Judging 2D versus 3D square-wave virtual gratings

Abstract

Haptic virtual texture can enhance people's experience in interacting with virtual objects by providing surface information. We present a study to analyze how people distinguish between 2D and 3D square-wave gratings using a point-source haptic interface. Our analyses were based on objective vibration and force measurements and psychophysical experiments with human subjects. The results indicated that people were unable to detect the difference between the two textures when they moved their hands across textures with either the amplitude or period smaller than 1.52 mm (0.06 inch) for a texture stiffness of 2 N/mm. This result implies that a simple 2-degree-of-freedom haptic interface may be sufficient to convey the same 3-dimensional tactile feeling for certain textures if the textures are small enough.

Full text

1
Abstract
Haptic virtual texture can enhance people’s
experience in interacting with virtual objects by providing
surface information. We present a study to analyze how
people distinguish between 2D and 3D square-wave
gratings using a point-source haptic interface. Our
analyses were based on objective vibration and force
measurements and psychophysical experiments with
human subjects. The results indicated that people were
unable to detect the difference between the two textures
when they moved their hands across textures with either
the amplitude or period smaller than 1.52 mm (0.06 inch)
for a texture stiffness of 2 N/mm. This result implies that
a simple 2-degree-of-freedom haptic interface may be
sufficient to convey the same 3-dimensional tactile feeling
for certain textures if the textures are small enough.
1. Introduction
The objective of this paper is to help understand how
humans distinguish between 2D and 3D textures in haptic
virtual environments. In particular, we would like to see
whether people can easily discriminate between 2D and
3D square-wave gratings using a point-source haptic
interface. Vibration and force exerted on the human hand
were measured when the hand was moved across the
texture gratings. Furthermore, we asked subjects to do a
series of psychophysical experiments in tactile perception
of these two types of virtual textures.
Force and vibration are two important factors that let
a person distinguish the characteristics of objects and
textures through touching. Lederman and Klatzky [6]
demonstrated that spatially distributed forces are
important for humans to perform a set of sensory tasks
(determination of force threshold and spatial resolution)
and perceptual tasks (roughness estimation and 2D bar
orientation determination). On the other hand, vibration
was also verified to be a critical factor to perform a series
of tactile feedback tasks by Kontarinis et al. [5] and
Wellman et al. [13]. Okamura et al. [9] created a library
to record the vibratory information of tapping on
materials and stroking textures and then played back the
simulated results on a force-feedback joystick.
Weisenberger and Krier [14] compared human
performance in tactile perception of surface textures using
both vibratory and force feedback devices. The results
from these researchers indicated that force and vibration
are critical factors in human tactile perception.
Many researchers have verified that virtual 2D
texture alone can provide a compelling feeling of
roughness and textures. Minsky [7] developed the 2D
Sandpaper system to simulate haptic texture using only
lateral force to construct textured surfaces that subjects
scanned with a 2-degree-of-freedom (DOF) force-
feedback joystick. She found that roughness perception
was influenced heavily by contact force and that lateral
force alone gave a compelling representation of haptic
textures. Siira and Pai [12] discussed the decomposition
of contact force in haptic texture and implemented only
the lateral force to represent textured surfaces in their 2-
DOF Pantograph haptic interface. Robles-De-La-Torre
and Hayward [10] suggested the use of only planar forces
to express 3D haptic shape. Their results indicated that
explicit 3D geometry of a shape was not always necessary
in the perception of a haptic shape.
Our study focuses on two types of textures – 2D and
3D square-wave gratings (see Figure 1). A 2D square
wave is defined as rectangular gratings (50% duty cycle)
parallel with one another without amplitude, whereas a
3D square wave is defined as rectangular gratings with
amplitude. Our hypothesis is that 2D and 3D square-
wave textures can provide an identical 3D tactile
sensation. We will investigate under what circumstance
this hypothesis is valid.
This study has potential benefit to both haptic
interface design and haptic rendering techniques for
virtual textures. If our hypothesis is valid, a 2-DOF
haptic interface, which typically would possess a simpler
Judging 2D versus 3D Square-Wave Virtual Gratings
Peter P. Ho Bernard D. Adelstein Hami Kazerooni
UC Berkeley NASA Ames Research Center UC Berkeley
Mechanical Engineering Dept. Mail Stop 262-2 Mechanical Engineering Dept.
2168 Etcheverry Hall Moffett Field, CA 94035 5124 Etcheverry Hall
Berkeley, CA 94720 Bernard.D.Adelstein@nasa.gov Berkeley, CA 94720
peterho@me.berkeley.edu kazeroon@me.berkeley.edu
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mechanical architecture, may be sufficient to convey
realistic 3D tactile information for certain textures.
Furthermore, because 2D square-wave gratings have
fewer texture features than true 3D square-wave gratings,
less computational effort would be required for rendering
of virtual haptic textures.
The possible paths that a human hand can take across
2D and 3D square-wave textures are shown in Figure 1.
For a 2D square wave, there is one general path. To feel
the square-wave gratings, users need to move their hand
on the flat textured surface. For a 3D square wave, there
are two possible paths of contact movement. The first
path is on the bottom layer of the textured surface. The
second is across the upper portion of the texture, in and
out of the gratings.
Figure 1. Possible paths to move across 2D
and 3D square-wave gratings (Regions 1, 2, and 3
are discussed in Sections 3.2 and 3.3)
In this study, our approach was to measure vibration
and force to see how they are related to the ability to
distinguish between the two texture types. Human
capability to distinguish between the two texture types
was examined in texture discrimination experiments. Our
study gives an initial step to understand how humans
perceive 2D and 3D textures.
2. Theory
The mechanical properties of the human arm have
been investigated by Hogan and Mussa-Ivaldi [3][8]. In
their studies, a human arm, displaced by an apparatus
from an equilibrium position, was moved back to its
original position by the arm’s restoring force. The
stiffness of the human arm was then derived from the
relation between the restoring force and displacement.
In Hogan and Mussa-Ivaldi’s numerical method, the
arm stiffness for planar arm movement was represented
by the matrix term in:
»
¼
º
«
¬
ª
»
¼
º
«
¬
ª
−−
−−
=
»
¼
º
«
¬
ª
dy
dx
KK
KK
F
F
yyyx
xyxx
y
x
(1)
A linear force-displacement relation is assumed for small
displacements (dx and dy). The off-diagonal terms in the
stiffness matrix (K
xy
and K
yx
) can cause a displacement in
one direction to exert a restoring force in another
direction. These off-diagonal terms of the stiffness
correspond to the interaction between the joints of the
arm. Because of such off-diagonal terms in a more
general three-dimensional stiffness matrix representing
the arm, when the human hand is moved across periodic
textures in x-direction, a restoring force may be generated
in z-direction (normal to surface). Similar to the arm, the
machine itself can also cause cross coupling to occur. As
a result, the human operator may feel that the texture
sticks out of the surface (3D tactile sensation) even
though he/she does not move in the direction normal to
the surface.
3. Vibration and Force Measurement
3.1. Measurement Setup
Figure 2. Haptic interface used for experiments
The haptic interface that we used permits three DOF
translational motion and force at the human-machine
interface (see Figure 2). The interface has a parallel
configuration in which all heavy actuator housings are
fixed to the common ground. This reduces both the
weight and inertia of the moving mechanical system.
Additionally, the parallel architecture is more rigid than
machines with serial configurations. The nominal
position resolution of the haptic interface is 0.016 mm.
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Its continuous exertable force is 19 N; peak force is 69 N
[2].
The haptic interface was controlled by a Pentium II
266 MHz PC running under MS-DOS. The sampling rate
of the software program was 1 kHz for vibration
measurement and 714 Hz for force measurement.
Figure 3. Orientation of texture display and hand
movement in vibration and force measurement
During the experimental measurements, the 2D and
3D square-wave gratings were rendered vertically on the
x-y plane when the hand was moved across the texture
grating in positive x-direction from left to right at about
127 mm/s (5 inch/s) (see Figure 3). The stiffness of the
texture was set to 2 N/mm. The periods of both 2D and
3D square-wave gratings were set to 5.08 mm (0.2 inch),
whereas the peak-to-peak amplitude of 3D square-wave
gratings was set to 50.8 mm (2 inch).
3.2. Vibration Measurement
Vibration is a cue that humans often use in tactile
perception [5][13]. In vibration measurement, a 3-axial
shear accelerometer (PCB Piezotronics, Inc.; Model No.:
356A16) was attached to the haptic interface at the link
closest to the handgrip. A spectral analyzer (Agilent
35670A) was used to measure the haptic interface’s
acceleration in both time and frequency domains while
the hand was moving across the texture gratings. During
the measurement, the 2D and 3D square-wave gratings
were displayed vertically. The subjects used their right
hand to grasp the handle, maintaining their arm
approximately in a horizontal plane, and moved the
handle across the textures from left to right once (see
Figure 8).
Sample acceleration measurements for 2D square-
wave gratings are shown in Figure 4. In the time domain,
the sharp rise of positive acceleration corresponded to the
moment that the joystick interaction point has just left a
bump because the sudden loss of resistant force made the
sharp rise of acceleration in the positive x-direction
(Region 1) (see Figures 1 and 4.1). After that, the linkage
decelerated because the hand was moved at a constant
velocity. As a result, the linkage acceleration fluctuated
as it reached steady state (Region 2). The linkage
acceleration kept dropping as the hand was moved inside
the next bump (Region 3) until another sharp rise of
acceleration after the hand passed through the bump.
For the acceleration measurements in the z-direction
(normal to the surface), big fluctuations of acceleration
occurred after the sudden rise of acceleration in x-
direction (see Figure 4.2). This big jump of acceleration
depended on the virtual texture shape and stiffness. The
fluctuations of acceleration in z-direction might provide
the human operator a 3D tactile feeling because the
vibration was in the direction normal to the surface.
-3
-2
-1
0
1
2
3
0.2 0.25 0.3 0.35 0.4
Time (sec)
Acceleration (g)
1. X-Axis
-1.5
-1
-0.5
0
0.5
1
1.5
0.2 0.25 0.3 0.35 0.4
Time (sec)
Acceleration (g)
2. Z-Axis
Figure 4. Acceleration measurements in time
domain when moving across
2D square-wave gratings
Acceleration patterns for hand interaction with the
bottom and upper portion of 3D square-wave gratings
were very similar to those for 2D square-wave gratings.
From the acceleration measurements, an observer would
unlikely be able to distinguish between the two textures
based on vibration cues when moving across the texture
gratings.
3.3. Force Measurement
Force is another main factor in tactile perception.
The 6-axis force/torque sensor (ATI F/T Mini 10/20) built
into the haptic interface below the handgrip was used to
measure the force exerted at the hand. The 3-axis force
measurements in transducer relative coordinates were
1 2 3
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then converted to the fixed world coordinates of the
haptic device.
Sample force measurements for hand interaction with
2D square-wave gratings are shown in Figure 5. The
force profiles for 2D square-wave gratings can be
explained using the study of Hajian and Howe [1] about
the transient response of an outstretched human index
finger. Hajian and Howe measured the force and
acceleration for flexion-extension of the
metacarpophalangeal (MCP) joint of an index finger and
used the data to fit the parameters of their linear second-
order, lumped-element model. The calculated values of
the three force components, the inertial force (ma), the
damping force (bv), and the stiffness force (kx) were
estimated individually and used to explain the behavior of
their model of human finger. In their experiment, during
the initial few milliseconds, inertial force was dominant.
Next, the effects of stiffness and damping forces
increased. Finally, at the end of the measurement, the
stiffness force became the dominant term.
For 2D square-wave gratings, the x-axis component
of the force profile is analyzed as follows (see Figures 5
and 1). After the joystick interaction point had just left
the bump, the sudden loss of resistance in the direction of
hand movement caused the x-coordinate force to drop
sharply (Region 1). The first peak of force after the
sudden drop was due to the inertia properties of the
machine and hand. This observation follows from the
results of Hajian and Howe. Later, after the first peak,
both the acceleration, a, and the inertial force, ma, of the
linkage oscillated left and right reaching steady state as
the participant attempted to produce constant velocity
hand movement (zero acceleration) (Region 2). As a
result, the fluctuation of force measurements in x-axis
was observed. The gradual rise of force in the positive x-
direction observed as the hand moved further into the
next bump was due to increasing stiffness force (Region
3).
-6
-4
-2
0
2
4
6
0.6 0.65 0.7 0.75 0.8
Time (sec)
X-Axis Z-Axis
Figure 5. Force measurements in time domain
when moving across 2D square-wave gratings
The force measurements in the z-axis (normal to the
surface) showed a sharp change when a sudden drop of
force occurred in the x-axis, i.e., when the hand had just
left a bump. Because the big change of force was in z-
direction, the human operator would feel a force normal
to the surface, contributing to a 3D tactile percept.
The force measurements of hand interaction with the
bottom layer and upper portion of 3D square-wave
gratings are shown in Figures 6 and 7. In general, there
was no observable difference between x-axis force
profiles when the hand was moved across 2D and 3D
square-wave gratings. However, the z-axis force profiles
of 2D square wave and 3D square wave (bottom layer)
had an approximate 1.7-N mean offset from zero. This
offset depended on how hard the hand pushed against the
virtual surface in z-direction. On the other hand, the
force profile of 3D square wave (upper portion) had no
offset because the hand did not have contact with the
bottom layer of the grating.
-6
-4
-2
0
2
4
6
0.8 0.85 0.9 0.95 1
Time (sec)
X-Axis Z-Axis
Figure 6. Force measurements in time domain
when moving across the bottom of
3D square-wave gratings
-6
-4
-2
0
2
4
6
0.6 0.65 0.7 0.75 0.8
Time (sec)
X-Axis Z-Axis
Figure 7. Force measurements in time domain
when moving across the upper portion of
3D square-wave gratings
In summary, it is unlikely that a person would feel
the difference between 2D and 3D square-wave grating
unless he/she interacts with the upper portion of the 3D
square-wave. To interact with the upper portion of the
grating, the person would need to pay close attention to
the displacement offset in z-direction. However, rather
than holding their hands in the air to interact only with the
1
2 3
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upper portion of the 3D square-wave gratings, we
observed that people tended to lean their hand against the
surface and interact with the bottom layer of 3D square-
wave gratings.
4. Tactile Perception Experiments
Along with the engineering measurement of vibration
and force, we conducted psychophysical experiments to
test whether human subjects can perceive any significant
difference between interactions with 2D and 3D square-
wave gratings. From the psychophysical results, we can
discuss under what conditions the 2D and 3D square-
wave gratings provide the same 3D tactile percept.
4.1. Procedure
Nine subjects (8 males and 1 female; age 18-39) with
no reported tactile and visual impairment participated in
all portions of this study. All used their right hand to
interact with the texture gratings during the experiments.
Subjects used the same 3-DOF haptic interface and
simulated haptic textures described above in the
psychophysical study. The 2D and 3D square-wave
gratings were displayed vertically on the inside back
surface of a 127 x 127 x 127 mm (5 x 5 x 5 inch) virtual
box (see Figure 8). In all the experiments, the subjects
were allowed to move freely within the box. The texture
stiffness was set to 2 N/mm, and the update frequency of
the haptic interface controller was 1 kHz.
Figure 8. Experimental setup of human tactile
perception in comparison of 2D and 3D
square-wave gratings (top view)
This study consisted of three separate experiments to
compare 2D and 3D square-wave gratings. The
experiments differed from one another in the manner that
the subjects interacted with the texture gratings. In each
experiment, the period and peak-to-peak amplitude of the
square-wave gratings could be either 0.51 mm (0.02
inch), 1.52 mm (0.06 inch), or 4.57 mm (0.18 inch). Each
combination of period and amplitude was repeated
according to the method of constant stimuli in blocks of
20 for a total of 180 judgments. The order of the nine
blocks was randomized in each experiment.
The subjects needed to respond whether pairs of
sequentially displayed textures were the same. The first
and the second textures could be either 2D or 3D square-
wave gratings. Both textures had the same spatial period,
while the amplitude of the 3D texture was varied. For
each amplitude-period combination, half (10) of the
presentations were “catch” trials, in which the stimuli
pairs were the same.
Before the start of the actual experiments, all subjects
were allowed to explore the 2D and 3D square-wave
gratings with the period and amplitude between 0.51 mm
(0.02 inch) and 4.57 mm (0.18 inch) in their own ways
until they noticed the difference between them. Then the
subjects were required to complete a practice run before
starting the actual study.
The required interaction with the texture gratings was
different in the three experiments. In Experiment 1, the
subject was paced by a position indicator on the computer
screen to move his/her hand across the texture gratings.
In each test, when the first texture appeared, the subject
needed to move his/her hand from the left end to the right
end of the box in 1 s and then return to the left end in the
next 1 s. Then the second texture appeared, and the
subject needed to make the same left-right-left paced
movement. After that, the subject judged whether or not
the two textures were identical.
In Experiment 2, the subjects were free to explore the
virtual gratings using any motion pattern they chose.
They were no longer required to follow the pace of the
position indicator. In this experiment, each texture was
displayed for 4 s for each test. The subject was required
to make a judgment after the two textures were displayed.
In Experiment 3, the subject was required to follow
the pace of the position indicator again. However, to
move across the texture gratings this time, the subject was
instructed to use a predetermined strategy described to
him/her by the experiment monitor. This strategy was for
the subject to move his/her hand toward himself/herself
by a small amount in the positive z-direction until the
subject felt the resistance of the first bump of the square-
wave gratings (see Figure 8). Because the subject needed
to move his/her hand a short distance toward
himself/herself in order to clear the first bump, the subject
might be expected to notice the peak-to-peak amplitude
of the square-wave gratings.
4.2. Results and Discussion
Detection theory was used to do the data analysis of
the experimental results [4]. The theory utilizes the
relationship between two types of response, hit and false
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alarm. The term “hit” refers to a correct judgment when a
stimulus or stimulus difference is present; the term “false
alarm” refers to the incorrect judgment that a stimulus or
stimulus difference is present on a “catch trial.”
Probability of Hits (Experiment 1)
0.0
0.2
0.4
0.6
0.8
1.0
0 0.05 0.1 0.15 0.2
Amplitude (in)
Probability
P=0.02in
P=0.06in
P=0.18in
Probability of Hits (Experiment 2)
0.0
0.2
0.4
0.6
0.8
1.0
0 0.05 0.1 0.15 0.2
Amplitude (in)
Probability
P=0.02in
P=0.06in
P=0.18in
Probability of Hits (Experiment 3)
0.0
0.2
0.4
0.6
0.8
1.0
0 0.05 0.1 0.15 0.2
Amplitude (in)
Probability
P=0.02in
P=0.06in
P=0.18in
Figure 9. Hit rates for all three experiments of
tactile perception in discrimination between 2D and
3D square-wave gratings
The experimental results of the hit and false alarm
rates are shown in Figures 9 and 10. The error bars of the
data points were determined from the standard errors of
binomial distribution [11]. From Experiment 1, in which
hand motion was paced by the position indicator, it
appears that subjects were unable to detect the difference
between the 2D and 3D square-wave gratings because the
proportions of hits remained at ~0.4 (below the 0.5 level
expected for equiprobable random guessing), regardless
of the spatial period and amplitude of the square-wave
gratings.
In Experiment 2, most subjects could notice the
difference between the 2D and 3D square-wave gratings
when both spatial period and amplitude of the texture
gratings were big. For example, when the square-wave
gratings were at 0.18-inch period and 0.18-inch peak-to-
peak amplitude, the average proportion of hits was as
high as 0.82 ± 0.11, and the average proportion of false
alarms was as low as 0.16 ± 0.11. From the graph of hit
rate, the proportion of hits tended to increase with
amplitude for a given period. It also tended to increase
with period for a given amplitude. When the amplitude
of the square-wave gratings was small, most subjects
could not feel the difference between the 2D and 3D
square-wave gratings, resulting in the low proportion of
hits. Similarly, when the period of the square-wave
gratings was low, subjects could pass through the texture
gratings easily with very little resistance, resulting in the
low proportion of hits.
Probability of False Alarms (Experiment 1)
0.0
0.2
0.4
0.6
0.8
1.0
0 0.05 0.1 0.15 0.2
Amplitude (in)
Probability
P=0.02in
P=0.06in
P=0.18in
Probability of False Alarms (Experiment 2)
0.0
0.2
0.4
0.6
0.8
1.0
0 0.05 0.1 0.15 0.2
Amplitude (in)
Probability
P=0.02in
P=0.06in
P=0.18in
Probability of False Alarms (Experiment 3)
0.0
0.2
0.4
0.6
0.8
1.0
0 0.05 0.1 0.15 0.2
Amplitude (in)
Probability
P=0.02in
P=0.06in
P=0.18in
Figure 10. False alarm rates for all three
experiments of tactile perception in discrimination
between 2D and 3D square-wave gratings
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Figure 11. Different touching strategies of the
subjects used to distinguish between 2D and 3D
square-wave gratings in Experiment 2
We asked the subjects to describe how they
developed their own methods for exploring the 2D and
3D square-wave gratings in Experiment 2. Three subjects
moved up on the edge of the square-wave gratings in
order to feel the depth (or amplitude) of the texture (see
Figure 11.1). Three subjects moved in a series of U-
shaped paths for two to three bumps (see Figure 11.2).
One subject moved in a U-shaped path back and forth
along the three edges in a single groove of the texture
(see Figure 11.3). Finally, one subject moved in a semi-
circular path across the texture gratings (see Figure 11.4),
and another subject moved back and forth in diagonal
direction across the texture (see Figure 11.5). From their
experimental results, the seven subjects who touched the
texture by the methods in Figures 11.1–11.3 did better
than the subjects who touched the texture using the
methods in Figures 11.4–11.5. In particular, these seven
subjects showed a higher proportion of hits and a lower
proportion of false alarms when they interacted with
textures that had big period and amplitude. On the other
hand, the remaining two subjects did not seem to use an
effective method to find the difference between 2D and
3D square-wave gratings. For example, in the
combination of 0.18-inch period and 0.18-inch amplitude
in Experiment 2, the mean proportion of hits was 0.82
and the mean proportion of false alarms was 0.16.
However, in this combination, two poorer performing
subjects had hit rates of 0.7 and 0.5 and false alarm rates
of 0.3 and 0.2, respectively. Therefore, the strategy used
to explore the texture gratings affected the outcome of the
subjects’ results in Experiment 2.
In Experiment 3, where the subjects were instructed
to move their hand toward themselves slightly in order to
feel the edge of the first bump, 6 out of 9 subjects could
tell the difference between 2D and 3D square-wave
gratings for the cases that both the spatial period and
amplitude of the texture gratings were big. Furthermore,
Figure 9 (Experiment 3) indicates that the proportion of
hits increased with grating amplitude and period.
In summary, from the results of Experiments 2 and 3,
the accuracy of distinguishing between 2D and 3D
square-wave gratings increased with increasing amplitude
and increasing period. Also, the exploration strategy used
to interact with the square-wave gratings affected
subject’s ability to determine whether the texture was 2-
dimensional or 3-dimensional. From the results of
Experiment 1, subjects could not tell the difference
between 2D and 3D square-wave textures when moving
their hand across the gratings at about 127 mm/s (5
inch/s). However, when the subjects had an opportunity
to move up over the edges of the square-wave gratings as
in Experiments 2 and 3, most of them (6 out of 9 subjects
in both experiments) could notice the difference between
2D and 3D square-wave gratings for the textures with the
largest peak-to-peak amplitude (0.18 inch) and period
(0.18 inch). Nevertheless, they still could not notice the
difference between the two textures when either the
spatial period or amplitude was below 0.06 inch.
5. Conclusions
Based on the engineering measurements of vibration
and force and the results of haptic perception
experiments, a person is unlikely to feel the difference
between 2D and 3D square-wave gratings when moving
his/her hand across the texture gratings if either the
spatial period or amplitude is below 0.06 inch for the
texture stiffness of 2 N/mm. From the measurements, the
vibration and force profiles for the interaction with 2D
and 3D square-wave gratings were similar. The only
difference between the two texture gratings was the
elimination of offset force normal to the surface which
occurred when hand interaction was restricted to the
upper portion of 3D square-wave gratings. There was no
observable difference in force profile when the hand
interacted with the 2D square-wave gratings and the
bottom portion of the 3D square-wave gratings.
Nevertheless, from tactile perception experiments, if the
spatial amplitude and period of the square-wave gratings
are big enough, the person may notice the difference
between the two textures when moving his/her hand up
slowly on the edges of the square-wave gratings.
Furthermore, our tactile perception experiments indicated
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that the accuracy of distinguishing between 2D and 3D
square-wave gratings increased with increasing amplitude
and increasing period.
From these results, if a person’s hand is moved
across the texture gratings in a manner similar to our
experimental setup, or if the period or peak-to-peak
amplitude of the square-wave texture is small (<0.06
inch), a 2D square-wave texture is sufficient to model a
true 3D square-wave texture. A person may not be able
to notice the difference between the two textures unless
his/her hand is moved slowly up on the edges of the
texture gratings for a big texture. However, from our
observation, people seldom touched the texture gratings
by moving up on the edges of texture; instead, they
tended to keep leaning against the texture surface while
moving across the gratings. Our results support the
observations from Minsky and Robles-De-La-Torre that
the lateral forces alone can effectively simulate surface
textures and can be used to emulate the experience of
touching true 3D textures [7][10], provided the grating
size remains below a specified certain threshold.
6. Acknowledgment
This research was supported at UC Berkeley by
NASA Ames Research Center Cooperative Agreement
NCC2-1255 with funding from the NASA Intelligent
Systems Human Centered Computing Program and the
NASA Space Human Factors Engineering Program.
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