easily follow the direction

of ﬂow lines.

P

1

and

P

2

are set to the same height to ensure sym-

metry such that the highest point will be at

t=0.5

, the mid-point of

the tube. We can use the height of two control points (

hc

) to precisely

control the height of the mid-point (h): hc=h

6×0.53=4

3h.

Three different height encodings were evaluated:

3D constant: All ﬂows have the same height (Fig. 2(c)).

3D quantity:

Height linearly proportional to ﬂow quantity (Fig. 2(d))

such that small quantity ﬂows will be at bottom, while large ones will

be on top. In the pilot we also tried the inverse (smaller ﬂows higher)

but this was found to be severely cluttered.

3D distance:

Height linearly proportional to Euclidean distance be-

tween the origin and destination (Fig. 2(e)). Close ﬂows will be lower,

while ﬂows further apart will be on top. Again the inverse was tried in

the pilot but quickly discarded as unhelpful.

Encodings common to all conditions:

Quantity was encoded in all

conditions using thickness of lines (in 2D) and diameter of tubes (in

3D). Several evaluations informed our choice of direction encoding.

Holten et al. evaluated encodings of unweighted edge direction in node-

link diagrams [27, 28] and found tapering of lines is the only direction

encoding to be more effective than colour gradient. In the context of OD

ﬂow maps a study by Jenny et al. [36] revealed difﬁculties interpreting

tapered connections in geographic context. Furthermore, the use of line

width/diameter to show weight makes tapered edges impractical (the

only part of the line where width could be reliably compared would be

at the origin). We therefore chose to use colour gradient in both 2D and

3D conditions, using the same colour gradient (red-green) from [27]

to present direction information in our study. To reduce the distortion

of shapes and also for aesthetic reasons, we chose to use the Hammer

map projection, an equal-area projection with an elliptical boundary.

See [65] for additional details of our use of this projection. The Natural

Earth raster map from

naturalearthdata.com

was used as the base

texture. Originally, we had concerns about the texture colour interfering

with ﬂow readability but in our pilot tests participants had no problem

with this. A legend was presented with all ﬂow maps, indicating

direction, quantity and other encodings (e.g. height for distance).

Rendering:

Geometry computation was accellerated with the GPU,

tessellation was used for curve and tube interpolation, and a geometry

shader was used to build the structure of line or tube segments.

Interactions:

We provided the same interaction across the ﬁve visual-

isations. First, viewers can move in space to change their viewpoint.

Second, we allowed viewers to change the 3D position and rotation of

the map. They could pick up the map using a standard handheld VR

controller, and reposition or rotate it in 3D space. We did not provide

explicit interactive widgets or dedicated manipulations for adjusting the

scale of the different maps. However, viewers could either move closer

to the maps, or pick maps with a VR controller and bring them closer

to their HMD. We did not allow other interaction such as ﬁltering as

we wished to focus on base-line readability of the representations.

4.2 Experiment

Stimuli and Task Data:

We used datasets based on real international

migration ﬂows between countries [1] for the study. We show only a

single net ﬂow between each pair of countries. To control the number

of ﬂows for our different difﬁculty conditions we symmetrically ﬁltered

the data by dropping the same percentage of small and large ﬂows. We

randomised the origin and destination of the original dataset to ensure

different data for each question.

Task: To keep the study duration for each participant to around one

hour, we chose to evaluate a single task: ﬁnding and comparing the

ﬂow between two given pairs of locations:

For the two ﬂows from A to B and X to Y, which is greater?

Following Feiner et al. [21], leader lines were used to link labels “A”,

“B” with the origin and destination of one ﬂow and “X”, “Y” with the

origin and destination of the other ﬂow. Labels were horizontal and

rotated in real-time so as to remain oriented towards the viewer.

This task was chosen because it combines two fundamental sub-

tasks: searching for the ﬂow line between two given locations and

comparison of magnitude of two ﬂows. We would expect visual clutter

to negatively impact on both of these sub-tasks while dual encoding

of magnitude might help with comparison. Besides the choice of ﬂow

representions, two factors may affect user performance: the number of

ﬂows, and the relative difference of quantity between two given ﬂows.

Number of ﬂows: In the study by Jenny et al. [36], the largest

number of ﬂows tested was around 40. To better understand scalability,

we decided to test three different difﬁculty levels in this study: (1) 40

ﬂows with 20% difference, (2) 40 ﬂows with 10% difference and (3)

80 ﬂows with 20% difference. We required the two ﬂows in question to

be separated by at least 15

°

on the great circle connecting them so as

to avoid situations where the origin and destination of a ﬂow were too

close to be clearly distinguished. To balance the difﬁculty of searching

for a ﬂow, all origins and destinations of ﬂows under comparison were

required to have more than three ﬂows.

Quantity encoding: The smallest (largest) ﬂow magnitude was

mapped to the thinnest (widest) ﬂow width, and intermediate values

were linearly encoded.

Experimental Set-up:

We used an HTC Vive with

110◦

ﬁeld of view

and 90Hz refresh rate as the VR headset for the experiment. The PC

was equipped with an Intel i7-6700K 4.0GHz processor and NVIDIA

GeForce GTX 1080 graphics card. Only one handheld VR controller

was needed in the experiment: participants could use this to reposition

and rotate the map in 3D space. The frame rate was around 110FPS,

i.e. computation was faster than the display refresh rate.

Visuals were positioned comfortably within the users’ reach and

sized by default to occupy approximately 60% of the viewers’ horizon-

tal ﬁeld of view. The map was texture-mapped onto a quad measuring

1

×

0.5 metre and placed at 0.55 metre in front and 0.3 metre under

participants’ eye position, and tilted to 45

°

. The map was centred on

0

°

longitude and 0

°

latitude. We repositioned the map at the beginning

of every question. The thickness of lines in 2D and diameter of tubes

in 3D were in the range of 2mm to 16mm. The height of 3D quantity

and 3D distance was linearly mapped to the range of 5cm to 25cm. The

constant height for 3D constant was 15cm.

Participants:

We recruited 20 participants (8 female) from our uni-

versity. All had normal or corrected-to-normal vision and included

university students and researchers. 1 participant was under 20, 15

participants were within the age group 20

−

30, 1 participant was be-

tween 30

−

40, and 3 participants were over 40. VR experience varied:

13 participants had less than 5 hours of prior VR experience, 5 par-

ticipants had 6

−

20 hours, and 3 participant had more than 20 hours.

While our encoding used colour to indicate direction, the tasks used

did not involve ambiguity regarding direction. Therefore, we did not

test participants for colour blindness.

Design and Procedure:

The experiment was within-subjects: 20 par-

ticipants

×

5 visualisations

×

1 task

×

3 difﬁculty levels

×

5 repetitions

= 1,500 responses (75 responses per participant) with performance mea-

sures and lasted one hour on average. Latin square design was used to

balance the order of visualisations.

Participants were ﬁrst given a brief introduction to the experiment.

Before they put on the VR headset, we measured the pupil distance (PD)

of the participants, and adjusted the PD on the VR headset. Two types

of training were included in this experiment: interaction training and

task training. Both were conducted when each ﬂow map representation

was presented to the participants for the ﬁrst time.

During interaction training participants were introduced to the ﬂow

map with details of the encodings and given sufﬁcient time to famil-

iarise themselves with interaction. They were then asked to pick up the

map and put it on a virtual table in VR. This activity familiarised partic-

ipants with each ﬂow map representation as well as the VR headset and

controller. This was followed by task training. Two sample tasks were

given to participants with unlimited time. We asked the participants to

check their strategies both when they were doing the training tasks and

when the correct answers for those tasks were shown.

Participants were presented with the ﬁve ﬂow map representations

in counterbalanced order. A posthoc questionnaire recorded feedback

on: (1) preference ranking of visualisations in terms of visual design

and ease of use for the tasks, (2) advantages and disadvantages of each

visualisation, (3) strategies for different ﬂow maps, and (4) background

information about the participant. In the questionaire the visualisations

were listed in the same order that they were presented to participants dur-

ing the experiment. All experimental materials are available for down-

load from https://vis.yalongyang.com/VR-Flow- Maps.html.

Fig. 3. Study 1: Accuracy score and response time for different ﬂow

map representations in ﬁrst study: (a1, b1, c1, d1) Average performance

with 95% conﬁdence interval, (a2, a3, b2, c2, d2) graphical depiction of

results of pairwise post-hoc test.

Measures:

We measured the time between the ﬁrst rendering of the

visualisation and the double-click on the controller trigger button.

After participants double-clicked, the visualisation was replaced by

two buttons to answer the question. Collected answers were binary

(i.e. participants chose between two options) and we therefore used

the accuracy score from [60] to indicate perfect performance with 1,

and a result equal to pure chance (i.e. randomly guessing) with 0:

(number o f correct responses

number o f t otal res ponses −0.5)×2.

We also recorded the number of clicks, head position, head rotation,

controller position, and map position every 0.1s. Recording these

parameters is important, as users can move in a relatively large open

space with the HTC Vive HMD.

4.3 Results

Accuracy scores were not normally distributed (checked with his-

tograms and Q

−

Q plots). Signiﬁcance was tested with the Friedman

test because we have more than two conditions; the Wilcoxon-Nemenyi-

McDonald-Thompson post-hoc test was used to compare pairwise [26].

Response times were log-normal distributed (checked with his-

tograms and Q

−

Q plots), so a log-transform was used for statistical

analysis [30]. We chose one-way repeated measures ANOVA with lin-

ear mixed-effects model to check for signiﬁcance and applied Tukey’s

HSD post-hoc tests to conduct pairwise comparisons [22]. For user pref-

erences we again used the Friedman test and the Wilcoxon-Nemenyi-

McDonald-Thompson post-hoc test to test for signiﬁcance.

The Friedman test revealed a statistically signiﬁcant effect of visual-

Fig. 4. (a) Demonstration of different view angles, (b) view angle distribu-

tion among different ﬂow maps with median line.

isations on accuracy (

χ2(4) = 12.29,p=.015

). Fig. 3(a1) shows the

average accuracy score of 3D distance (0.98) was higher than that of

3D quantity (0.87) and of 2D ﬂow maps (straight with 0.85 and curve

with 0.83). While 3D distance also outperformed 3D constant (0.89),

this was not found to be statistically signiﬁcant. A post-hoc test showed

statistical signiﬁcances as per Fig. 3(a2).

The ANOVA analysis showed signiﬁcant effect of visualisations

on time (

χ2(4) = 50.63,p< .0001

). 2D straight (avg. 12.0s) was

signiﬁcantly faster than other ﬂow maps. 3D distance (avg. 14.9s) and

2D curve (avg. 15.2s) were signiﬁcantly faster than 3D constant (avg.

17.6s) and 3D quantity (avg. 19.1s) (see Fig. 3(a3)).

By difﬁculty condition the Friedman test did not reveal signiﬁcant

effect for accuracy. The ANOVA analysis revealed:

40 ﬂows (20%):χ2(4) = 36.39,p< .0001

.2D straight (avg. 10.3s)

was signiﬁcantly faster than other ﬂow maps except 2D curve (avg.

12.2s). 3D distance (avg. 12.9s) was only slower than 2D straight.

3D quantity (avg. 17.7s) was slower than other ﬂow maps, except 3D

constant (avg. 15.7s).

40 ﬂows (10%):χ2(4) = 31.30,p< .0001

.2D straight (avg. 14.0s)

was signiﬁcantly faster than other ﬂow maps except 2D curve (avg.

16.4s). 3D quantity (avg. 21.0s) was signiﬁcantly slower than 3D

distance (avg. 16.5s). It also seemed to be slower than 3D constant

(avg. 18.0s), but no statistical signiﬁcance was found.

80 ﬂows (20%):χ2(4) = 34.39,p< .0001

.2D straight (avg. 11.6s)

was signiﬁcantly faster than other ﬂow maps: 2D curve (avg. 16.8s),

3D distance (avg. 15.3s), 3D constant (avg. 19.2s) and 3D quantity

(avg. 18.5s).

When analysing the details of interac-

tion, we sampled every second frame.

If the head or the map moved more than

1cm or rotated more than 5

°

, we consid-

ered it as an interaction, and accumu-

lated the interaction time for every user

and then normalised the time related

to the percentage of time spent on that

question. Friedman test revealed a

statistically signiﬁcant effect of visualisations on map movements

(

χ2(4) = 30.4,p< .0001

). Participants tended to move the map sig-

niﬁcantly more in all 3D conditions than 2D conditions (all

p< .05

).

Wilcoxon signed rank test also revealed participants spent statistically

signiﬁcant more percentage of time moving the map than their head in

3D distance (at level p=.10) and 3D quantity (at level p=.06).

We also analyzed the view angle, i.e. the angle between viewers’

heads forward vector and the normal vector of the map plane. The Fried-

man test revealed that the effect of visualisations on the percentage

of time spent with a view angle larger than 45

°

per user was statis-

tically signiﬁcant (

χ2(4) = 64.88,p< .0001

). As one might expect,

participants spent signiﬁcantly more percentage of time with large view

angles in all 3D conditions than all 2D conditions (see Fig. 4).

User preference and feedback:

Participant ranking for each of the

four visualisations by percentage

of respondents is shown by colour:

1st

,

2nd

,

3rd

,

4th

and

5th

. For

visual design, the Friedman test re-

vealed a signiﬁcant effect of visu-

alisations on preference (χ2(4)

Visual Design Ranking

=38.6,p< .0001

). The strongest preference was for 3D distance, with

95% voting it as top three. The post-hoc tests also found a stronger

preference for 3D distance than 3D constant (65% voting it as top

three), 2D curve (40% voting it as top three) and 2D straight (30%

voting it as top three). Participants also seemed to prefer 3D quantity

(85% voting it as top three), however, the post-hoc tests only suggested

it was preferred to 2D straight.

For readability, the Friedman test

indicated signiﬁcant effect of visu-

alisations on preference (

χ2(4) =

23.32,p=.0001

). The strongest

preference is again for the 3D dis-

tance, with 90% of respondents

voting it top three. The post-hoc

Readability Ranking

tests again showed stronger preference for 3D distance than 3D constant

(50% voting it as top three), 2D curve (45% voting it as top three) and

2D straight (45% voting it as top three). Participants also seemed to

prefer 3D quantity (70% voting it as top three), however, the post-hoc

tests again only revealed it was preferred over 2D straight.

The ﬁnal section of the study allowed participants to give feedback

on the pros and cons of each design. Qualitative analysis of these

comments reveal (overall):

2D straight

was found to be easy for small data sets, however, lines

were found to be hard to distinguish due to increasing overlaps in large

data sets. Several participants reported: “I answered sometimes with a

very low conﬁdence, close to luck.”

2D curve

was found to have fewer overlaps than 2D straight. However,

many participants reported the curvature made it difﬁcult to follow

lines, and sometimes, the curvature was found to be unexpected, which

apparently increased difﬁculty.

3D constant

was found to have considerable numbers of overlaps by

most participants. However, some participants also found it efﬁcient

with interaction: “I could look at the line from a straight angle, plus

wiggle the map around a little to conﬁrm the line.”

3D quantity

was more trusted. Many participants reported: “If I

couldn’t work out from thickness, I could move the visualisation to

compare heights from the side to conﬁrm my answer. I felt more conﬁ-

dent.” However, they also commented about the extra time they spent

for this conﬁrmation.

3D distance

was easy to distinguish ﬂows. “This one left enough

gaps between the curves to clearly distinguish the curves” and “it

was visually appealing.” However, a few participants commented they

felt more conﬁdent with 3D quantity, and a few commented that this

might be due to the double encoding used by 3D quantity (3D quantity

encodes quantity with height and width).

4.4 Key Findings

The main ﬁnding of this study was that the 3D distance was more

accurate than the other 3D conditions and both 2D visualisations. It

was also the preferred visualisation. We also found that:

•

The 2D straight-line ﬂow map was the fastest in almost all conditions

but least preferred.

•

Participants tended to look more often from the side in 3D conditions

than in 2D conditions.

•

Participants tended to interact with the map more in 3D conditions

than 2D conditions.

•

Participants tended to move the map more than their heads in 3D

distance and 3D quantity.

5 ST UDY 2: FL OWS ON FL AT MAP S, GLO BES A ND MA P

PAIR S

In the second study, we focused on exploring different 2D and 3D

representations of the reference space.

5.1 Visualisations and Interactions

We evaluated 4 different representations.

2D straight

and

3D distance

: The ﬁrst two used a ﬂat map to represent

the reerence space. These were the best performing representations

from our ﬁrst study (fastest with 2D straight, most accurate with 3D

distance).

Fig. 5. Study 2: (a) 3D globe ﬂow map, (b, c, d) MapsLink: ﬂow tubes

linking a pair of ﬂat maps.

Globe:

A 3D globe has proven to be an effective way to present global

geometry [65] but the effectiveness for showing OD ﬂows has not

been previously evaluated. We represented ﬂow in the globe using 3D

tubes, i.e. we linked two locations on the globe with their great circle

trajectory (Fig. 5(a)). Based on the result of our ﬁrst study, we chose to

use curve height to encode the great circle distance between two points

where height here refers to the distance between the curve’s centre

point and the centre of the globe. We used a cubic transformation with

interpolation factor

0≤t≤1

,

ht= ((−|t−0.5|/0.5)3+1)×h+radius

.

MapsLink:

We also evaluated a novel ﬂow map representation which

used a separate reference space for the origin and destination. This

used two ﬂat maps in 3D space: the origin map showing origins and

the destination map showing destinations (Fig. 5 (b)). Flows from

origin to destination were rendered with curved tubes linking origins in

the origin map and destinations in the destination map. The 3D tubes

were cubic B

´

ezier curves (see Equ. 1) with orgin and destination as

the ﬁrst and last control point. As the two maps might not be in the

same plane, we could not control the height in the same way as the ﬁrst

experiment, instead, the two control points were raised from the orign

and destination maps to the same height, which was proportional to

the Euclidean distance in 3D space between the origin and destination

points. This meant when the origin and destination map were facing

each other, origins and destinations were linked by straight lines and

by smooth curves at other orientations.

Interactions:

As in the ﬁrst study participants could rotate and repo-

sition the visualisation. In addition we allowed participants to adjust

the centre of the geographic area in the visualisation in VR. Viewers

could pick any location and drag it to a new position using the VR

controller. This interaction (called geo-rotation) was presented in [65]

and allows the viewer to bring the geographic area of interest to the

centre of the visualisation. This changes the relative position of points

and straight line ﬂows on the ﬂat map, thus providing some of the

beneﬁts that changing viewpoint provided for the 3D representations of

ﬂow. We were interested to see if it improved accuracy of the ﬂat map

with straight line 2D ﬂows.

5.2 Experiment

Stimuli and tasks:

The same task of ﬁnding and comparing ﬂows

between two origin-destination pairs was used in this study. The same

raw data was used as well. With the addition of the geo-rotation

interaction, we assumed participants could complete the task more

easily. We therefore increased the difﬁculty of the three conditions: (a)

80 ﬂows with 20% difference, (b) 80 ﬂows with 10% difference and (c)

120 ﬂows with 20% difference. Pilots demonstrated participants could

handle these difﬁculty conditions.

Set-up:

The headset and PC setup were the same as used in Study 1,

except that two controllers were given to the participants so that they

could use one controller to position and rotate the map/globe while the

other is used for geo-rotation. In MapsLink two controllers also affords

bimanual gestures to manipulate both maps simultaneously.

The 2D straight and 3D distance setup was the same as for Study

1. As for was the case for 3D maps in Study 1, the thickness of tubes

in globe and MapsLink was linearly mapped to the range of 0.1cm to

0.8cm.

The globe had a radius of 0.4 metre. The starting position for

the centre of the globe was 1 metre in front and 0.3 metre under the

participant’s eye position. The geographic centre of the globe was set

at 0

°

longitude and 0

°

latitude, facing towards the viewer. As for 3D

distance, the height was linearly mapped to the range of 5cm to 25cm.

The two maps of MapsLink measure 75% of the size of the ﬂat map

in the ﬁrst study (0.75

×

0.375 metre). We reduced size to reduce the

chance of the two maps intersecting. The two maps were ﬁrst placed

0.55 metre in front and 0.3 metre under participant’s eye position, then

the origin map was moved left 0.4 metre, and the destination map was

moved right 0.4 metre. Finally, both maps were tilted towards partic-

ipants around the y-axis by 30

°

and around the x-axis by 45

°

. Flows

were modeled with cubic B

´

ezier curves: The two control points were

placed on a line orthogonal to map planes; distances between control

points and planes were between 5 and 50cm, and were proportional to

the distances between origins and detinations (which were assumed to

be between 0 and 2m).

Participants:

We recruited 20 participants (6 female) from our univer-

sity campus, all with normal or corrected-to-normal vision. Participants

included university students and researchers. 14 participants were

within the age group 20

−

30, 5 participants were between 30

−

40, and 1

participant was over 40. VR experience varied: 14 participants had less

than 5 hours of prior VR experience, 4 participants had 6

−

20 hours,

and 2 participants had more than 20 hours.

Design and Procedure:

A similar design to the ﬁrst user study was

used, within-subjects: 20 participants

×

4 visualisations

×

1 task

×

3

difﬁculty levels

×

5 repetitions = 1,200 responses (60 responses per

participant) with performance measures and lasted one hour on average.

Latin square design was used to balance the order of visualisations, and

4 data sets were ordered to balance the effect of tasks across participants

(i.e. every ﬂow map was tested on all data sets).

The procedure was similar to Study 1 but with two modiﬁcations. In

interaction training, in addition to asking participants to place the ﬂow

maps on top of a table, we also asked them to use geo-rotation to rotate

Melbourne to the centre of the map or to the centre of participant’s

view. In the posthoc questionnaire, we added a question to rate their

conﬁdence with each ﬂow map with a ﬁve-point-Likert scale.

Measures:

In addition to real-time recording of participant’s head,

controller and map position and rotation information, we also recorded

the time duration whenever a participant used geo-rotation.

5.3 Results

As in the ﬁrst study, after checking normality of the data with his-

tograms and Q

−

Q, we used the Friedman test to check for signiﬁ-

cance of accuracy score and applied the Wilcoxon-Nemenyi-McDonald-

Thompson post-hoc test to conduct pairwise comparisons. For response

time, we chose one-way repeated measures ANOVA with linear mixed-

effects model to check for signiﬁcance of its

log

transformed values

and applied Tukey’s HSD post-hoc to conduct pairwise comparisons.

The Friedman test revealed a statistically signiﬁcant effect of visu-

alisations on accuracy (

χ2(3) = 18.06,p=0.0004

). Fig. 6 (a1) shows

the average accuracy score of globe (avg. 0.99) was higher than that

of 2D straight (avg. 0.88) and of MapsLink (avg. 0.83). While globe

also outperformed 3D distance (avg. 0.91), this was not found to be

statistically signiﬁcant. A post-hoc test showed statistical signiﬁcances

as per Fig. 6 (a2).

The ANOVA analysis showed signiﬁcant effect of visualisations

on time (

χ2(3) = 107.87,p< .0001

). MapsLink (avg. 50.9s) was

signiﬁcantly slower than other visualisations. Globe (avg. 20.7s) was

signiﬁcantly faster than 3D distance (avg. 23.4s). 2D straight (21.0s)

had no signiﬁcances between globe and 3D distance.

By difﬁculty condition the Friedman test revealed a signiﬁcant effect

on accuracy score:

80 ﬂows (20%):χ2(3) = 0.69,p=.8750

. All visualisations had simi-

lar performance in this condition.

80 ﬂows (10%):χ2(3) = 13.28,p=.0041

.Globe (avg. 0.98) was

Fig. 6. Study 2: (a1, b1, c1, d1) Average performance with 95% conﬁ-

dence interval, (a2, a3, b2, c2, c3, d2, d3) graphical depiction of results

of pairwise post-hoc test.

signiﬁcantly more accurate than MapsLink (avg. 0.68). 2D straight

(avg. 0.80) and 3D distance (avg. 0.82) had no statistical signiﬁcance

with other visualisations.

120 ﬂows (20%):χ2(3) = 9.9,p=.0194

. Responses with globe were

perfect (with an accuracy score 1), and it was signiﬁcantly more accu-

rate than both 2D straight (avg. 0.86) and MapsLink (avg. 0.86). 3D

distance (avg. 0.92) had no statistical signiﬁcance with other visualisa-

tions.

By difﬁculty condition the ANOVA analysis revealed signiﬁcant

effect on time:

80 ﬂows (20%):χ2(3) = 97.62,p< .0001

.MapsLink (avg. 48.6s) was

signiﬁcantly slower than other visualisations. Globe (avg. 15.1s) was

also signiﬁcantly faster than 2D straight (avg. 17.3s) and 3D distance

(avg. 18.5s).

80 ﬂows (10%):χ2(3) = 71.6,p< .0001

. Again, MapsLink (avg.

50.7s) was signiﬁcantly slower than other visualisations: 2D straight

(avg. 18.5s), 3D distance (avg. 22.6s) and globe (avg. 20.9s).

120 ﬂows (20%):χ2(3) = 58.72,p< .0001

. Again, MapsLink (avg.

53.6s) was found to be signiﬁcantly slower than other visualisations:

2D straight (avg. 27.3s), 3D distance (avg. 29.2s) and globe (avg.

26.2s).

Interactions:

The percentage of time spent in different interactions

per user was investigated (see Fig. 7). The Friedman test was used to

determine statistical signiﬁcance between different visualisations and

between different interactions.

For head movement, participants tended to spend a smaller per-

centage of time moving their heads in 2D straight than 3D distance

(

p=.09

), globe (

p=.03

) and MapsLink (

p< .0001

). In map move-

ment, participants tended to move MapsLink signiﬁcantly more than

Fig. 7. Study 2: Interaction time percentage with 95% conﬁdence interval

Fig. 8. Study 2: Participants preference ranking (

1st

,

2nd

,

3rd

and

4th

)

and conﬁdence rating (from fully conﬁdent to not conﬁdent at all ).

other visualisations and there was more head movement for 3D distance

than for 2D straight (all

p< .05

). In geo-rotation, participants used

geo-rotation signiﬁcantly more in globe and in 2D straight than with

3D distance and MapsLink (all p< .05).

In 2D straight, the percentage of time was signiﬁcantly different

across interaction types: geo-rotation

>

head movement

>

map move-

ment (all

p< .05

). In 3D distance, no signiﬁcant difference was found

among different interactions. In globe,geo-rotation

>

map move-

ment (p=.0025). In MapsLink, map movement >head movement >

geo-rotation (all p< .05).

We also investigated the beneﬁts of adding geo-rotation to 2D

straight and 3D distance. We compared the responses of 80 ﬂows,

20% in the ﬁrst (without geo-rotation) and second (with geo-rotation)

studies.

For 2D straight, Exact Wilcoxon-Mann-Whitney test revealed [29]

an increase of accuracy with geo-rotation at level

p=.0530

with

Z=

−1.5072

. Log-transformed time values have been analysed with mixed

ANOVA, the result demonstrated a signiﬁcant increase in response

time with geo-rotation (

χ2(1) = 13.07,p< .0001

). For 3D distance,

Exact Wilcoxon-Mann-Whitney test and mixed ANOVA did not show

a signiﬁcant difference between with and without geo-rotation.

User preference and feedback:

Participant ranking for each of the

four visualisations by percentage of respondents is shown by colour

(see Fig. 8). For visual design, the Friedman test revealed a signiﬁcant

effect of visualisations on preference (

χ2(3) = 38.58,p< .0001

). The

strongest preference was for the globe, with 100% voting it in the top

two. The post-hoc tests also proved the strongest preference for globe

compared to other ﬂow maps with all

p< .05

.3D distance (70% voting

it top two) was also statistically preferred to 2D straight (0% voting it

top two). MapsLink, with 30% voting it top two, did not show statistical

difference between 2D straight or 3D distance. For readability, the

Friedman test indicated signiﬁcant effect of visualisations on preference

(

χ2(3) = 25.5,p< .0001

). The strongest preference is again for the

globe, with 85% of respondents voting it top two. The post-hoc revealed

stronger preference of globe than 2D straight (25% voting it top two)

and MapsLink (20% voting it as top two). 3D distance (70% voting it

top two) was also statistically preferred to MapsLink.

A ﬁve-point-Likert scale was used for rating participants’ conﬁdence

(see Fig. 8). The Friedman test revealed a signiﬁcant effect of visu-

alisations on conﬁdence (

χ2(3) = 24.82,p< .0001

). Participants felt

signiﬁcantly more conﬁdent in globe and 3D distance than MapsLink.

Globe was also found more conﬁdent than 2D straight (all p< .05).

The ﬁnal section of the study allowed participants to give feedback

on the pros and cons of each design. Qualitative analysis of these

comments reveal (overall):

2D straight

was found to be very difﬁcult at the beginning. However,

many participants commented: “With the map rotating, it is usually

possible to keep track of the pair of points.”

3D distance

was found to be more visually appealing than 2D straight,

and more efﬁcient than 2D straight for small data. However, “things

become very difﬁcult when data size increases”, and “sometimes, it felt

more difﬁcult than 2D (straight) map”.

Globe

was found to be the most intuitive. Many participants also

commented that the visualisation “felt very sparse so it was easy to

tell which lines were connected to the points”. Some participants also

suggested to have a snapshot functionality to store the current globe

rotation or two globes positioned side by side.

MapsLink

: was found to be “very interesting to play with, but very difﬁ-

cult to use when it comes to the questions”. However, some participants

liked the freedom of manipulating it: “You can almost ﬁnd the certain

answer for each question by patiently manipulating map positions and

rotating the maps.” Meanwhile, many participants reported it took a

long time to answer questions.

5.4 Key Findings

The main ﬁnding of this study was that user performance with the globe

was signiﬁcantly more accurate than with 2D straight and MapsLink.

There was also some evidence that the globe was more accurate than 3D

distance, but this was not statistically signiﬁcant. There was also some

evidence that the globe is resistant to increased clutter density (per-

formance was stable with increasing ﬂows, while other visualisations

degraded with the number of ﬂows). Additionally, we found:

•

MapsLink was signiﬁcantly slower than other representations and

that participants spent most of their time moving the maps in Maps-

Link (more than 80% in average).

•

Geo-rotation increased accuracy and slowed response time for 2D

straight. With geo-rotation there was no longer a signiﬁcant differ-

ence in accuracy or speed between 2D straight and 3D distance.

•

Globe had the strongest preference in terms of visual design, while

participants were more conﬁdent with both globe and 3D distance

and preferred them for readability.

•

Participants chose to use different interactions in different repre-

sentations. Compared to other visualisations, participants do not

like to move their heads in 2D straight and participants liked to use

geo-rotation in 2D straight and globe.

6 ST UDY 3: DE NSE FL OW DATA SETS

The third study was designed to investigate the scalability of the dif-

ferent ﬂow maps. As participants spent signiﬁcantly more time on

MapsLink and qualitative feedback indicated limited scalability for this

design, we decide to test only the other three visualisations: 2D straight,

3D distance and globe. We tested them with 200 and 300 ﬂows, both

with 10% difference.

We recruited 12 participants (6 female) from our university campus,

all with normal or corrected-to-normal vision. Participants included

university students and researchers. 9 participants were within the age

group 20–30, 2 participant was between 30–40, and 1 participant was

over 40. VR experience varied: 10 participants had less than 5 hours of

prior VR experience, 2 participants had 6–20 hours.

Otherwise, experimental design and setup was identical to Study

2, within-subjects: 12 participants

×

3 visualisations

×

1 task

×

2

difﬁculty levels

×

8 repetitions = 576 responses (48 responses per

participant) with performance measures and duration of one hour on

average.

6.1 Results

The same statistical analysis methods were used for accuracy score

and

log

transformed responding time. The Friedman test revealed a

statistically signiﬁcant effect of visualisations on accuracy (

χ2(2) =

7.79,p=.0203

). Fig. 9 (a1) shows Globe (avg. 0.93) was signiﬁcantly

more accurate than 3D distance (avg. 0.77) and 2D straight (avg. 0.73).

The ANOVA analysis also showed signiﬁcant effect of visualisations

on time (

χ2(2) = 11.82,p=.0027

). Globe (avg. 39.2s) again was

signiﬁcantly faster than 3D distance (avg. 60.9s) and 2D straight (avg.

56.8s). While 3D distance was slightly more accurate than 2D straight

this was not statistically signiﬁcant.

By difﬁculty condition the Friedman test revealed signiﬁcant effect

for accuracy score:

200 ﬂows (10%):χ2(2) = 2.47,p=.2910

. No statistical signiﬁcance

effect was found in this condition of visualisations.

300 ﬂows (10%):χ2(2) = 6.26,p=.0437

.Globe (avg. 0.94) was

signiﬁcantly more accurate than 2D straight (avg. 0.67). No signiﬁcant

difference between 3D distance (avg. 0.77) and other ﬂow maps.

Fig. 9. Study 3: (a1, b1, c1) Average performance with 95% conﬁdence

interval, (a2, a3, b2, c2, c3) graphical depiction of results of pairwise

post-hoc test.

Fig. 10. Study 3: Interaction time percentage with 95% conﬁdence

interval

By difﬁculty condition the ANOVA analysis revealed signiﬁcant

effect for time:

200 ﬂows (10%):χ2(2) = 13.73,p=.0010

.Globe (avg. 35.0s) was

signiﬁcantly faster than both 2D straight (avg. 46.5s) and 3D distance

(avg. 56.4s).

300 ﬂows (10%):χ2(2) = 8.72,p=.0128

.Globe (avg. 43.4s) again

was signiﬁcantly faster than both 2D straight (avg. 67.1s) and 3D

distance (avg. 65.4s).

Interactions

: The percentage time difference between interactions per

user is demonstrated in Fig. 10. The Friedman test was used to analyse

the relationship between interactions and visualisations. In head move-

ment, there is no signiﬁcant difference among the visualisations. In map

movement,3D distance

≈

globe

>

2D straight (

≈

means no statistical

signiﬁcance found between two visualisations). In geo-rotation,2D

straight

>

3D distance (

p< .0001

), 2D straight

>

globe (

p=.0637

)

and globe

>

3D distance (

p=.0637

). In 2D straight,geo-rotation

>

head movement

>

map movement (all

p< .05

). In 3D distance, no

statistical signiﬁcance found among different interactions. In globe,

geo-rotation >map movement (p=.0216).

User preference

: Participant ranking for each of the three visualisa-

tions by percentage of respondents is shown by colour (see Fig. 11).

For visual design, the Friedman test revealed a signiﬁcant effect of

visualisations on preference (

χ2(2) = 17.17,p=.0001

). Both globe

(75% voting it the best) and 3D distance (25% voting it the best) were

preferred to 2D straight (0% voting it as the best) with all

p< .05

. For

readability, the Friedman test revealed a signiﬁcant effect of visuali-

sation on preference (

χ2(2) = 11.17,p=.0038

). Globe (75% voting

it the best) was preferred to 2D straight (8.33% voting it the best) at

signiﬁcant level

p=.0030

and 3D distance (16.67% voting it the best)

at signiﬁcance level

p=.0638

. As in Study 2, a ﬁve-point-Likert scale

Fig. 11. Study 3: Participants preference ranking (

1st

,

2nd

and

3rd

) and

conﬁdence rating (from fully conﬁdent to not conﬁdent at all ).

was used for rating participants’ conﬁdence (see Fig. 11). The Fried-

man test revealed a signiﬁcant effect of visualisations on conﬁdence

(

χ2(2) = 5.19,p=.07463

). Participants felt more conﬁdent with globe

than 2D straight at signiﬁcance level p=.0954.

6.2 Key Findings

The main ﬁnding of Study 3 was conﬁrmation that the ﬁndings of Study

2 extend to larger data sets. We found that globe was more accurate

and faster than 2D straight and 3D distance for larger datasets. Overall,

globe was the preferred visualisation and again participants tended to

use geo-rotation more than other interactions with both 2D straight

and globe. There was some evidence that even with geo-rotation 3D

distance scaled better to larger data sets than 2D straight but this was

not statistically signiﬁcant.

We were surprised by the performance of globe, as viewers can only

see half of the globe at a time. We therefore investigated performance

on items where the OD ﬂows were more than 120

°

apart. Again we

found that in both Studies 2 and 3, performance was better with the

globe than the other two representations.

7 CONCLUSION

The current paper signiﬁcantly extends our understanding of how to vi-

sualise spatially embedded data in modern immersive environments by

systematically investigating and evaluating different 2D and 3D repre-

sentations for OD ﬂow maps. We have conducted the ﬁrst investigation

and empirical evaluation of OD ﬂow map visualisation with a modern

head-tracked binocular VR HMD. We have found strong evidence that

2D OD ﬂow maps are not the best way to show origin-destination ﬂow

in such an environment, and that the use of 3D ﬂow maps can allow

viewers to resolve overlapping ﬂows by changing the relative position

of the head and object. However, the particular 3D design choices of

the visualisation have a signiﬁcant effect, for example, encoding ﬂow

height to distance was clearly better than to quantity while our most

novel use of 3D space, MapLink, had the worst performance.

We found that for global ﬂows, the most accurate and preferred

representation was a 3D globe with raised ﬂows whose height is pro-

portional to the ﬂow distance, while for regional ﬂow data the best view

would be a ﬂat map with distance-proportional raised 3D ﬂows. We

found that accuracy of a standard ﬂat ﬂow map with straight lines could

be signiﬁcantly improved by the use of geo-rotation, in which the user

can interactively reposition the centre of the map. Nonetheless, the 3D

representations were still more accurate and preferred.

Our ﬁndings suggest that globes are preferrable for visualising global

OD ﬂow data in immersive environments. For regional OD data, ﬂow

should be shown using 3D ﬂows with heights proportional to ﬂow

distance. Further work could include testing additional encodings and

additional tasks including collaborative tasks in multiuser immersive

environments. This study used VR HMDs, as these currently offer the

best ﬁeld-of-view. The results should be applicable to improved AR

headsets as they become available but this should also be tested.

ACKNOWLEDGMENTS

This research was supported under Australian Research Councils

Discovery Projects funding scheme (project number DP180100755).

Data61, CSIRO (formerly NICTA) is funded by the Australian Govern-

ment through the Department of Communications and the Australian

Research Council through the ICT Centre for Excellence Program. We

would like to thank all of our user study participants for their time and

feedback. We would also like to thank the reviewers for their valuable

comments.

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