Easy-to-Recognize Bump Shapes using only Lateral
Force Cues for Real and Virtual Surfaces
Mirai Azechi

Shogo Okamoto

Tokyo Metropolitan University
Hino, JapanTokyo Metropolitan University
Hino, Japan

Abstract—Friction-variable-type surface texture displays canpresent macroscopic bumps and dents on ﬂat touch panels. In thisstudy, bumps and dents of different shapes were identiﬁed only
when frictional or lateral resistance forces were presented. Shapesthat were easy to recognize were then investigated. The tested
surfaces varied in height and width, whereas their maximum
gradients were the same; those with greater widths also exhibited
greater heights or depths. We conducted experiments with thesesurfaces under virtual conditions using an electrostatic friction
display (Experiment 1) and under real conditions, where actual
bumps and dents were explored using a lateral force presenter(Experiment 2). The experimental results were not consistent
between the virtual and real conditions. In the virtual condition,
bumps and dents with moderate heights/depths and widths weremost likely to be recognized as bumps and dents. This suggeststhat adjusting the heights and widths of the bumps and dents
increases their perceptual clarity when the maximally applicable
voltages are limited owing to safety regulations. Under realconditions, we did not observe signiﬁcant differences among
the different bump shapes. Pursuing the incongruency between
virtual and real conditions will lead to a better understanding of
the haptic perception for macroscopic surface shapes.
Index Terms—electrostatic texture display, surface display,
dent, Gaussian

I. I NTRODUCTION
A technique for delivering macroscopic bumps and dents
on a ﬂat touch panel (e.g., [1]–[3]) may lead to a varietyof new applications for surface tactile displays. For example,
the simultaneous tactile presentation of ﬁne textures andlocal bumps on touch panels [4]–[6] produces entertaining
multimodal contents. As described in Section II, the bumppresentation is achieved via the lateral or frictional forces
generated by the friction-variable-type surface display. Suchlateral forces are perceived when a ﬁngertip traverses local
bumps on a ﬂat plane.
A drawback of the surface bump presentation technique isthat the bumps delivered by surface tactile displays are notnecessarily felt with clarity [7]. This is potentially due to theinherent ﬂatness of the touch panel and limited variation of
the friction forces on the panel. In the case of electrostatic
friction displays, the presentation of large friction requires
large-voltage applications, which may be hazardous or limitedby hardware. In an earlier study, bumps and dents presented onelectrostatic tactile displays were less likely recognized thanThis study was in part supported by #23H04360, #21H05819, and#20H04263.

979-8-3503-9993-6/23/$31.00 © 2023 IEEEﬁne textures by approximately 20% with no visual cues [7].
This motivated us to conduct the present study.
The objective of this study was to investigate the shapes ofmacroscopic bumps and dents that are easy to recognize using
only lateral resistance forces under virtual and actual conditions. To date, such shapes have not been pursued, althoughshape recognition under different multimodal conditions [1]and realisms [2] has been studied. In a study by Sun et al. [6],participants categorized a randomly presented convexity as
either Gaussian, triangular, or sinusoidal. The Gaussian convex
was judged most correctly. In our study, the primary concern
was whether the virtual shape was correctly categorized asa bump or dent. Thus, the research question is completely
different from that of earlier studies. Furthermore, studies on
shape perception typically involve three-dimensional force anddisplacement cues (e.g., [8]), whereas only lateral forces are
involved in the present study.
In this study, under the virtual condition, we use electrostatic
friction forces on touch panels. In contrast, under the actual
condition, a force decoupling mechanism using a leaf springis used to transmit lateral forces generated by the contact
between a bump and spherical contactor. It is important
to conﬁrm whether the perceptual properties of the actualand virtual stimuli are consistent. Understanding the reasonsfor the inconsistency is critical for advancing the rendering
techniques. We used exponential bumps and dents for which
the height and width were varied, and their maximum gradients are restricted to the same values. This equal maximum
gradient indicates that the maximum voltages applied to theelectrostatic tactile displays are the same for different bumps
and dents, which is consistent with the hardware limitationsof the tactile displays. Furthermore, as described in Section II,
gradient cues are a major determinant of lateral resistance insliding over bumps. The ﬁndings of this study are expected
to provide knowledge for delivering clear bumps on surface
texture displays.
II. B UMP AND DENT PERCEIVED ON FLAT SURFACES
For the haptic perception of macroscopic bumps during
stroking, the contact force between the ﬁnger pad and bumpy
surface is a major perceptual cue [9]. Fig. 1 shows therelationship between the surface gradient and contact forcesat the contact point. The ﬁngertip, indicated by a black point,
moves from left to right. An early study demonstrated that

397

2023 IEEE World Haptics Conference (WHC)
WHC 2023, Delft, Netherlands, July 10–13, 2023

Gaussian surface y(x)
fpy

fp
fpx

y

fbx

𝜃𝜃

fby

x

ITO panelfb
The gradient of
the surface tan(𝜃𝜃(𝑥𝑥))LoadcellStainless-steel rod

𝑌𝑌

Fig. 2. Electrostatic friction surface display used in Experiment 1. The
participants slide their ﬁngers on the panel holding stainless-steel rod toperceive virtual bumps.

𝑋𝑋

Fig. 1. Action and reaction forces generated on a Gaussian bump (upper) andits gradient (lower). The ﬁngertip, represented by a black point, moves fromleft to right. Lateral reaction force fpx is proportional to the gradient of thesurface.

α = 0.5
A = 2A1

α = 1.0
A = A1

humans feel a surface bump only with a lateral resistanceforce, without an actual surface gradient and displacement [9].
This principle was subsequently used in surface tactile displays
to present bumps and dents on ﬂat touch panels (e.g., [1]–[4],[6], [7]). The lateral force imparted to the ﬁnger pad of theuser is proportional to the surface gradient.
Fpx = Fpy tan α(x).

α = 0.5
A = − 2A1yA10

α = 2.0
A = A1 Τ 2

α = 1.0
A = −A1y0x (cm)x (cm)

α = 2.0
A = − A1 Τ 2(1)As shown in Fig. 1, the lateral resistance force increases
on a rising slope and decreases on a descending slope. In
this study, we used an electrostatic friction display to change
the lateral force when a ﬁnger strokes a ﬂat touch panel.
Furthermore, a force decoupler was used to transmit only thelateral component of the contact force generated by a spherical
tip traversing a bump or dent.

Fig. 3. Gaussian virtual bumps and dents used in Experiment 1, where α andA are the exponent and height, respectively. The maximum and minimum
gradients of all the shapes are equal.

were estimated from the center of gravity of the load. Similarsystems were used by Otake et al. [12], [13].
B. Stimuli: Virtual bumps on electrostatic friction display

III. M ETHODS OF E XPERIMENT 1 USING ELECTROSTATIC

Three types of macroscopic virtual bumps and dents wereused (Fig. 3). These virtual surfaces are expressed using
Gaussian functions, as follows:

FRICTION DISPLAY

A. Apparatus: Electrostatic surface friction display
Electrostatic friction displays manipulate the frictional force
applied to the ﬁnger by creating an electrostatic attraction
force between the ﬁnger and touch panel [10], [11]. This
electrostatic attraction increases adhesive friction when theﬁnger pad slides on the panel. In the experiments, we usedelectrostatic friction displayed in Fig. 2. Voltage was applied tothe electrostatic touch panel with indium tin oxide (ITO) electrodes (SCT3260, 3M, MN), and the participant touched thevirtual surface while holding a stainless-steel rod connectedto the ground. The applied voltage was amplitude modulated
at a carrier frequency of 2 kHz and ampliﬁed (PD-206-150B;
Matsusada Precision Inc., Japan). The upper surface of theelectrostatic touch panel was insulated, and the current does
not ﬂow through the participant’s body. Load cells (USLG25,
TecGihan Co., Ltd., Japan) were placed at the four cornersof the panel, and the positions of the ﬁngers on the panel

x2 α
))
(2)
σ2
where σ = 1 cm. Their shapes differ because of the different
power components α, by which the shape of the Gaussianfunction can be changed. The larger the value of α, the steeper
and narrower is the slope. In contrast, the smaller the value ofα, the more gradual and wider the gradient. In the experiment,
α values were 0.5, 1.0, or 2.0. The height and depth parameters
A were determined such that the maximum gradients of thesix types of bumps and dents√ were identical. For the bump and
2A1 . For the bump and dent withdent with α = 0.5, A=√
α = 2.0, A = A1 / 2. Here, A1 was 1.0. Equal maximum
gradients are important for bumps and dents. As described in
Section II, the lateral resistance force generated when sliding
over a bump is proportional to its gradient. Therefore, the398

y = ±A(exp(−

maximum voltages applied to the panel were the same for boththe bumps and dents. This condition, that is, equal maximum
voltages, was set considering that surface displays have limited
applicable voltages.
The relationship between the lateral frictional force F (x)and applied voltage V (x) is determined according to the lawsof electrostatic force and Coulomb friction, as follows:

Lateral force F [N]μ (W + kV2
max )

(3)

where µ, W , and k are the coefﬁcient of friction, ﬁnger load,and electrostatic force constant, respectively. Fig. 4 shows theresultant friction forces using this formula.
The lateral force generated when a ﬁnger slides over a bumpsurface is expressed as a function of the surface gradient [9],[14], [15]. Thus, the voltage Ve (t) to be applied is expressed
as
√ √
√
2α
1 αx2
2α
1
V (x) = GA ∓exp( − 2 )x +exp(− )
σ
2
σ
σ
2
(4)
The positive and negative signs correspond to bumps anddents, respectively. The value of G was adjusted for eachparticipant during the training session because the perceived
intensity of the stimuli varied among individuals. The resultant maximum applied voltages ranged 30–55 V among theparticipants.

α = 2.0

α = 1.0

μW
0

-4

-2

0

2

4

Position 𝑥 (cm)μ (W + kV2
max )Lateral force F [N]F (x) = µ{W + kV 2 (x)}α = 0.5

μW
0

-4

-2

0

2

4

Position 𝑥 (cm)Fig. 4. Lateral forces applied to the ﬁnger while perceiving virtual bumps(upper) and dents (lower) in Experiment 1, where µ, W , and k are thecoefﬁcients of friction, load of the ﬁnger, and electrostatic force constant,respectively. Vmax is the applied voltage, which is determined by the voltage
gain adjusted to each participant.

C. Participants
Nine adults (four females) participated in the study after
providing written informed consent. The participants were
unaware of the study objectives.
D. Procedures
The experiments were divided into two parts: a training
session and main session. Before the training session, theelectrostatic friction stimulus was applied to each participant.
The voltage gain gradually increased starting from a low value;
it was ﬁxed at a value where the participant could adequately
perceive the stimulus.
During the training sessions, participants learned about
the virtual stimuli. They were presented with six different
tactile stimuli and told which stimulus corresponded to Fig. 3.
Training was continued until the participants felt familiar withthe stimuli.
In the main session, participants identiﬁed six randomly
presented virtual surfaces. The number of trials was 60,
and each stimulus was presented a total of 10 times. The
participants were allowed to perceive a stimulus as many times
as they wished during each trial. The experimental participant
perceived the stimulus, that is, the bump or dent, from the left
to right with the index ﬁnger of the right hand while holding
a stainless-steel rod connected to the ground. The participants
wore earplugs and earmuffs.

E. Data analysis
We calculated the proportions in which the six types ofstimuli were correctly identiﬁed by the participants; we also
calculated the proportions in which the bumps and dents were
judged correctly. For example, when a bump of α = 1.0 waspresented and the participant’s answer was a bump of α = 2.0,
this answer was included in the latter proportion but not in
the former. The two proportions were compared among thedifferent stimuli.
IV. M ETHODS : E XPERIMENT 2 USING ACTUAL BUMPS
A. Apparatus: Lateral force presenter using leaf-spring force
decoupler
The lateral force presenter shown in Fig. 5 was used when
the actual bumps were perceived. The main components of theapparatus include a leaf spring, linear slider, and guide. Eachparticipant laid his/her ﬁnger on the linear slider and moved
it laterally. With this motion, the leaf spring also moved. A
plastic sphere was ﬁxed to the tip of the leaf spring, which is inconstant contact with the bump and dent surfaces. The stiffnessof the leaf spring is high in the lateral direction; therefore,
the lateral force generated at this point is transmitted to theﬁnger on the linear slider. In contrast, the participants could
not perceive any normal displacement or force generated at
the leaf-spring tip. Thus, the apparatus allowed us to remove399

unaware of the study objectives.

Wooden bump or dent
Leaf spring

D. Procedures of Experiment 2

Linear guideFig. 5. Lateral force presenter using a leaf-spring force decoupler usedin Experiment 2. This apparatus transmits only the lateral force generated
at the contact point. The ﬁnger moves on a linear guide with no verticaldisplacement.

Participants moved the linear slider along the x-axis using
the index ﬁnger of their writing hand and explored the actual
bumps and dents. The experiment consisted of training andmain sessions. During the training session, they could lookat and haptically explore each of the six actual bumps. Thissession lasted until the participants became familiar with thebumps, which typically required a few trials.
In the main session, the participants wore blindfolds andearmuffs to prevent visual and auditory cues. The number oftrials was 60, with each surface shape presented 10 times
in a random order. The participants were allowed to slide
their ﬁngers over a bump fewer than six times. With moreor unlimited exploration, the participants could recognize
the shapes nearly perfectly. After each trial, the participants
answered the question that best suited their experience among
the six shapes in a forced-choice manner.
E. Data analysis
We calculated the proportions in which each of the six typesof stimuli was correctly identiﬁed by the participants. We also
calculated the proportions at which the bumps and dents were
judged correctly. The two proportions were compared among
the different stimuli.

yx

V. R ESULTS
Fig. 6. Actual wooden bumps and dents used in Experiment 2. Three bumps
and dents with different height/depth and width; their maximum gradientswere equal.

normal cues, that is, force and displacement, when exploring
surface bumps and dents.
B. Stimuli: Actual bumps
For actual surface bumps and dents, the surface displacement y (cm) along x (cm) was deﬁned as
x2 α
))
(5)
σ2
where σ = 1.0 cm. Similar to Experiment 1, the α values
were 0.5, 1.0, or 2.0. Their height or depth B values were
determined such that their shapes could not be perfectly
recognized. The surface heights were B = 0.14 cm for
α = 0.5, B = 0.10 cm for α = 1.0, and B = 0.071 cm for
α = 2.0. The actual surface was created by cutting a mediumdensity ﬁberboard using a laser cutter (Hajime CL1, Oh-Laser
Co., Ltd., Japan). Subsequently, the cut surfaces were polishedusing a #1500 sandpaper and greased. This reduced friction
resulting from the surface roughness of the material.
y = ±B(exp(−

C. Participants
Eight adults (three females) participated in the study after
providing written informed consent. The participants were

A. Experiment 1: Virtual surface
Table I lists the mean and standard errors of the answer
proportions obtained from the participants in Experiment 1.
The table also shows the proportion of correct categorizations,wherein the categories of bumps and dents were judged
correctly, as mentioned in Section III-E. Fig. 7 shows thecorrect categorization of each virtual surface. Bumps anddents with moderate height/depth and width of α = 1.0
were most likely to be correctly categorized as bumps anddents. For the bump shapes, no signiﬁcant differences wereobserved between α = 1.0 and others (z-test, p > 0.05). For
dent shapes, no signiﬁcant difference was observed between
α = 1.0 and α = 0.5; however, the shape with α = 1.0
was signiﬁcantly greater than the shape with α = 2.0 (z-test,p < 0.05).
B. Experiment 2: Actual surface
Table II lists the results of Experiment 2. Fig. 8 shows the
proportion of correct categorizations for each actual surface.
For the bump, the shape with the greatest height and widthat α = 0.5 was most likely correctly categorized as a bump.
In contrast, for the dent, the shape with the smallest depth
and width with α = 2.0 was most likely to be correctly
categorized as a dent. Nonetheless, no signiﬁcant differenceswere observed between these two α values and the others forthe bumps and dents.

400

TABLE I
E XPERIMENT 1: V IRTUAL CONDITION USING ELECTROSTATIC TACTILE DISPLAY. M EAN AND STANDARD ERRORS OF ANSWER PROPORTIONS . M OSTRIGHT COLUMN SHOWS THE PROPORTION OF CORRECT CATEGORIZATION INTO BUMP OR DENT.

Presented

Answerα = 0.5
α = 1.0
α = 2.0
α = 0.5
α = 1.0
α = 2.0

Bump
Dent

α = 0.5
0.48 ± 0.07
0.26 ± 0.06
0.17 ± 0.05
0.04 ± 0.02
0.03 ± 0.02
0.02 ± 0.02

Bump
α = 1.0
0.22 ± 0.06
0.38 ± 0.04
0.21 ± 0.05
0.09 ± 0.04
0.04 ± 0.02
0.09 ± 0.04

α = 2.0
0.12 ± 0.04
0.23 ± 0.05
0.41 ± 0.08
0.04 ± 0.02
0.03 ± 0.02
0.12 ± 0.02

α = 0.5
0.11 ± 0.02
0.06 ± 0.03
0.08 ± 0.03
0.46 ± 0.09
0.20 ± 0.06
0.13 ± 0.06

Dent
α = 1.0
0.04 ± 0.03
0.06 ± 0.02
0.06 ± 0.03
0.21 ± 0.04
0.43 ± 0.06
0.20 ± 0.06

α = 2.0
0.01 ± 0.01
0.02 ± 0.02
0.09 ± 0.04
0.16 ± 0.06
0.26 ± 0.07
0.43 ± 0.10

Correct
categorization
0.82 ± 0.04
0.87 ± 0.04
0.79 ± 0.06
0.82 ± 0.05
0.89 ± 0.04
0.77 ± 0.04

TABLE IIE XPERIMENT 2: ACTUAL CONDITION USING LATERAL FORCE PRESENTER . M EAN AND STANDARD ERRORS OF ANSWER PROPORTIONS . M OST RIGHTCOLUMN SHOWS THE PROPORTION OF CORRECT CATEGORIZATION INTO BUMP OR DENT.

Presented

Answerα = 0.5
α = 1.0
α = 2.0
α = 0.5
α = 1.0
α = 2.0

Bump
Dent

α = 0.5
0.32 ± 0.09
0.09 ± 0.03
0.13 ± 0.05
0.11 ± 0.06
0.02 ± 0.02
0.02 ± 0.02

Bump
α = 1.0
0.31 ± 0.06
0.34 ± 0.06
0.19 ± 0.05
0.06 ± 0.03
0.10 ± 0.02
0.06 ± 0.02

α = 2.0
0.23 ± 0.05
0.38 ± 0.07
0.43 ± 0.08
0.04 ± 0.04
0.07 ± 0.02
0.03 ± 0.02

α = 0.5
0.04 ± 0.04
0.07 ± 0.04
0.08 ± 0.04
0.34 ± 0.05
0.20 ± 0.06
0.12 ± 0.04

Dent
α = 1.0
0.04 ± 0.02
0.09 ± 0.05
0.04 ± 0.03
0.27 ± 0.04
0.27 ± 0.05
0.33 ± 0.04

α = 2.0
0.04 ± 0.03
0.03 ± 0.03
0.12 ± 0.02
0.18 ± 0.07
0.34 ± 0.04
0.43 ± 0.07

Correct
categorization
0.86 ± 0.06
0.81 ± 0.07
0.75 ± 0.06
0.78 ± 0.06
0.81 ± 0.03
0.88 ± 0.02

VI. D ISCUSSION

Correct categorization

1.00

N.S.

N.S.

N.S.

*

0.80
0.60
0.40
0.20
0.00

α=0.5

α=1.0

α=2.0

α=0.5

α=1.0

Bumps

α=2.0

Dents

Fig. 7. Experiment 1: Virtual bumps and dents: The proportions and standard
errors of correct categorization into bumps and dents. * indicates p < 0.05.

Correct categorization

1.00

N.S.

N.S.

N.S.

N.S.

0.80
0.60
0.40

0.20
0.00

α=0.5

α=1.0
Bumps

α=2.0

α=0.5

α=1.0

α=2.0

Dents

Fig. 8. Experiment 2: Actual bumps and dents: The proportions and standard
errors of correct categorization into bumps and dents.

For the virtual bumps, shapes with moderate height/depth
and width with α = 1.0 tend to be correctly categorized,
suggesting the existence of optimal height/depth and width
for bumps/dents to be recognized. Interestingly, although the
maximum gradients were the same for the three α values, thedent with α = 1.0 was more likely to be correctly recognized
as a dent. Intuitively, the maximum gradients appear to be themajor determinants of the ease of recognition of the shapes.
However, other factors also inﬂuence the recognition of bumps
on ﬂat touch panels. One such factor is the rate of change ofthe friction force. As shown in Fig. 4, the rates of change
differed for different α values. When α = 0.5, the rate ofchange was the smallest and change in the virtual surface
shape could not be easily recognized. With α = 2.0, therate of change was the highest, and the surface irregularity
could have been easily recognized. However, bumps and dents
with α = 2.0 tend to be incorrectly categorized. According to
introspective reports from the participants, for the bumps anddents with α = 2.0, surface irregularity was easily detected;
however, the participants occasionally confused the bumps anddents. It is possible that the large rate of change in the friction
force over a short period is difﬁcult to be recognized correctly.
In other words, with α = 2.0, the change in the friction force
might have been too rapid to correctly classify bumps anddents.
In the actual conditions, for both bumps and dents, nosigniﬁcant difference was observed in the proportions correctly
categorized as a bump/dent for each shape. Moreover, theparticipant responses seemed different for bumps and dents. A
possible explanation for this is the difference in the perceptual
properties for the rate of change of the lateral force during theincrease and decrease. The bump shape reached a maximum

401lateral force and subsequently decreased to a minimum. However, the dent shape reached a minimum in the lateral force;
subsequently, it increases to a maximum. The rate of changeof lateral force decreased with smaller power values α andincreased with larger power values. A smaller rate of change
is more likely to be perceived during an increase, whereas alarger rate of change is more likely to be perceived during
a decrease, which may explain this tendency. Provided that
the Weber’s law holds for friction perception [16], where thejust-noticeable level of friction change is nearly a constantpercentage of the reference friction level, a rapid increase infriction after a rapid decrease is easier to recognize than a rapid
decrease in friction after a rapid increase. Thus, the perceptual
performances against bumps and dents can be different.
It is intriguing that the easy-to-recognize α values differed
between the actual and virtual conditions. The root causeof this difference is unknown; however, one of the majordifferences between the two experimental conditions may havecaused this difference in the results, that is, the slippage of the
ﬁnger pad. In the virtual condition of Experiment 1, the ﬁnger
pad slipped onto the touch panel, whereas it was constantly
in contact with the linear slider in the actual condition ofExperiment 2. Therefore, the microscopic contact conditions
differed signiﬁcantly between the two experiments.
VII. C ONCLUSION
Friction variable surface tactile displays can deliver macroscopic shapes on ﬂat touch panels. However, when the applicable voltage is limited, it is difﬁcult to discriminate between
bumps and dents based solely on the lateral force cues. We
investigated the surface shapes that were easy to recognize
under actual and virtual conditions, which the previous studies
have not pursued. We used bumps and dents with different
heights and widths; however, their maximum gradients wereidentical. The virtual bumps and dents with moderate heights,
widths, and change rates in the friction force were likely
to be recognized, suggesting that optimal ranges exist forthese parameters. For the actual bumps and dents, although
the statistical differences were not observed, distinctive trends
were seen for the bumps and dents. Bumps with large heights
and widths and dents with small depths and widths tended
to be correctly recognized with relative ease. The features ofeasy-to-recognize bumps and dents should be studied in the

future. Such studies will help developers of surface displays
to present clear surface features on touch panels.
R EFERENCES[1] R. H. Osgouei, J. R. Kim, and S. Choi, “Improving 3D shape recognition with electrostatic friction display,” IEEE Transactions on Haptics,
vol. 10, no. 4, pp. 533–544, 2017.
[2] S.-C. Kim, A. Israr1, and I. Poupyrev, “Tactile rendering of 3D features
on touch surfaces,” in ACM Symposium on User Interface Software andTechnology, 2013, pp. 531–538.
[3] M. Janko, Z. Zhao, M. Kam, and Y. Visell, “A partial contact frictional
force model for ﬁnger-surface interactions,” in 2018 IEEE Haptics
Symposium, 2018, pp. 255–261.
[4] S. Saga and R. Raskar, “Simultaneous geometry and texture display
based on lateral force for touchscreen,” in IEEE World Haptics Conference, 2013, pp. 437–442.
[5] S. Ryu, D. Pyo, B. K. Han, and D. S. Kwon, “Simultaneous representation of texture and geometry on a ﬂat touch surface,” in Haptic
Interaction, S. Hasegawa, M. Konyo, K.-U. Kyung, T. Nojima, and
H. Kajimoto, Eds. Springer, 2018, pp. 83–86.
[6] X. Sun, C. Zhang, and G. Liu, “Improved tactile perception of 3D geometric bumps using coupled electrovibration and mechanical vibration
stimuli,” Computer Journal, vol. 65, pp. 621–630, 2022.
[7] M. Azechi and S. Okamoto, “Combined virtual bumps and textures onelectrostatic friction tactile displays,” in IEEE 11th Global Conference
on Consumer Electronics, 2022, pp. 315–317.
[8] K. Drewing and L. Kaim, “Haptic shape perception from force andposition signals varies with exploratory movement direction and the
exploring ﬁnger,” Attention, Perception, & Psychophysics, vol. 71, no. 5,
pp. 1174–1184, 2009.
[9] G. Robles-De-La-Torre and V. Hayward, “Force can overcome object
geometry in the perception of shape through active touch,” Nature, vol.
412, pp. 445–448, 2001.
[10] O. Bau, I. Poupyrev, A. Israr, and C. Harrison, “Teslatouch: electrovibration for touch surfaces,” in ACM Symposium on User Interface Software
and Technology, 2010, pp. 283–292.
[11] Y. Vardar, B. Guclu, and C. Basdogan, “Effect of waveform on tactile perception by electrovibration displayed on touch screens,” IEEE
Transactions on Haptics, pp. 488–499, 2017.
[12] K. Otake, S. Okamoto, Y. Akiyama, and Y. Yamada, “Tactile texture rendering for electrostatic friction displays: Incorporation of low-frequency
friction model and high-frequency textural model,” IEEE Transactions
on Haptics, vol. 15, no. 1, pp. 68–73, 2022.
[13] ——, “Tactile texture display combining vibrotactile and electrostaticfriction stimuli: Substantial effects on realism and moderate effects on
behavioral responses,” ACM Transactions on Applied Perception, vol. 19,
no. 4, p. 18, 2022.
[14] Y. Fujii, S. Okamoto, and Y. Yamada, “Friction model of ﬁngertip sliding
over wavy surface for friction-variable tactile feedback panel,” Advanced
Robotics, vol. 30, no. 20, pp. 1341–1353, 2016.
[15] ——, “Interactive forces caused by scanning wavy surfaces,” in IEEE
Haptics Symposium, 2014, pp. 449–453.
[16] E. Samur, E. Colgate, and M. A. Peshkin, “Psychophysical evaluation ofa variable friction tactile interface,” in SPIE - The International Society
for Optical Engineering, vol. 7240, 2009, pp. 167–173.

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