CHI 2019 Paper

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

Pseudo-Haptic Weight: Changing the Perceived
Weight of Virtual Objects By Manipulating
Control-Display Ratio
Majed SamadFacebook Reality Labs
Redmond, Washington
majed.samad@oculus.com

Elia Gatti
Facebook Reality Labs
Redmond, Washington
elia.gatti@oculus.com

Hrvoje Benko
Facebook Reality Labs
Redmond, Washington
benko@fb.com

Anne Hermes
Facebook Reality Labs
Redmond, Washingtonanne.hermes@oculus.com

Cesare Parise
Facebook Reality Labs
Redmond, Washington
cesare.parise@oculus.com

Figure 1: An illustration of the Control/Display Ratio manipulation utilized in the experiment. The user is shown lifting an
optically tracked cube with the corresponding virtual representation, the movements of which are a fraction of the user’s
movements.

ABSTRACT
In virtual reality, the lack of kinesthetic feedback often prevents users from experiencing the weight of virtual objects.
Control-to-display (C/D) ratio manipulation has been proposed as a method to induce weight perception withoutkinesthetic feedback. Based on the fact that lighter (heavier) objects are easier (harder) to move, this method induces
an illusory perception of weight by manipulating the rendered position of users’ hands—increasing or decreasing
their displayed movements. In a series of experiments we
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CHI 2019, May 4–9, 2019, Glasgow, Scotland UK© 2019 Copyright held by the owner/author(s).
ACM ISBN 978-1-4503-5970-2/19/05.
https://doi.org/10.1145/3290605.3300550

Paper 320demonstrate that C/D-ratio induces a genuine perception ofweight, while preserving ownership over the virtual hand.
This means that such a manipulation can be easily introducedin current VR experiences without disrupting the sense ofpresence. We discuss these fndings in terms of estimation ofphysical work needed to lift an object. Our fndings provide
the frst quantifcation of the range of C/D-ratio that can beused to simulate weight in virtual reality.
CCS CONCEPTS• Human-centered computing → Mixed / augmented reality; Virtual reality; Haptic devices; HCI theory, concepts
and models; User interface programming.
KEYWORDS
pseudo-haptics; multisensory integration; virtual weight
ACM Reference Format:
Majed Samad, Elia Gatti, Anne Hermes, Hrvoje Benko, and Cesare
Parise. 2019. Pseudo-Haptic Weight: Changing the Perceived Weightof Virtual Objects By Manipulating Control-Display Ratio. In CHIPage 1CHI 2019 Paper

Conference on Human Factors in Computing Systems Proceedings(CHI 2019), May 4–9, 2019, Glasgow, Scotland UK. ACM, New York,NY, USA, 13 pages. https://doi.org/10.1145/3290605.3300550

1 INTRODUCTION
Fully immersive virtual reality (VR) presents many technicalchallenges in its efort to provide the user with believable
and rich experiences. One of the biggest and potentially mostvexing of these is the lack of kinesthetic (force feedback) cues.
When one lifts an object, the stretch and elongation receptors
in the muscles and tendons convey to the brain how muchload is being placed on the musculoskeletal system as well as
the extension and rotation of the limb. When a user grasps apurely virtual object—that is, an object that does not exist
in the physical world, but which can be interacted with in
VR—the arm does not receive kinesthetic cues, and moves
without being encumbered by an additional mass. In theabsence of kinesthetic feedback, therefore, other means need
to be used to deliver the perception of “weight”.
This paper makes the following contributions:• Formulating the weight perception problem in VR asa physical work estimation problem• Proposing a method for simulating the weight of virtual objects by manipulating the control-to-display(C/D) ratio• Reporting a series of experiments that quantify the
relationship between C/D ratios and the perception ofweight• Providing a predictive model of weight perception forinteraction designers
The primary appeal of this work is that it provides a principled way in which to design VR experiences that simultaneously achieves two goals: a) to give users a perceptual
experience of the weight of virtual objects, and b) to preserve
the sense of ownership over the virtual limbs as well as theoverall sense of presence. Framing the model as the result ofa work estimation process provides interaction and experience designers with a way to induce a directional modulationof perceived weight of virtual objects.
2 RELATED WORK
Rendering the weight of virtual objects constitutes a challenge for VR applications. Grounded haptic devices havebeen proposed as a solution to this problem. Such devices
can deliver forces to users to simulate mass and weight ofobjects, and stifness and damping forces. However, suchhaptic devices must be grounded on the foor, often have alimited workspace, and thus may not appeal to the averagecustomer. These drawbacks clearly collide with the recent
development of VR, which is becoming more ubiquitous andPaper 320

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

afordable by the year, and which aims to continue to expand
the usable virtual space with untethered devices.
Some authors have proposed body-grounded devices toprovide haptics to users of VR, such as the elastic-arm device[1], the FlexiFingers device that utilizes passive haptics tocreate a sense of stifness for virtual objects [2], among others[25]. Relatedly, Choi et al., have recently presented “Grabity”,
which is a body mounted device that provides combined
kinesthetic and vibrotactile feedback simulating grip forcesthat are cleverly oriented to always point downwards andtherefore can provide a sensation of weight [4]. Despite theirappeal, body-grounded devices are encumbering and canlimit the user’s naturalistic range of motion.
An alternative is provided by the so-called “pseudo-haptic
feedback” [13]. In general, pseudo-haptic feedback induces
the illusory perception of some haptic cue by introducing
conficts across the senses. For example, introducing an ofset between the real and rendered position of the hand while
pushing against a virtual object conveys the illusion of stifness [14]. Similar methods have been shown to be efective in redirected walking [18, 22] and redirected touching[3, 11, 12].
Pseudo-haptics has also been proposed as a method tosimulate the “weight” of objects [5, 9, 16, 19]. In the so-called
force-causes-displacement metaphor [16], for example, theforce that is desired to be simulated can be rendered by displacing the visual object upon which the force is made tohave acted. In their study, Palmerius and colleagues used asimulated spring linked to a visual cursor that participants
used to pick up several virtual cubes of varying implied mass
[16]. The spring conveyed the mass of the cubes in the extent
of stretching it underwent. Similarly, Jauregui and colleagues
investigated three diferent methods for simulating weightlifting [9]. The most efective method was to manipulate thecontrol/display (C/D) ratio between the body’s movements
and the visual display of those movements. Dominjon andcolleagues also used a manipulation of C/D ratio along withactual physical mass and observed a systematic modulationof participants’ perceptions of mass [5]. Nakakoji and colleagues used a similar method to create the sense of mass ofobjects interacted with on a computer screen [15]. However,none of these studies were conducted in virtual reality. Thismeans that they did not include a frst-person perspective
and visible contact between hand and object, greatly limiting
the naturalism of the interaction.
In fact, when introducing confict between the real and thedisplayed position of the hand in VR, there is the non-trivial
risk of breaking the embodiment/“sense of presence” of theusers, spoiling their experience in the virtual environments[21]. Recently, Rietzler and colleagues [19] implemented analgorithm similar to C/D ratio manipulation, and found thatusers’ experience decreased in quality for large diferences

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3 CONTROL/DISPLAY RATIO MANIPULATIONIn our study, we induced and modulated the perceived weightof objects by visually manipulating the control/display (C/D)
ratio of the hand movements. Our method applies a gainon the limb’s rendered movements while grasping an object.
The gain is inversely proportional to the weight of the virtual
object that we wish to render. For example, if an object is intended to be perceived as heavy, we would set the C/D ratio
to be <1 such that rendered movements are compressed (seeFigure 2). The manipulation is applied to all 3 Euclidean components of the rendered movement, but in a weighted fashionsuch that the horizontal and depth movements received 65%of the manipulation of the vertical dimension, in order toapproximate the combination of inertial and gravitational
forces that act on real objects.
Collision detection was implemented by a custom function that detected when any of the nodes of the renderedhands came within 1 cm of any of the faces of the cubes.
A collision event triggered the C/D ratio manipulation to
begin, which applied a gain on the movements in accordancewith the assigned value for that cube. This was achieved bynumerically integrating instantaneous velocity, thus maintaining a running measure of the total distance moved while
in contact with the object. This measure was multiplied by
the desired C/D ratio—weighted by the 3 spatial dimensions—and was then used to apply an ofset on the render locationof both the virtual hand and the virtual cube. When the handbroke contact with the cube, if there was any residual ofset
that lead to the hand being rendered at a location diferent
than its true location, the algorithm began a process of rapid
reduction of the ofset.
4 EXPERIMENT 1: C/D RATIO MANIPULATIONAFFECTS WEIGHT PERCEPTIONIn the frst experiment, we investigated the use of visual
manipulation of the C/D ratio for providing participants
with an illusory sensation of increased or decreased weight

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10

Rendered Hand Position (a.u.)

between the positions of the real and virtual hands. Nonetheless, their paper constitutes a strong argument in favor of
pseudo-haptic illusions as a means of rendering weight inVR.
Our method marks a substantial contribution in providing
a high-resolution virtual hand that is tracked at the individual fnger joint level, and gives a strong sense of embodiment[21]. We apply rigorous psychophysical methods in order toobtain a direct comparison between real and illusory weight,
coupled with a model for the integration between proprioceptive and visual information. Finally, we discuss our resultsin terms of optimal observer and multisensory integration[8, 10] and devise a predictive model of the user’s experience[23].

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

C/D Ratio

1.3

5

0

1.0
0.7

-5

-10
-10

-5

0

5

Real Hand Position (a.u.)

10

Figure 2: Manipulation of control/display ratio (C/D ratio).
In this graph, we plot the rendered hand position as a function of the true hand position as measured by the opticaltracking system. We depict the C/D ratio range from 0.7
to 1.3, which was the range tested in the experiment. The
dashed line plots the identity line and represents the C/Dratio of 1, where there is no manipulation. a.u. signifes arbitrary units.

using qualitative and quantitative methods. The hypothesis
was that the cube for which the C/D ratio was set to a valueless than 1 would be perceived heavier than the cube with
the C/D ratio set to a value greater than 1.
Participants
A total of 8 participants (age: {M = 29, SD = 8.4}, 3 female, 7
right handed) were recruited for this study from the general
population. Study protocols and materials were approved by
the Western Institutional Review Board and complied with
the Declaration of Helsinki.
Apparatus
Materials for this experiment included a table measuring
100 cm by 60 cm and placed in the middle of a cubic aluminum cage with linear dimension of 183 cm. To capture
and track participants’ movements, 17 cameras (OptiTrack
Prime 17W, 1664x1088 pixels, 70 degree FOV, 120 FPS, 2.8 ms
latency) were mounted to the cage. Additionally, a regularcamcorder was also attached to the cage at a location that
had optimal viewing angle of the participants’ hand movements and was used to record audio and video of the entiretyof the interview process. The virtual environment consistedof a virtual replica of the real table that was co-located with
it and displayed on a head-mounted display (HMD; Oculus
Rift, 2160x1200 pixels, 110 degree feld-of-view, 90 Hz refreshrate) marked by a unique three-dimensional arrangement

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CHI 2019 Paperof fducial markers on its upper surface allowing for headtracking using the OptiTrack motion-capture system. Participants wore a pair of fexible powermesh tracking gloves
that were ftted with 19 fducial markers each to enable hand
tracking [7]. Two wooden cubes with linear dimension 6.23
cm and mass of 185 g each that were also each marked on
the upper surface with a unique three-dimensional arrangement of fducial markers for motion tracking were also used(see Figure 3a). The cubes were represented in the virtual
scene as white and black cubes that were co-located with
their physical counterparts and which participants could
interact with by grasping with virtual hands that were also
co-located with their own hands (see Figure 3b). These cubes
were selected because their mass coincides approximately
with the mass of consumer handheld VR controllers.

abFigure 3: Experiment 1 Methods. a. The wooden blocks thatparticipants interacted with. Participants wore custom motion capture gloves not pictured here. b. The virtual representation of the cubes that participants interacted with.
The conical shape on their upper surface was included tomatch the tracking markers that were present on the physical cubes.

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CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

Procedure
The frst experiment used a mix of qualitative and quantitative research methods. As we were interested in determining whether our method would manipulate the weight perceived by participants, we opted for a design that minimized
observer-expectancy efects. Specifcally, we allowed participants to freely explore the cubes guided by a few motion
constraints. If participants experienced a phenomenology ofweight, they should spontaneously report it even if not cued
to do so by any explicit questions to that efect. Conversely,
if their free, uncued reports did not contain any reference tothe phenomenology of weight, then we would have to revise
our expectations regarding the potential use of this method.
The entire experimental session was recorded in audio andvideo to support the qualitative research methods that aredescribed below. Additionally, participants’ hand positions
and those of the two cubes were recorded during the entire
experimental session using the motion capture system.
Free Exploration. The frst phase of the experiment consistedof presenting one black and one white virtual cube (see Figure 3b) and allowing participants to freely explore them. Notethat participants were not allowed to see the real physicalcubes before the beginning of the experiment to minimize
expectancy. The virtual cubes received opposing C/D ratio
manipulations such that one of them had a C/D ratio of 1.25
and the other had a C/D ratio of 0.75, counterbalanced acrossparticipants. Thus, for half of the participants, the black cube
was manipulated to feel heavier than its true weight and thewhite cube was manipulated to feel lighter, and vice versa
for the other half.
The constraints on the movements that participants could
make while holding the cubes were as follows. They were
not permitted to grasp them from the top so as to avoid themtouching the fducial markers (see Figure 3a). They could not
use two hands to grasp a single cube because of the ofset
that would have been accumulated for the hand that had
picked it up from the table, and the lack thereof for the newly
grasping hand, which would lead to a diferential visualproprioceptive incongruence across the hands. Nevertheless,they were encouraged to repeatedly swap which hand was
holding each cube to get a better sense of the diferences
between them. Finally, they were advised to pick up the cubesand lift them up to eye-level and then set them back down.
This was to allow enough of the ofset to accumulate to makethe desired efect apparent, as it was noticed in pilots thatparticipants preferred to keep them in their hand and lookat them without moving them.
During this phase, participants were instructed to vocalize
freely anything they noticed or any thoughts that arose. Afterthey had explored the cubes for a couple of minutes, a shortinterview was conducted while they continued to interact

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with the cubes. They were asked questions such as: “Howdo the two cubes compare to each other?”, and “Was there
any diference in the way they behaved or reacted to you?”.
If they spontaneously mentioned anything relating to theperceived weight of the objects, they were probed to follow
up by saying more about their specifc feeling.
Following this phase, a short psychophysical experiment
was conducted, described below. After that, participants
could take a break and were debriefed about the manipulation and allowed to see the physical cubes. At this point,
they were told that the cubes had identical mass. Then, they
were instructed to freely explore the black and white cubes
again in VR exactly as before, but this time were specifcallyprobed to report on whether the efect persisted despite theirknowledge of the fact that the cubes were physically identical. Again, they were instructed to freely report on any otherinsights they might have had while freely exploring.
Weight Discrimination Task. To determine the robustnessof the illusion of weight in a psychophysical task and inorder to quantify the relation between the C/D-ratio and theillusion, we administered a weight discrimination task in
between the two free exploration phases mentioned above.
Here, participants performed a 2-alternative forced choice
experiment where they compared a randomized sequence ofpairs of gray cubes and selected the heavier one. The cubesthat participants held were the same physical cubes as before
and therefore always had the same physical mass. However,
the C/D ratio was manipulated across trials (N = 24) suchthat one cube (the standard stimulus) always had a C/D ratio
equal to 1 while the other cube (the comparison stimulus)
could take one of the following values: 0.7, 0.8, 0.9, 1.1, 1.2,
1.3. The virtual cubes were both textured with a gray color
making them visually indistinguishable, thus avoiding any
possible confounding efect of a crossmodal correspondence
between color/luminance and weight [17].
Trials started with participants placing the two cubes atmarked positions indicated as the starting positions on eitherside of the table. The virtual cubes then disappeared briefy
and reappeared; participants were instructed to treat the
newly appeared cubes as entirely new and not to respondwith the same cube on each trial. The cube that was assigned
a C/D ratio of 1 was counter-balanced across trials to ensurethat there was equal proportion of trials where the left cube
was heavier and trials where the right one was heavier. They
were then instructed to lift the cubes and make the same
sort of motion described above: pick them up, bring them to
eye-level, set them back down. They were to place the cubethat felt heavier in a newly marked position indicated as the
response position in the center of the table.

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

implemented in the software and administered the questions
shown in Table 1. Participants could respond along a continuum ranging from “strongly disagree” to “strongly agree”,
using a slider that they could adjust with the thumb-stick on
the right touch controller. The order of presentation of thequestions was randomized. The questionnaire was composedof 14 questions, divided into three topics: weight, limb ownership, and object believability. Each topic had some diagnostic
items and one or more control items, which were included
to control for suggestibility and observer-expectancy efects.
Importantly, participants were asked to respond with theirlevel of agreement for the statements related to their average experience during the free exploration phases only
and not to think about their experience during the weight
discrimination task.
Category

WeightAbbrev.

QuestionWf

One cube felt heavier in my handthan the other.
One cube visually appeared heavier than the other.
One cube felt warmer than theother.
Disregarding their color, the cubes
felt like they were made of diferent materials.

Wv
Wcon1*
Wcon2*

LO1
Limb
Ownership

LO2
LO3
LO4
LOcon*
OB1

ObjectOB2
Believability
OB3
OB4
OBcon*The virtual hands appeared in thesame location as my hands.
The virtual hands seemed to belong to my body.
Grasping the cubes made myhands not feel like my own.
I could touch the cubes using myhand.
My hands felt like they were becoming virtual.
The cubes that I grasped were not
the same cubes that I saw.
The cubes that I saw were always
in the same location as the cubesthat I felt.
My interaction with the cubes felt
natural.
The cubes were believable.
The cubes were immaterial or
ghostly.

Table 1: Questionnaire administered at the end of the experiment. Items marked with an asterisk were included as controls.

Qestionnaire. Following the second free exploration phase,participants were asked to fll out a questionnaire that was

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CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

Results
Qalitative Analysis. The whole session was recorded, transcribed, anonymized, and coded by two diferent coders.
Coders agreed beforehand on the main categories of interest
in which participants comments were more likely to fall,
but were unaware of each other’s ratings. When necessary,coders were allowed to add a category to the list.
The following categories were selected and encompassed
all participants’ comments: comments on tracking quality,comments on visual rendering, perceived weight and movement, comments on the overall experience, and cognitive
efects of the experience. Each category was further divided
into a number of sub-categories to better represent participants’ comments. Figure 4 shows the fve main categories
and relative sub-categories (blue, on the left), including an
example from each sub-category (green, on the right).
Haptics

Visuals

Perceived
Weight“this one feels heavier”

General Visibility of
the Scene“the images get blurry at eyelevel”

Perceived
Work/Effort“it is easier to makemovements with the lighter
cube”

Visibility of the Upper
Part of the Objects“the upper part of the object
is hovering on top”

Perceived
Movement“this one looks lighter because
it moves faster when I lift it”

Weight Appearance(e.g. looks
heavier/lighter)“the color black suggests the
cube is heavier”

Perceived
Fatigue“the repetitive motions mademy arm tired”

Size

Category

Sub-category

Count

Haptics

WeightWork
Movement
Fatigue

71
11
39
2

Tracking

Object Tracking
Hand Tracking

1117

Visuals

Visibility of the scene
Upper part of the object
Weight Appearance
Size

13
4
6
16

Experience

Positive
Negative

20
4

Cognitive

Realism
Expectations
Interpretations
Materials

9
8
16
21

Table 2: Qualitative interview analysis of participants’ utterances during the free exploration part of the experiment.

“they look the same size”
Cognitive

Tracking
Object Tracking“one object is glitchier”

Hand Tracking“it is very fluid”
Experience

Positive“this is cool”

Negative“this is freaky”

Realism“they look how they feel”

Expectations“I expected them [theobjects] to have the same
weight”

Interpretations“the cubes have physicallydifferent weights”

Materials“the heavy one felt denser”

Figure 4: The fve main categories used for the coding of theinterviews during Experiment 1 and the sub-categories they
were divided into, with some example statements.

Coders assigned a score to each sub-category. The score
refected, for each participant, the number of times a comment was expressed that fell into the categories. However, if
the same concept was reiterated twice, the two comments
were counted as one. For example, if the same participant
commented on the category “Haptic: weight” as: “the dark
[cube] felt heavier during the frst exploratory phase”, and“the dark [cube] felt heavier during the second exploratory
phase”, the comments were counted as separate commentsin the category “Haptic: weight”. On the contrary, comments
such as: “the dark [cube] felt heavier during the frst exploratory phase” and “the white [cube] felt lighter during
the frst exploratory phase” were counted as one, as theyreiterated the same concept. Scores between coders werethen added. Results are reported in Table 2.
Comments regarding the perceived haptic properties ofthe objects were predominant throughout the experiment.

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Often participants referred to diferent cubes as if they weremade of diferent materials (“...the heavier one feels like marble, or concrete or rock...”). No visual diference in size wasreported by participants (“...they look the same size to me...”).
Noteworthy, participants were particularly pleased by thequality of the hand tracking, and by the overall experience(“this is so cool...”).
Notably, four of the eight participants spontaneously mademention of any weight diferences between the cubes during
the frst Free Exploration phase. This number increased toseven of the eight during the second Free Exploration phaseand after the participants were cued as to the nature of themanipulation and were asked explicitly about weight.
Weight Discrimination Task. Responses to the weight discrimination task were analyzed to refect the proportion of trials
on which the the comparison stimulus was reported to beheavier than the standard stimulus as a function of the C/Dratio of the comparison stimulus (shown in Figure 5). Whatis notable in these data is that participants could discriminate the implied weight diferences despite the fact that thetwo cubes had identical physical mass. We also ft a psychometric function to these average responses (also shown in
the fgure). The slope was found to be negative and signifcantly diferent from 0, indicating that the increases in the
C/D ratio reduce perceived weight. To our best knowledge,
this represents the frst psychometric function showing therelationship between C/D ratios and the illusion of weight.

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CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

1

Normalized Response

0.8
0.6
0.4
0.2

0.4
0.2

0.9

1

1.1

Control/Display Ratio

1.2

1.3

Qestionnaire. First, responses to the questionnaires were
aggregated across subjects. Here, because items LO3 andOB1 were worded in the negative, they were inverted bycomputing LO3’ = 1 – LO3, and OB1’ = 1 – OB1. The aggregated responses were then analyzed by using a Wilcoxon
signed-rank test. We tested whether the median difered signifcantly from 0.5, which would have indicated a neutral
response. These data are plotted in Figure 6, and the asterisks indicate the items that were found to be signifcantlydiferent from 0.5. As can be seen in Figure 6, ratings on
all LO and OB items were signifcantly diferent from 0.5,
except those that referred to locations (Items LO1 and OB2;
the cubes/virtual hands I saw were at the same location as
the cubes I felt/my hands).
For the weight items, ratings on the item stating that oneof the cubes felt heavier than the other (Item Wf) were signifcantly diferent from 0.5, whereas the item stating that
one of the cubes visually appeared heavier than the other(Item Wv) produced a much larger variety of ratings thatwere therefore not signifcantly diferent from 0.5.
Discussion
To summarize, this frst experiment was aimed at replicating
the efects of C/D ratio manipulation reported in the literature, and to evaluate the extent to which these efects may
be used to simulate the sensation of the weight of virtual
objects. To that end, we modulated the control/display ratioof the movements of participants’ hands—and the motion
tracked physical cubes they held—while they lifted the cubes.
When the C/D ratio was smaller than 1, this resulted in the

co
W n1
co
n2
LO
1
LO
2
LO
3`
LO
LO 4
co
O n
B1
`
O
B2
O
B3
O
O B4
Bc
on

0.8

W

0.7

v

f

0

Figure 5: Psychometric function showing the probability ofreporting that the comparison cube felt heavier than thestandard cube (C/D ratio = 1) as a function of the C/D ratio.
The plotted line in red is the ftted psychometric function.

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0.6

W

0

0.8

W

Prob(Respond "Heavier")

1

Item

Figure 6: Responses to Questionnaire, grouped by category
in accordance to Table 1. Asterisks indicate median is significantly diferent from 0.5 according to the Wilcoxon signedrank test, and plus signs represent outliers.

compression of these movements, and when it was larger
than 1 the motion was amplifed.
Before participants were cued to report any phenomenology of weight, four out of the eight participants spontaneously reported that one cube felt heavier than the other.
After having experienced the efect longer and then being
asked specifcally about weight, that number increased toalmost all participants, or seven out of eight. This gives anindication that the modulation of perceived weight may be
more than just metaphorical, as has often been assumed, butrather a perceptual efect. Adding support to this is the large
number of mentions of weight-related statements, as shownin Table 2.
As regards the results of the weight discrimination task,
shown in Figure 5, participants consistently judged the object with a C/D ratio less than 1 to be heavier than an unmanipulated object for the more extreme, and thus easier,comparison stimulus levels.
Therefore, making use of both qualitative and quantitative
methods we have provided converging evidence of pseudohaptic feedback as a cue to the weight of virtual objects.
Given these promising results, we next wanted to quantify
the efect of C/D manipulation on perceived weight. Thus, we
conducted a second experiment where participants estimatedthe weight of a cube that was subjected to this C/D ratio
manipulation.

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5 EXPERIMENT 2: QUANTIFYING C/D RATIOMANIPULATION OF ACTUAL WEIGHTPERCEPTIONIn this experiment, for the frst time in VR, we performeda direct comparison between illusory and actual weight. In
particular, we show that pseudo-haptic feedback can lead tooverestimation or underestimation of real weight. We discuss
the results in terms of multisensory integration and argue
for a new perspective in explaining this particular efect,
delivering a predictive model that starting from the notionof physical work explains how mass gets overestimated orunderestimated as a function of C/D ratio.

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

a

b

c

Participants
We enrolled 14 participants from the general population
using ads placed by recruitment agencies (age: {M = 34.4,
SD = 9.3}, 7 female, 12 right handed). Study protocols andmaterials were approved by the Western Institutional Review
Board and complied with the Declaration of Helsinki.
Apparatus
Materials for this experiment were the same as in Experiment
1 but also incorporated a PHANToM force feedback device,with a small foam cube (linear dimension = 5 cm) afxed toits end efector (see Figure 7a).
Procedure
To assess the extent to which C/D ratio manipulated the perception of weight, we used a method of adjustment whereparticipants directly reported the weight of the cube underthat manipulation. To do so, they adjusted the mass simulated by the PHANToM until it matched the mass of thephysical cube. They used two virtual buttons rendered on thetable’s surface to either increase or decrease the PHANToM’s
simulated mass in increments of 10 grams, and a third one
which they used to record their response. The control/display
ratio manipulation was applied to the cube across 7 diferent
levels: {0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3}, and each was repeated
12 times, in a randomized order.
On a given trial, participants had 25 seconds to make theadjustment, and did so as follows. They frst grasped andlifted the physical cube vertically with the right hand to aheight of 20 cm that was specifed by a visual marker in thevirtual scene. The marker changed color to a dark shade ofblue to indicate that they had fulflled the requirement to lift
the cube to that point, as shown in Figure 7b. Then, with theirleft hand they picked up the foam cube that was attached to
the PHANToM—they were guided by the experimenter tothis foam cube at the start of the experiment and kept theirleft hand continuously grasping it as there was no visual
representation of it. They then used their right hand to click

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Figure 7: Experiment 2 Methods. a. The tabletop setup showing the PHANToM on the left, the Oculus Rift HMD in the
middle, and the wooden block on the right. b. The virtual
scene from the perspective of the participant as they lift the
cube towards the foating visual marker (in blue). c. The participant interacting with the three virtual buttons used for
adjustment of the force delivered by the PHANToM. The
numbers displayed on the top side of the cube show the remaining time to complete the trial in seconds.

on the virtual buttons on the table (see Figure 7c) increasingor decreasing the mass simulated by the PHANToM until itmatched the mass of the physical cube. The starting mass
was randomly chosen to either be 70 grams heavier or lighter
than what they perceived the cube’s mass to be when the C/Dratio was set to 1, which was determined in a pretest phaseof the experiment for each participant (see below for thedetails of this procedure). Participants were instructed not
to lift the PHANToM’s cube in synchrony with the physicalcube so as to minimize direct comparisons of the lift height,
and to instead direct their attention to the perceived massitself.
After registering their response, there was a mandatory
timeout of 12 seconds in between trials, to ensure that the
PHANToM did not overheat. If the participant failed to provide a response within the alloted time, the trial repeateditself after the timeout. There were six 1-minute breaks during the experiment.

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CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

Model of Physical Work and Multisensory
Integration
We conducted a principled analysis of the modulation of perceived weight that is produced by manipulation of the C/Dratio—a manipulation that has the consequence of changing the distance that the user’s arm must move in order toachieve a target extent of movement in the virtual scene.
Thus, in seeking a natural connection between displacement
and mass, we made use of the notion of work from physics,
which provides a direct relationship between the two.
First, we begin by assuming that the hand moves verticallyin a straight path while grasping the cube. Assuming thatthe path begins and ends in stationary points—i.e., points
at which the kinetic energy is zero, the work done, W , issimply calculated as the change in potential energy. Thus,
it is a function of the change in height, h, the mass of thehand and grasped cube, m, and the constant of gravitational
acceleration, д.
W =m ×д ×h(1)
Let us frst consider the situation from the perspective of thephysical reality. In the experiment described in this paper,
participants were required to lift the cube until its rendered
position was level with a foating visual marker that wasplaced 20 cm above the surface of the table. Therefore, participants moved their actual hands by 0.2/λ meters, where λrepresents the control/display ratio. Let us call this true hand
trajectory hpr op , signifying that the sensory signal arrives
to the nervous system via the proprioceptive modality. We
similarly call the proprioceptive sensation of the mass ofthe cube mpr op . Equation 1 can be amended to calculate thephysical work done by the participants’ arms, as follows.
W = mpr op × д × hpr op(2)

Although the hand’s true trajectory covered a distance of
0.2/λ m, the virtual hand would have moved a distance of 0.2
m visually. As it is known that signals from proprioception

Paper 320and vision are integrated [6], this implies that participants
will perceive their arm to have covered a distance that is aweighted combination of the two, namely
hper = αhpr op + βhvision(3)= α(0.2/λ) + β × 0.2(4)

with α and β denoting the proprioceptive and visual combination weights, respectively, and constrained such thatα + β = 1. Note that this assumes that the two cues are always integrated, a scheme known as Forced Fusion [8] (butsee [20, 24] for alternative approaches).

2.5
mvision2

Work (J)Participants were able to adjust the mass simulated by
the PHANToM within a range defned based on their own
estimation of the physical cube’s mass. They completed 16
practice trials with no C/D ratio manipulation (i.e., it was setto 1). The mean reported mass on the last 12 of these trials
was used to defne the range, such that a range of 140 grams
was centered around the participant’s mean.
After the trials were completed, participants were asked
to respond to a shortened version of the questionnaire usedin Experiment 1 (see Table 1). The questions were changed
to the singular form as in this experiment there was only
one cube, and the questions assessing weight comparisons
between the cubes were removed, leaving just those questions assessing the feelings of limb ownership and object
believability.

mprop

1.5
1
0.5

hvision hper

0

0

0.1

0.2

hprop

0.3

Height (m)

0.4

0.5

Figure 8: A schematic simulating the modeled relationshipbetween work, mass, and height of the cube lift. We assume
that the nervous system estimates work from the proprioceptive signals, hprop and mprop (black horizontal line). That
estimate of work is then used in conjunction with the perceived height, hper , of the lifted cube in order to infer theperceived mass, mper , of the cube (the slope of maroon colored line). hper is obtained by multisensory integration of
the proprioceptive and visual signals. Values used in thissimulation were chosen for clarity of the illustration and do
not represent our choice of experimental values.

Similarly, the perceived mass, mper , will be a multisensory
percept that emerges based on the inference regarding thetotal amount of work done (equation 2), and the perceived
distance moved by the hand (equation 3).
mper =

W
д × hper(5)

Equation 5 represents the core of the model we are here
proposing as it relates weight perception to displacement
via the estimation of the work done by the arm.

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CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

Substituting and rearranging the equations above,
mper =

mpr op × hpr op
mpr op × 0.2/λ=α(0.2/λ) + β × 0.2
hperFinally, we arrive at the form relating perceived mass to the
optimal integration weights.
mpr opmper =(6)
α + βλResults
Perceived Mass. We frst analyzed perceived mass by looking
at the mass that participants adjusted in the PHANToM
as a function of C/D ratio. We found that perceived massof the cube was systematically afected by the C/D ratio
manipulation such that lower values of C/D ratio caused the
cube to be perceived as heavier and vice versa for higher
values (see Figure 9).
This was further analyzed in accordance to equation 6 by
ftting its 2 parameters (mpr op and α; note that β = 1 − α) tothe data at a group level. We obtained very good fts to thedata (R 2 = 0.93; see model ft in Figures 9 and 10). To the bestof our knowledge, this is the frst model of pseudo-haptic
weight that gives designers the ability to predict the efectof C/D ratio on the perceived mass, provided comparable
assumptions and methods are used.
0.08kg(7)0.82 + 0.18λExamination of equation 7 shows that the optimal integramper =Perceived Mass Change (g)

10

Data
Model

5

0

-5

-10
0.6

0.8

1

Control/Display Ratio

1.2

1.4

Figure 9: Perceived mass of the cube in grams as a functionof the control/display manipulation applied.

tion weights for the combination of visual and proprioceptive
height are α = 0.82 for proprioception and β = 1 − α = 0.18

Paper 320

for vision. This indicates that participants are indeed combining information across modalities when forming theirestimates of weight. Interestingly, it seems that participants
weighted the signal from vision substantially less than the
one from proprioception. This may indicate that proprioception generally provides the more reliable cue to theweight/mass of an object. In addition, it may indicate thatparticipants noticed that the virtual hand and cube are notcompletely faithfully co-located at all times with the real
hand and cube, and therefore discounted the informationfrom the visual channel.
As our primary interest was to uncover the relationship between weight and the underlying work estimation process—a
process that relies on the perception of the height change
when lifting objects, we next analyzed the relationship between perceived mass and the height. Since participants
always lifted the physical cube to the same visual marker
that was at a height of 20 cm, their real hands moved byan amount that is equal to 20 cm divided by the C/D ratio.
We replotted the data shown in Figure 9 as a function ofthis true height change (Figure 10). This fgure shows thata 5-10 cm height diference between the real and virtual
hand movements corresponds to about a ±5 g diference inmass estimation. While the fgure appears to suggest thatthe perceived mass change grows to −∞ when the physicalheight of the lift is reduced to 0 cm, such a large discrepancy
between the movements of the real and virtual hands mustcause the illusion to break down at some point.
Finally, we combined the data from Experiment 1 (Figure5) and the data from Experiment 2 (Figure 9) to assess how
the modulation of perceived mass measured in Experiment
2 relates to the psychophysical discriminability measured inExperiment 1. To do so, we used the mapping function observed in the second experiment (equation 7) to convert C/Dratios to their equivalent mass modulations in grams, andthen replotted the data and psychometric function from theweight discrimination experiment as a function of the mass
modulations (Figure 11). This analysis revealed that the ±5 g
mass modulation corresponds to 1.55 units of just noticeable
diference. Despite the mass diference being small, it is more
discriminable than would be expected if the manipulation
was purely experienced as mass; it is less than the Weber
fraction for this reference mass. Therefore, it is possible that
there are other perceptual factors and/or cognitive biases
that are involved to make these cues more salient, and allow
for more subtle discriminations of mass to be possible.
Qestionnaire. To analyze the responses to the questionnaire,
we conducted a Wilcoxon signed-rank test to compare themagainst the null hypothesis that they were sampled from a
distribution with median equal to 0.5. For the Limb Ownership items, participants rated items LO1, LO2, LO3’, andPage 10

CHI 2019 Paper

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

Believability items, participants rated all diagnostic items
signifcantly higher than 0.5 indicating that they believedthat the cube was at the same location where they felt it
and that the interaction with it was believable. They rejected
the claim that the cube was immaterial or ghostly. Figure 12
plots these results.

0.7

5

0.9

1.0

1.1

0

0.8

1.2
1.3

Exp't 1: Prob(Respond "Heavier")

1

4

LO

co
n
O
B1
`
O
B2
O
B3
O
B4
O
Bc
on

0

Item

Figure 12: Responses to Questionnaire. Asterisks indicate
median is signifcantly diferent from 0.5 according to the
Wilcoxon signed-rank test, and plus signs represent outliers.

Discussion
In conclusion, C/D ratio manipulation produces a change inthe perceived mass—and hence, weight—of a cube as measured by estimates of mass provided by participants who
used a PHANToM force feedback device to report the mass
they perceived. This phenomenon can be explained as a perceptual illusion resulting from the integration of conficting
visual and proprioceptive signals regarding the displacementof the hand and its virtual representation.

0.9

0.6
0.4

1.2 1.1
1.3

0.2

-10

-5

0

5

Exp't 2: Perceived Mass Change (g)10Figure 11: Discrimination results from Experiment 1 plotted against the equivalent perceived mass modulation from
Experiment 2 (calculated using equation 7) for each C/D ratio tested. The numbers above each data-point represent the
C/D ratio corresponding to that stimulus.

LO4 signifcantly higher than 0.5 indicating that they felt asense of ownership for the virtual limb and perceived it as
the same location as their own limb. In regards to the Object

Paper 320

0.2

0.7
0.8

0.8

0

0.4

3`

Figure 10: Perceived mass of the cube in grams as a functionof the height of the lift performed in physical space. The
vertical dashed line represents the height reached by the virtual hand (20 cm) and is added for clarity and to emphasizethat the x-axis represents the height reached by the physicalhand, and that data points away from the vertical dashedline represent greater discrepancies between the real andrendered movements. The numbers above each data point
represent the C/D ratio corresponding to that height.

0.6

LO

0.3

2

0.25

LO

0.2

Physical Height of Lift (m)

1

0.15

0.8

LO

-10

Data
Model
Virtual Lift

Normalized Response

1

-5

LO

Perceived Mass Change (g)106 GENERAL DISCUSSION
This paper examines the infuence of pseudo-haptic feedback on mass and weight perception in virtual reality. In ourinvestigation, we frame the problem of weight in VR as aprocess of estimation of work done by the user’s arm. Then,
we describe two experiments that collectively: a) establishthat dissociating the movements of the real and virtual arms
through control/display ratio manipulation is an efective
way to manipulate the perceived weight of virtual objects;
and b) propose a predictive model that captures this manipulation.
In the past, the efect of C/D ratio on weight has beeninterpreted as a metaphor—a way to communicate diferent

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CHI 2019 Paper

weights [16]. Here we replicate the results from the literature,and build on them substantially by applying a psychophysicsbased methodology to quantify the efect of the illusion onlifting real objects. Moreover, starting from the notion ofphysical work, we interpret our results from the perspectiveof multisensory integration, shedding new light on the mechanism underlying the illusion. In fact, our results suggest
that—at least for the range of C/D ratio we tested—this illusion is not a metaphor. Rather, we provide evidence that it
may actually be a perceptual bias induced by the integrationof conficting sensory signals regarding the movements of
one’s own arm.
These results have application potential as they provide
a tool to render mass in VR by simply changing the user’s
visual feedback. By using our model (see equation 7), designers can directly afect the perceived weight of a virtual object
in a systematic way. This is particularly useful in modern
VR applications since users are almost always holding controllers in their hands as they interact with the user interface.
The intrinsic weight of the controller—which in most cases
is close to the weight of the cube used in this study—can be
modulated by changing the C/D ratio thereby making purely
virtual objects seem to have more or less weight.
Nevertheless, it is a limitation of the current study that we
made use of only one reference mass, namely 185 g. However,that particular mass was chosen because it is representativeof many conceivable interactions as it is near the mass of
consumer VR handheld touch controllers. In particular, sincemost interactions in VR in the near future will be performed
using the handheld controllers, which have a mass near ourreference mass, the model presented here and the range ofmanipulations described will be appropriate for modulating
mass of virtual objects interacted with while grasping thecontrollers.
Our method might have some relevance also for situations
where the user is not holding any kind of proxy object suchas a controller. Indeed, the human arm itself is a mass that isin principle capable of being modulated under the current
framework of work estimation. Future studies should investigate the extent to which this method is applicable for objects
that are purely virtual, and when the user is just using theirbare hands to interact with them.
These results nicely complement recent research showingthat an ungrounded gripper-style device can be used to simulate the weight of virtual objects by providing a combinationof fnger joint kinesthetic feedback through the use of brakes
and vibrotactile stimulation [4]. As the C/D ratio manipulation approach presented here flls the gap with regard to armkinesthetics, in combination with the approach of Choi et al.
[4], we hypothesize that the result would be very compelling.
Finally, we would like to comment on another limitationof this method, namely that the size of the perceived mass

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CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK

modulation is relatively restricted. Indeed, we fnd that areference mass of 185 g can be modulated by ±5 g underconditions that induce hand displacement diferences of 5-10
cm. Though this is appears to be a rather circumscribed efectin absolute mass terms, it is strongly systematic and robust
across participants. Moreover, considering the results of bothExperiments 1 and 2, we fnd that these implied masses arehighly discriminable, indicating that pure consideration of
the perceived mass modulation may not reveal the wholestory. At the very least, this method promises to be able togive directional manipulations of a reference mass that can
add a layer of believability onto interactions with virtual
objects not otherwise possible.
7

CONCLUSION

This research advances the ability to create immersive and believable VR experiences, specifcally by providing a method
for rendering objects in a way that manipulates their weightthat users can feel. Many games include the manipulation ofvirtual objects, but this is always slightly frustrating due tothe lack of a sensation of force that the user expects theseobjects to exert back. As much as we can simulate suchforces without the need for large and specialized hardware
to provide them, this will allow VR games and experiences tobecome that much more appealing and accessible to a large
user base.
ACKNOWLEDGMENTS
We thank all our study participants, and the anonymous
reviewers for their valuable comments. We are grateful forthe software and hardware support and the many fruitful
discussions that were made possible by our institution.
REFERENCES[1] Merwan Achibet, Adrien Girard, Anthony Talvas, Maud Marchal, andAnatole Lécuyer. 2015. Elastic-Arm: Human-scale passive haptic feedback for augmenting interaction and perception in virtual environments. 63–68. https://doi.org/10.1109/VR.2015.7223325[2] M. Achibet, B. Le Gouis, M. Marchal, P. Léziart, F. Argelaguet, A.
Girard, A. Lécuyer, and H. Kajimoto. 2017. FlexiFingers: Multi-fngerinteraction in VR combining passive haptics and pseudo-haptics. In
2017 IEEE Symposium on 3D User Interfaces (3DUI). 103–106. https://doi.org/10.1109/3DUI.2017.7893325[3] Mahdi Azmandian, Mark Hancock, Hrvoje Benko, Eyal Ofek, andAndrew D. Wilson. 2016. Haptic Retargeting: Dynamic Repurposing of Passive Haptics for Enhanced Virtual Reality Experiences. In
Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems (CHI ’16). ACM, New York, NY, USA, 1968–1979.
https://doi.org/10.1145/2858036.2858226[4] Inrak Choi, Heather Culbertson, Mark R. Miller, Alex Olwal, and Sean
Follmer. 2017. Grabity: A Wearable Haptic Interface for Simulating
Weight and Grasping in Virtual Reality. In Proceedings of the 30th
Annual ACM Symposium on User Interface Software and Technology(UIST ’17). ACM, New York, NY, USA, 119–130. https://doi.org/10.
1145/3126594.3126599

Page 12

CHI 2019 Paper[5] L. Dominjon, A. Lécuyer, J. Burkhardt, P. Richard, and S. Richir. 2005.
Infuence of control/display ratio on the perception of mass of manipulated objects in virtual environments. In IEEE Proceedings. VR 2005.
Virtual Reality, 2005. 19–25. https://doi.org/10.1109/VR.2005.1492749[6] Marc O. Ernst and Martin S. Banks. 2002. Humans integrate visualand haptic information in a statistically optimal fashion. Nature 415,
6870 (Jan. 2002), 429–433. https://doi.org/10.1038/415429a[7] Shangchen Han, Beibei Liu, Robert Wang, Yuting Ye, Christopher D.
Twigg, and Kenrick Kin. 2018. Online Optical Marker-based Hand
Tracking with Deep Labels. ACM Trans. Graph. 37, 4 (July 2018),
166:1–166:10. https://doi.org/10.1145/3197517.3201399[8] Hannah B. Helbig and Marc O. Ernst. 2007. Optimal integration ofshape information from vision and touch. Experimental Brain Research
179, 4 (June 2007), 595–606. https://doi.org/10.1007/s00221-006-0814-y[9] David Antonio Gómez Jáuregui, Ferran Argelaguet, Anne-Hélène
Olivier, Maud Marchal, Franck Multon, and Anatole Lécuyer. 2014.
Toward “pseudo-haptic avatars”: modifying the visual animation ofself-avatar can simulate the perception of weight lifting. IEEE transactions on visualization and computer graphics 20, 4 (April 2014), 654–661.
https://doi.org/10.1109/TVCG.2014.45[10] Luv Kohli, Eric Burns, Dorian Miller, and Henry Fuchs. 2005. Combining Passive Haptics with Redirected Walking. In Proceedings of the 2005
International Conference on Augmented Tele-existence (ICAT ’05). ACM,
New York, NY, USA, 253–254. https://doi.org/10.1145/1152399.1152451[11] L. Kohli, M. C. Whitton, and F. P. Brooks. 2013. Redirected touching:
The efect of warping space on task performance. In 2012 IEEE Symposium on 3D User Interfaces (3DUI). 105–112. https://doi.org/10.1109/
3DUI.2012.6184193[12] Luv Kohli, Mary C. Whitton, and Frederick P. Brooks. 2013. Redirected
Touching: Training and adaptation in warped virtual spaces. In IEEE
Symposium on 3D User Interface 2013, 3DUI 2013 - Proceedings. 79–86.
https://doi.org/10.1109/3DUI.2013.6550201[13] A. Lécuyer. 2009. Simulating Haptic Feedback Using Vision: A Surveyof Research and Applications of Pseudo-Haptic Feedback. Presence 18,
1 (Feb. 2009), 39–53. https://doi.org/10.1162/pres.18.1.39[14] Anatole Lécuyer, Sabine Coquillart, Abderrahmane Kheddar, Paul
Richard, and Philippe Coifet. 2000. Pseudo-Haptic Feedback: Can
Isometric Input Devices Simulate Force Feedback?. In Proceedings of theIEEE Virtual Reality 2000 Conference (VR ’00). IEEE Computer Society,
Washington, DC, USA, 83–. http://dl.acm.org/citation.cfm?id=832288.
835776[15] Kumiyo Nakakoji, Yasuhiro Yamamoto, and Yasuharu Koike. 2010.
Toward Principles for Visual Interaction Design for Communicating
Weight by Using Pseudo-haptic Feedback. In Proceedings of the 2010
International Conference on The Interaction Design (Create’10). BCS
Learning & Development Ltd., Swindon, UK, 34–39. http://dl.acm.org/
citation.cfm?id=2227001.2227008
vfll

Paper 320

CHI 2019, May 4–9, 2019, Glasgow, Scotland, UK[16] Karljohan Lundin Palmerius, Daniel Johansson, Gunnar Höst, and Konrad Schönborn. 2014. An Analysis of the Infuence of a Pseudo-haptic
Cue on the Haptic Perception of Weight. In Haptics: Neuroscience,
Devices, Modeling, and Applications (Lecture Notes in Computer Science). Springer, Berlin, Heidelberg, 117–125. https://doi.org/10.1007/
978-3-662-44193-0_16[17] Cesare V. Parise. 2016. Crossmodal Correspondences: Standing Issues
and Experimental Guidelines. Multisensory Research 29, 1-3 (Jan. 2016),
7–28. https://doi.org/10.1163/22134808-00002502[18] Sharif Razzaque, Zachariah Kohn, and Mary C. Whitton. 2001. Redirected Walking. Eurographics Association. https://doi.org/10.2312/
egs.20011036[19] Michael Rietzler, Florian Geiselhart, Jan Gugenheimer, and Enrico
Rukzio. 2018. Breaking the Tracking: Enabling Weight Perception
Using Perceivable Tracking Ofsets. In Proceedings of the 2018 CHI
Conference on Human Factors in Computing Systems (CHI ’18). ACM,
New York, NY, USA, 128:1–128:12. https://doi.org/10.1145/3173574.
3173702[20] Majed Samad, Albert Jin Chung, and Ladan Shams. 2015. Perceptionof Body Ownership Is Driven by Bayesian Sensory Inference. PLoS
ONE 10, 2 (Feb. 2015), e0117178. https://doi.org/10.1371/journal.pone.
0117178[21] Majed Samad, Cesare V. Parise, Sean Keller, and Massimiliano Di Luca.
2018. A common cause in the phenomenological and sensorimotor
correlates of body ownership. Journal of Vision in press (2018).
[22] F. Steinicke, G. Bruder, J. Jerald, H. Frenz, and M. Lappe. 2010. Estimation of Detection Thresholds for Redirected Walking Techniques.
IEEE Transactions on Visualization and Computer Graphics 16, 1 (Jan.
2010), 17–27. https://doi.org/10.1109/TVCG.2009.62[23] Matthew Streit, Kevin Shockley, Anthony W. Morris, and Michael A.
Riley. 2007. Rotational kinematics infuence multimodal perception ofheaviness. Psychonomic Bulletin & Review 14, 2 (April 2007), 363–367.
[24] Loes van Dam, Cesare Parise, and Marc O. Ernst. 2014. ModelingMultisensory Integration. In Sensory Integration and the Unity ofConsciousness. https://pub.uni-bielefeld.de/publication/2624797[25] A. Zenner and A. Krüger. 2017. Shifty: A Weight-Shifting Dynamic
Passive Haptic Proxy to Enhance Object Perception in Virtual Reality.
IEEE Transactions on Visualization and Computer Graphics 23, 4 (April2017), 1285–1294. https://doi.org/10.1109/TVCG.2017.2656978

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