manual and virtual rotation manual and virtual rotationcontrols the rotation of objects via motor...
TRANSCRIPT
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Manual And Virtual Rotation
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
MANUAL AND VIRTUAL ROTATION
Manual and Virtual Rotation of a Three-Dimensional Object
Roy A. Ruddle
Dylan M. Jones
Cardiff University
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Manual And Virtual Rotation
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Abstract
An orientation-matching task, based on a mental rotation paradigm, was used to investigate
how participants manually rotated a Shepard-Metzler object in the real world and in an
immersive virtual environment (VE). Participants performed manual rotation quicker and
more efficiently than virtual rotation but the general pattern of results was similar for both.
The rate of rotation increased with the starting angle between the stimuli meaning that, in
common with many motor tasks, an amplitude-based relationship such as Fitts’ Law is
applicable. When rotation was inefficient (i.e., not by the shortest path) it was often because
participants incorrectly perceived the orientation of one of the objects, and this happened
more in the VE than in the real world. Thus, VEs allow objects to be manipulated naturally to
a limited extent, indicating the need for timing scale factors to be used for applications such
as method-time-motion studies of manufacturing operations.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Manual and Virtual Rotation of a Three-Dimensional Object
A goal of many virtual environment (VE; virtual reality) applications is to allow users
to interact “naturally” with 3D computer-generated objects. If natural interaction can be
achieved then not only would the interface exploit well-practiced motor skills, but real-world
operations such as manual handling tasks, that involve human operators, could be realistically
simulated in real time. This holds manifold advantages in manufacturing design. For
example, it would allow accurate method-time-motion studies to be performed using VEs to
optimize processes within each cell of a manufacturing facility, the lifting requirements of
different tasks to be assessed using actual human motion, “what if” scenarios to be easily
investigated, and provide a new mechanism for training production operators.
One component of interaction is the free-form (unconstrained) rotation of objects.
This is an everyday task, but one that is poorly understood in the cognitive domain. The
present article reports the findings of three experiments that studied aspects of free-form
manual (real world) and virtual object rotation, and had three primary goals. First, to
understand the effect of axes of rotation and angles of separation on the manner in which
people perform manual rotation. Second, to determine the extent to which people can rotate
objects naturally in a VE and, third, to investigate some of the factors that cause the
differences between manual and virtual rotation. First, however, we consider existing studies
of manual and virtual rotation, and investigations of a related task, mental rotation.
Background
The first study of mental rotation was published approximately 30 years ago (R.
Shepard & J. Metzler, 1971) and the primary finding, the linear relationship between reaction
time and angular displacement for a handedness recognition task, has proved to be very
robust. Although there are circumstances under which mental rotation does not appear to take
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
place (Cohen & Kubovy, 1993), the original finding has been repeated for both 2D and 3D
objects, drawings of objects and the objects themselves, binocular and monocular viewing
conditions, stimuli of different complexities, and “possible” and “impossible” shapes (e.g.,
Bethell-Fox & R. Shepard, 1988; Dror, Ivey, & Rogus, 1997; Kaushall & Parsons, 1981; S.
Shepard & D. Metzler, 1988).
Wohlschläger and Wohlschläger (1998, see also Wexler, Kosslyn, & Berthoz, 1998)
put forward a common-processing hypothesis which suggested there is a single process that
controls the rotation of objects via motor commands and mental changes in the visuospatial
representation of objects. This hypothesis states that mental and manual rotation should be
affected in the same way by the same factors, and this type of relationship is found in some
other types of motor task, for example, both imagined and actual pointing follow Fitts’ law
(Maruff et al., 1999).
In the context of the mental rotation paradigm, the common processing hypothesis
predicts that the time taken to perform manual rotation will increase linearly with the angle
between two objects’ orientations, and will be affected by the orientation of the objects with
respect to three different sets of axes (Parsons, 1995; see Figure 1): the major limb of the
objects (O), the principal axes of the person (viewer; V), and the axis that defines the shortest
angular path of rotation (R; this is unique for any pair of orientations, unless they differ by
180°). Alignment of all three produces an arrangement known as the OVR condition, whereas
the general condition occurs when none are aligned. In between are conditions where either
the rotation and object, or rotation and viewer, axes are aligned. Parsons showed that people
are progressively less accurate at imagining rotational transformations as the alignment is
changed from the OVR to the general condition.
Manual and virtual rotation involve the comparison of the orientations of different
objects and the execution of motor tasks to change those orientations. The purpose of the
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
present study is to compare manual and virtual rotation, and to explain the differences that
occur in terms of the differences that exist between real and virtual environments in the
perception of objects’ orientations and the interface used to perform motor tasks.
A variety of object manipulation interfaces have been developed for use in VEs (for a
review, see Hand, 1997). Studies have shown that efficient (i.e., straight line) translations are
straightforward to perform, although accuracy is more difficult to achieve in depth than in the
viewing plane (Boritz & Booth, 1997). Rotational movements are performed less efficiently
(Zhai & Milgram, 1998) and, therefore, are of particular interest to researchers. However,
general 3D rotations are performed more quickly if all three degrees-of-freedom (DOFs) can
be controlled simultaneously using a single input device, rather than separately (Chen,
Mountford, & Sellen, 1988; Hinckley, Tullio, Pausch, Proffitt, & Kassell, 1997).
The two most common interfaces that allow simultaneous control are props and
virtual hands. A prop is a physical object that contains a six DOF sensor and which a user
holds in their hands. Hence, some haptic feedback is provided. The sensor continually
measures position and orientation of the prop and, typically, movements of the prop produce
corresponding changes in the position and orientation of the virtual object that is being
manipulated. With a virtual hands interface a six DOF sensor is attached to each of the user’s
hands and the user places their hands around the virtual object, as if they were holding it. A
disadvantage of this type of interface is that clutching (the process of swapping hands when
turning an object through a large angle) has to be specified explicitly (e.g., by holding down a
button) instead of being automatic. For this reason, props are most likely to facilitate natural
interaction and have been shown experimentally to allow rotations to be performed 20%
quicker than with virtual hands (Zhai, Milgram, & Buxton, 1996).
Props vary in terms of their haptic correspondence with the object that is being
manipulated. Rotation becomes quicker when the prop has the same size, shape and inertial
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
characteristics as the object (Wang & MacKenzie, 1999a; see also Ware & Rose, 1998), and
slower when orientation disparity is deliberately introduced (Wang & MacKenzie, 1999b).
However, in manufacturing design applications, where the virtual objects do not yet exist in a
physical form, “realistic” props are not a viable option. A common, practical alternative is to
use a sphere-shaped prop, and this also minimises the haptic conflicts that occur when many
different objects are being manipulated in a VE.
Another factor that affects interfaces for object rotation is the number of hands that
are used. Small rotations (e.g., up to 45°) can be performed quickly using one hand (Wang &
MacKenzie, 1999a; 1999b; 2000) but two hands are typically preferred by users (Mapes &
Moshell, 1995) and aid clutching when large rotational movements are being performed.
The orientation of a hand-held object can be perceived both haptically and visually. In
contrast, only visual information can be used to perceive the orientation of a virtual object
that is manipulated using an interface such as sphere-shaped prop. Lighting conditions and
surface shading affect the way objects are perceived (e.g., Mamassian & Kersten, 1996; Tarr,
Kersten, & Bülthoff, 1998) and, although studies of object recognition are often performed
using computer-generated (i.e., virtual) images rather than physical objects, and Johnston and
Curran (1996) found similar effects when they compared real and virtual (Phong-shaded)
stimuli, the former contain more subtle variations in appearance which may aid orientation
perception and the discrimination of the different parts of an object.
To determine fully the extent to which a person can rotate an object naturally in a VE,
measures must be made of the time taken, the path through which the object is moved, and
the movements made by the person. The term “mental rotation” was coined because the
linear relationship found by Shepard and Metzler (1971) was what would have occurred if
participants had performed the task by rotating their mental image of the objects at a constant
angular velocity, along a path that increased linearly in length with the angular separation
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
between the two stimuli. Rotation about the shortest path satisfies this linear relationship, but
other geometrical bases of rotation, for example, spin-precession (simultaneous rotation
about two different axes (e.g., axes in the object’s and viewer’s reference frame)), and
rotation-by-dimensions (a sequence of rotation axes; Parsons, 1987), do not.
To date, however, most studies of mental, manual and virtual rotation have only
measured rotation time, and used the shortest path to infer the rotation rate. Exceptions are
Wohlschläger and Wohlschläger (1998) who analyzed the threshold at which participants
were as likely to turn the object in the opposite direction to the shortest path as follow the
shortest path (the object was turned using a knob), and Zhai & Milgram (1998) who
compared the cumulative angle participants turned a virtual object through with the minimum
possible angle. Human body movements have not been studied in manual or virtual rotation
tasks and, although shape and orientation affect the way objects are grasped (Mamassian,
1997) and biomechanical limitations affect the way in which objects are manipulated, these
factors are outside the scope of the present study.
We used the simultaneous presentation mental rotation paradigm to study how
participants rotated a 3D object in the real world (Experiment 1) and in an immersive VE
(Experiments 2 and 3). All the experiments used three different initial angular separations
between pairs of objects (90º (practice trials), and 45º and 135º (test trials)) and two
combinations of axis alignment (OVR and general; see Figure 1). In all of the trials the
stimuli had the same handedness. The studies were designed to investigate the paths through
which participants rotated manual and virtual objects, as well as how long they took.
Experiment 1
Method
Participants. Six men and six women, aged 19 to 24 years, took part in the
experiment. All the participants were either undergraduates or graduates, who volunteered for
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
the experiment and were paid an honorarium for their participation. A repeated measures,
within-participants design was used (see below).
Materials. Two wooden models of the Shepard-Metzler object used by Parsons (1995)
were constructed. The wood had a 50 x 50 mm cross section, so the longest side of each
object was 250 mm. Each object’s orientation was measured by a Polhemus Fastrak magnetic
sensor that transmitted data via the MR Toolkit (Green, 1995). Six orientation pairs for each
angle/axis were pre-computed using random rotations that satisfied the OVR and general
alignment conditions, as appropriate. For the OVR condition the principal axis of the object
coincided with the axis of the shortest path of rotation, and there were two pairs of
orientations in which these axes were aligned with each of the viewer’s axes (X, Y and Z; see
Figure 1). For the general condition the shortest rotation axis was always in a direction that
bisected the principal axes of the viewer (e.g., {x, y, z} = {0.58, 0.58, 0.58} or {-0.58, 0.58,
0.58}) and in one orientation of each pair the principal axis of the object bisected the
principal axes of the viewer in another direction (e.g., {x, y, z} = {-0.58, 0.58, 0.58} or {-
0.58, 0.58, -0.58}). For both the OVR and the general condition the rotation of the object
about its principal axis was calculated randomly.
Procedure. Participants were run individually and performed the trials in a standing
position because this allowed greater freedom of movement than when sitting down. One
object (the target object) was mounted on a tripod 0.8 m in front of a participant and 0.8 m
below their eye level, and they held the other (mobile) object in their hands. After
familiarizing themselves with the shape of the object, each participant performed 12 practice
trials, had a short rest, and then performed 24 test trials.
At the start of each trial the participant was blindfolded. The experimenter then used
the VE software of Experiment 2 to set the target object at a pre-computed orientation. Next,
the experimenter placed the mobile object in the participant’s hands and used the VE
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
software to set the object at another pre-computed orientation. Then the experimenter pressed
a key to blank the VE display and begin recording orientation data for the mobile object, and
removed the participant’s blindfold. They rotated the mobile object “as fast and as accurately
as possible” until they judged that it matched the orientation of the target, and said “OK”. The
experimenter pressed a key that caused the data recording to be stopped and the angular
difference between the two finishing world-referenced orientations (the error) to be displayed
as a text message on a computer monitor for the participant to see. A world (scene-based)
reference frame was used because that has been shown to be dominant when participants
make orientation-matching judgements (Hinton & Parsons, 1988). The purpose of this
message was to help ensure each participant placed a similar emphasis on finishing accuracy
in the trials. Error feedback proved to be a more practical way of achieving this than
terminating each trial automatically once participants had held the mobile object within a
certain angular tolerance of the target’s orientation for a given amount of time. Every
participant used the same pre-computed orientation pairs but the order of presentation was
random, as was the orientation within each pair that was chosen for the target and mobile
objects.
Results
Preliminary Data Analysis. The orientation of the mobile object was recorded at a rate
of 12.5 Hz. Inspection of these data showed that participants quickly rotated the object until it
was in approximately the correct orientation (the rotation stage) and then sometimes spent a
considerable time trying to get the orientation exactly right (fine tuning). In fact the task was
“impossible” because two identical objects can only have an identical appearance if they
overlap with one another in space. Our interest lay in the large manipulations that were made
so the data for the rotation stage of each trial were extracted using the following two
techniques that identified the beginning and end of the rotation stage, respectively. The
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
techniques were implemented in software but, for clarity, are described as if they were
performed by hand. Both started by plotting a curve that showed how the angle between the
mobile and target objects varied during a trial. For each data point, this angle was the
absolute value of the angular separation between the objects, calculated for rotation about the
shortest angular path between the objects at that moment in time.
The data at the start of each trial contained a period of time when participants were
still blindfolded. The beginning of the rotation stage was identified by fitting a cubic Bezier
spline to the curve and calculating the time at which the gradient of the spline first exceeded
10 degrees/sec. The end of the rotation stage was defined as the time at which the mobile
object first came within 20º of the target and then remained within 20º for the remainder of
the trial.
Clearly, the two parameters that were used (10 deg/sec and 20º amplitude) are
subjective but graphical inspection of the data for every trial indicated that they were
appropriate. A trial was discarded if the spline indicated that the rotation stage started at the
beginning of the trial (an impossibility because the participant was still wearing the
blindfold), the orientation of mobile object at the beginning of the rotation stage differed by
more than 10º from it’s “official” starting orientation, or the mobile object never satisfied the
20º criterion. Overall, 9% of the trials were discarded.
The amplitude criterion meant that it was possible for a participant to complete each
trial by rotating the mobile object through much less than the nominal angle (45º or 135º).
However, inspection of the data showed that the mean angular difference between mobile
object’s orientation at the start and end of the rotation stage of the non-discarded trials was
only 6º less than the nominal angles.
The data reported below are for the rotation stage of the non-discarded trials. All the
data were analyzed using analyses of variance (ANOVAs) that treated the angle (45º or 135º)
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
and axis alignment (OVR or general) as repeated measures. Only significant interactions are
reported. Mean data for these analyses are shown in Table 1, along with the mean time taken
in the fine tuning stage. Overall, the mean time for the initiation stage was 1.7 s.
Rotation time. The distribution of participants’ time data was normalized using a
logarithmic transformation. A repeated measures ANOVA showed that, as expected,
participants took less time to complete the rotation stage in the 45º trials than in the 135º
trials, F(1, 11) = 63.78, MSE = 0.02, p < .01, and they also took less time to complete the
OVR trials than the general trials, F(1, 11) = 28.45, MSE = 0.02, p < .01.
Mean rotation rate. The distribution of these data was normalized using a logarithmic
transformation. A repeated measures ANOVA showed that participants mean rate of rotation
was slower in the 45º trials than in the 135º trials, F(1, 11) = 38.35, MSE = 0.01, p < .01, but
there was no effect of axis combination, F(1, 11) = 3.00, MSE < 0.01, p = .11. This indicates
that the principal reason participants took longer to complete the general trials than the OVR
trials was because they rotated the mobile object further, rather than more slowly.
Rotation efficiency. One of the primary goals of this study was to provide information
about how participants rotated the mobile object, as well as the length of time they took. Two
measures of participants’ rotation efficiency were used: the percentage extra angle of rotation
(PE-angle), and the object’s root mean square (RMS) angular deviation from the shortest
path. The PE-angle metric was suggested by Zhai & Milgram (1998) and a similar technique
has been used to measure wayfinding efficiency in navigation studies (e.g., Ruddle, Payne, &
Jones, 1999). It is calculated as PE-angle = 100 * (Ac - Am) / Am, where Ac is the cumulative
angle of rotation during the rotation stage of a trial and Am is the angle between the starting
and finishing orientations of the mobile object. The RMS deviation metric is calculated as
RMS = √(∑(ai * a
i) / n), where i is in the range 1 to n, n is the number of time steps in the
rotation stage, and ai is the angular separation of the mobile object’s orientation from the
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
shortest path of rotation between the mobile object’s orientation at the start of the rotation
stage and the target’s orientation (calculated using an iterative algorithm). Neither the PE-
angle nor the RMS deviation metric is suitable on its own because a trial with a large PE-
angle might not deviate far from the shortest path, and a trial with a low RMS error could still
contain a lot of back and forth movement.
The distributions of participants’ PE-angle and RMS deviation data were both
normalized using a logarithmic transformation. For the former, a repeated measures ANOVA
showed no effect of angle, F(1, 11) = 2.19, MSE = 0.08, p = .17, but there was an effect of
axis combination, F(1, 11) = 36.47, MSE = 0.09, p < .01. For the RMS deviation, a repeated
measures ANOVA showed main effects of angle, F(1, 11) = 79.43, MSE = 0.02, p < .01, and
axis combination, F(1, 11) = 51.07, MSE = 0.03, p < .01. Taken together, these data show
that the OVR trials were very efficient. Participants rotated the mobile object approximately
25% further than they had to and deviated by only a small amount from the shortest path. By
contrast, the 135º-general condition was particularly inefficient.
To provide an explanation each trial was classified according to whether the mobile
object was initially rotated towards or away from the target, with the latter referred to as
incorrect direction of rotation (IDOR). The amount of rotation required before this
classification was performed only had a small effect on the percentage of trials in each
category and didn’t change the overall pattern of the data. Using a 20º rotation criterion, a
repeated measures ANOVA showed main effects of angle, F(1, 11) = 8.63, MSE = 402.46, p
= .01, and axis combination, F(1, 11) = 6.43, MSE = 335.41, p = .03, and there was also a
significant interaction, F(1, 11) = 8.11, MSE = 407.63, p = .02. IDOR trials occurred more
than three times more frequently in the 135º-general condition than in any other condition
and manual inspection showed that, after the initial incorrect rotation, participants quite often
paused with the short and long stubs of the object swapped over (180º error) before correcting
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
themselves. Referring back to Table 1, the frequency of the IDOR trials and the 180º errors
explain why the RMS deviation was so large in the 135º-general condition.
Discussion
The results of this experiment are interpreted in the context of the common processing
hypothesis (Wohlschläger & Wohlschläger, 1998). The time and rotation rate data show that
participants took longer to complete the trials when the axes were not aligned (the general
condition) and the rate of rotation increased with the angle between the stimuli. The first
finding is in agreement with mental rotation studies. The second finding is in agreement to
studies of simple motor tasks but contrary to mental rotation. Thus manual and mental
rotation may share some common processes but there is also at least one notable difference.
The manner in which participants rotated the mobile object is indicated by the
efficiency data. These show that participants used a near-shortest path when the experimental
design was “friendly” (the OVR condition) but a very inefficient path in the 135º-general
condition. With all three types of rotation strategy that were suggested by Parsons (1987) (the
optimum axis (shortest path), spin-precession (simultaneous rotation about two different axes
(e.g., axes in the object’s and viewer’s reference frame), and rotation-by-dimensions (a
sequence of rotation axes)) the angle between the mobile and target object would have
decreased throughout the trial. The present experiment is not able to test for particular
rotation strategies but the data do indicate that the angle between the objects sometimes
initially increased (the IDOR trials) and often oscillated. This suggests that the primary
causes of rotation inefficiency were errors in participants’ perceptions of the objects
orientations or execution of the rotational responses, rather than following a deliberate, but
non-optimal, path.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Finally, the metrics used to analyze the data from Experiment 1 provided stable
measures of rotation performance. In turn, this establishes a baseline for manual rotation of
one particular object that can be used to compare rotation tasks that are performed in VEs.
Experiment 2
Experiment 2 recreated the first experiment in an immersive VE (a VE shown using a
head-mounted display (HMD)). As well as viewing a virtual, rather than physical, object two
additional differences between the two experiments should be noted. First, the interface used
in Experiment 2 was a spherical prop. A two-handed, prop-type interface was chosen because
it allows more rapid rotation than virtual hands, and the process of clutching becomes
automatic. It would have been possible to use a prop that was the same size and shape as the
Shepard-Metzler object but in most VE applications, as has already been noted, users
manipulate many different objects. Therefore, a spherical shape is a more practical choice
because it has neutral orientation disparity. Second, the virtual objects were scaled by a factor
of 0.3 compared with the physical objects so that the target and mobile objects could be seen
simultaneously in the HMD, but it should be emphasised that participants never saw the
physical objects.
Method
Participants. Six men and six women, aged 19 to 37 years, took part in the
experiment. All the participants were either undergraduates or graduates, who volunteered for
the experiment and were paid an honorarium for their participation. None had participated in
Experiment 1.
Materials. The VE software was designed and programmed by the authors, and ran on
a Silicon Graphics Maximum IMPACT workstation. The HMD was a Virtual Research VR4
(247 x 230 pixel resolution; 48º x 36º field of view) and head-tracking was performed using a
Fastrak sensor. Images were displayed in stereo in the HMD and the inter-pupilary distance
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
was adjusted for each participant. Participants rotated the mobile object by rotating a hockey
ball prop (a 72 mm diameter sphere that contained a Fastrak sensor) and there was 1:1
correspondence between rotations of the object and prop. The design of the application meant
that the maximum lag in the system was the same as the graphics frame rate (80 ms). At the
fastest of the mean rotation rates in Experiment 1 (135-OVR), this corresponds to an angular
lag of 7°.
The virtual objects were displayed one above the other in the HMD at a center-to-
center spacing of 0.11 m, corresponding to a visual angle of 18°. A pilot investigation showed
that this was preferable to displaying them side by side. The mid-point between the upper
(target) and lower (mobile) object was horizontally in front of the participant’s eyes. This
meant the HMD was balanced and minimized neck strain.
Procedure. People are used to manipulating objects in the real world but none of the
participants had previously used a prop interface for a VE, so the experiment was divided into
two phases. In the first phase a participant was trained to rotate virtual objects using the prop.
In Phase 2 the participant performed the orientation-matching task of Experiment 1.
A participant started Phase 1 by rotating a virtual object for a few minutes to
familiarize themselves with using the prop and the HMD. Then they did thirty trials in which
they had to rotate the prop so a mobile virtual object continuously matched the orientation of
a spinning target. The trials were split into five blocks, and within each there were three
different shapes of object (an aircraft, a cow and a canon), three rates of spin (30, 60 and 90
degrees/sec) and spinning axes that were either constant or changed continuously. The axes
always lay in the participant’s XY, XZ, or YZ plane (the orientation of participants’
(viewer’s) axes are shown in Figure 1), which meant they were different to the shortest path
axes used in the orientation-matching task. In each trial the target object was stationary for 3
s and then spun for 30 s. As a whole, this phase trained the participant to use the prop,
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
without familiarizing them with the Shepard-Metzler object used in Phase 2, or specifically
training them to perform rotations using either a constant axis or a constantly-varying axis.
The virtual objects used for the orientation-matching task (Phase 2) were the same
shape as the physical objects used in Experiment 1, but were scaled by a factor of 0.3 (see
above). The objects were texture mapped with the pattern of wood. The task used the same
practice (90º) and test (45º and 135º) orientation pairs as Experiment 1 and, as before, they
were presented in a random order. At the start of each trial a sphere was displayed in the
position where the objects would appear. When the participant was looking at the sphere the
experimenter pressed a key, which caused the sphere to be replaced by the two objects in one
set of the pre-computed orientation pairs. The participant rotated the mobile object “as fast
and as accurately as possible” until they judged that it matched the orientation of the target,
and said “OK”. Then the experimenter pressed a key that terminated the trial and caused the
angular error message to be displayed in the HMD.
As precautionary measure, symptoms of VE sickness were monitored for 1 hr at the
end of the experiment, using the Short Symptom Checklist developed by Cobb, Nichols,
Ramsey, and Wilson (1999). These data are not reported here.
Results
For consistency, the rotation stage was extracted from the data for each trial using the
same two techniques that were used in Experiment 1. The rotation stage data were then
analyzed using the same type of data transformation (logarithmic) and repeated measures
ANOVAs as were used in Experiment 1. Mean data for all of these analyses except the
interface training are shown in Table 2, along with the mean time taken in the fine tuning
stage.
Interface training. Participants’ mean orientation error during the interface training
was analyzed using an ANOVA that treated the trial block and rotation rate as repeated
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
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measures. This ANOVA showed main effects of trial block, F(4, 11) = 8.78, MSE = 329.22,
p < .01, and rotation rate, F(2, 11) = 63.55, MSE = 290.14, p < .01 (see Figure 2). The
magnitude of the mean errors is an indication of the difficulty of the task, particularly with
rotation at 90 degrees/sec. The important things to note are the improvement that took place
in participants’ performance, and the plateauing-out of the errors in the final two blocks.
Rotation time and rate. A repeated measures ANOVA showed that participants took
less time to complete the rotation stage in the 45º trials than in the 135º trials, F(1, 11) =
59.55, MSE = 0.03, p < .01, and there was a reduced effect of axis combination, F(1, 11) =
4.27, MSE = 0.03, p = .06. Analysis of the mean rotation rate data showed that participants
rotated the object slower in the 45º trials than in the 135º trials, F(1, 11) = 130.17, MSE <
0.01, p < .01, but there was no effect of axis combination, F(1, 11) = 1.18, MSE < 0.01, p =
.30.
Rotation efficiency. As in Experiment 1, the efficiency of each trial was analyzed
using the PE-angle, RMS deviation, and IDOR data. For the PE-angle data, a repeated
measures ANOVA showed reduced effects of angle, F(1, 11) = 4.20, MSE = 0.05, p = .07,
and axis combination, F(1, 11) = 3.52, MSE = 0.09, p = .09. A repeated measures ANOVA of
the RMS deviation data showed main effects of angle, F(1, 11) = 50.92, MSE = 0.03, p < .01,
and axis combination, F(1, 11) = 14.93, MSE = 0.02, p < .01, and a significant interaction,
F(1, 11) = 11.35, MSE = 0.01, p < .01. For the IDOR data, a repeated measures ANOVA
showed a main effect of angle, F(1, 11) = 13.65, MSE = 349.30, p < .01, but not of axis
combination, F(1, 11) = 0.17, MSE = 407.00, p = .68. However, there was a significant
interaction, F(1, 11) = 9.18, MSE = 249.55, p = .01.
Comparison with Experiment 1. The general pattern of results was similar in the two
experiments, but that for some of the data there was also a considerable difference in
performance. To investigate real-world vs. VE differences the data were reanalyzed using
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
ANOVAs that treated the angle and axis combination as repeated measures (as before) and
the experiment as a between-participants factor.
Participants completed the rotation stage significantly faster in the real world than in
the VE, F(1, 22) = 18.91, MSE = 0.07, p < .01, and the rotation rates were slightly greater in
the real world, F(1, 22) = 3.02, MSE = 0.04, p = .10. Participants’ PE-angle was significantly
lower in the real world than in the VE, F(1, 22) = 9.14, MSE = 0.35, p < .01, and there was a
significant interaction between experiment and axis combination, F(1, 22) = 9.23, MSE =
0.09, p < .01. There were similar effects for the RMS data. Participants’ RMS deviation was
significantly lower in the real world experiment than in the VE experiment, F(1, 22) = 13.00,
MSE = 0.07, p < .01, and there was a significant interaction between experiment and axis
combination, F(1, 22) = 7.75, MSE = 0.03, p < .01. There was no difference between the two
experiments for the IDOR data, F(1, 22) = 1.35, MSE = 790.21, p = .26.
Discussion
Although the general pattern of results in the two experiments was similar,
participants’ rotations took 80% more time in the VE experiment than in the real world
experiment. The difference was because virtual rotation was less efficient than manual
rotation (participants rotated the object through a greater angle in the former), rather than a
significant change in the rate of rotation, and the change in efficiency was particularly
notable in the OVR condition. All the participants performed clutching while rotating the
prop.
Factors that are likely to have contributed to the reduced efficiency of virtual rotation
can be divided into those that affected participants’ ability to: (a) perceive the objects’
orientation, or (b) efficiently perform the motor task of rotation. Within the perception
category there are four factors. First, the objects’ position (horizontally in front of
participants’ eyes) may have made it more difficult for participants to discriminate between
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
the short and long stubs of the objects and, therefore, to determine the objects’ orientations.
However, an earlier VE study found similar rotation performance when objects were
positioned in front of participants’ eyes or at waist level (Ruddle, Huddart, & Jones, 1999).
Second, in the real world experiment participants were instructed to hold the mobile object
with one hand on each stub. This meant that participants could identify the two stubs and,
hence, obtain information about the object’s orientation both visually and haptically. In the
VE experiment, participants were only provided with the visual information. Third, informal
observation suggests that participants used different strategies to match the orientations in the
two experiments. In the VE experiment participants often matched the appearances of
particular surfaces on the objects, using the VE’s lighting conditions, whereas in the real
world experiment participants matched the overall orientation of the objects’ three parts.
Similarities can be drawn between this and mental rotation, where the effects of stimulus
complexity disappeared with continued practice, suggesting that participants rotated an object
piece by piece when it was unfamiliar but as a whole once it was well learned (Bethell-Fox &
Shepard, 1988). However, it should be emphasized that participants peformed equal amounts
of practice in Experiments 1 and 2 of the present study. Fourth, in Experiment 2 participants
may have deliberately rotated the mobile object to help determine its orientation. In other
words, participants may have made pragmatic actions (Kirsh & Maglio, 1994) to help
overcome their difficulty in perceiving the mobile object’s orientation.
In the motor task category it was noticeable that there were occasions during the
spinning object training when participants had difficulty rotating the mobile object in the
direction they intended. Although participants improved significantly during the training
there are likely to be some inherent difficulties rotating virtual objects. One is the conflict
between the shape and inertia of the prop and the virtual object. Although this could be
overcome a key objective of many VE applications, particularly those concerned with
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
manufacturing design, is to allow people to interact with virtual objects that do not exist
physically. A second is that in the real world experiment participants were instructed to hold
the object with one hand on each stub, so the axis that defined the shortest path of rotation in
the OVR trials was also the axis that connected participants’ hands. In the VE experiment
participants tended to rotate the prop by moving their fingers.
The first two experiments demonstrated that people can perform virtual rotation in a
similar manner to manual rotation, but questions remain as to the cause of the performance
decrease that was observed. In Experiment 3 participants performed the orientation-matching
task under three conditions that differed either in the difficulty with which the objects’
orientations could be perceived, or the amount of time for which the objects were visible
prior to rotation commencing.
Experiment 3
The three perception conditions used were: (a) immediate response using the wood-
textured object, (b) immediate response using the three-colored object, and (c) delayed
response using the wood-textured object. These are referred to as the textured, colored and
observe conditions, respectively. The textured condition was the same as in Experiment 2. In
the colored condition the short and long stubs of the objects were different colors, allowing
the relative orientation of the mobile and target objects to be easily discriminated, and
meaning that orientation matching was predicted to take place more quickly than in the
textured condition. In the observe condition, participants had 10 s in which to perceive the
objects’ orientation and plan their rotation response. This was also predicted to lead to
quicker orientation matching than in the textured condition, but no prediction was made
between the colored and observe conditions.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Method
Participants. Three men and nine women, aged 19 to 26 years, took part in the
experiment. All the participants were either undergraduates or graduates, who volunteered for
the experiment and were paid an honorarium for their participation. None had participated in
the other experiments.
Materials. The experiment used the same hardware, software, and prop interface as
Experiment 2. A second version of the Shepard-Metzler object was created. This was the
same size and shape as the wood-textured version used in Experiment 2 but, instead of being
textured, the three limbs of the object were each a different color (magenta, cyan or yellow).
Procedure. The experiment was divided into two phases. Phase 1 was identical to
Experiment 2. A participant was trained to use the prop interface, using the spinning object
trials. In Phase 2 the participant performed the orientation-matching task under the three
perception conditions.
The textured condition was similar to Experiment 2 but participants were instructed to
respond immediately the objects became visible. The colored condition was identical to the
textured condition except that the three-colored version was used for the target and mobile
objects. In the observe condition participants looked at the objects for 10 s and then
performed the rotation. During the observation period the prop was de-coupled from the
mobile object so participants could not change its orientation. The end of the 10 s observation
period was indicated by a short tone.
The order in which participants performed the three conditions was balanced using a
Latin square design. For each condition they performed practice trials (90º angular
difference) and then test trials (45º and 135º angular differences). Each set of trials used a
different set of pre-computed orientation pairs. Within each condition the pairs were
presented in a random order, and within each pair the two orientations were allocated at
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
random to the target and mobile objects. The participant performed 12 practice trials for their
first condition (as in Experiments 1 and 2) and 6 practice trials for the other conditions. As in
Experiment 2, symptoms of VE sickness were monitored for 1 hr at the end of the
experiment, but these data are not reported here.
Results
In the textured and colored conditions participants were instructed to respond
immediately the objects became visible. This meant that there was a greater emphasis on
speed of response than in Experiments 1 and 2. Data recording started at the same time as the
objects became visible and that time was taken as the beginning of the rotation stage. The end
of the rotation stage was defined using the same technique that was used in Experiments 1
and 2. Overall, the mean lengths of the fine-tuning stages were 3.9 s (textured), 3.6 s
(colored) and 1.0 s (observe). The rotation stage data were analyzed using the same type of
data transformation (logarithmic) as were used in the other experiments, and ANOVAs that
treated the perception condition (textured vs. colored vs. observe), angle (45º vs. 135º) and
axis combination (OVR vs. general) as repeated measures.
Rotation time and rate. For the time data, a repeated measures ANOVA showed main
effects of perception condition, F(2, 11) = 30.53, MSE = 0.01, p < .01, angle, F(1, 11) =
130.50, MSE = 0.01, p < .01, and axis combination, F(1, 11) = 38.63, MSE = 0.01, p < .01,
and there was also a significant three-way interaction, F(2, 22) = 3.62, MSE = 0.01, p = .04
(see Figure 3). Trial completion time became faster as perception of the orientations became
easier, and within each perception condition the pattern of the results were similar to the other
experiments. For the rate data, repeated measures ANOVA showed main effects of
perception condition, F(2, 11) = 5.79, MSE = 0.02, p < .01, and angle, F(1, 11) = 562.34,
MSE < 0.01, p < .01, but not of axis combination, F(1, 11) = 2.72, MSE < 0.01, p .13. Means
for the perception conditions were 83 deg/sec (textured), 85 deg/sec (colored) and 71 deg/sec
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
(observe), and were 59 deg/sec and 100 deg/sec for the 45º and 135º angles, respectively. The
lack of an effect of axis combination is in line with the findings of the other experiments but
there were significant interactions between axis combination and angle, F(1, 11) = 8.54, MSE
< 0.01, p = .01, and angle and perception condition, F(2, 22) = 5.48, MSE = 0.01, p = .01.
Rotation efficiency. The efficiency of each trial was analyzed using the PE-angle,
RMS deviation, and IDOR data. For the PE-angle data, a repeated measures ANOVA showed
main effects of perception condition, F(2, 11) = 48.10, MSE = 0.10, p < .01, and axis
combination, F(1, 11) = 45.23, MSE = 0.03, p < .01, but not of angle, F(1, 11) = 0.02, MSE =
0.03, p = .88. However, there were significant interactions between axis combination and
angle, F(1, 11) = 5.57, MSE = 0.06, p = .04, and perception condition and angle, F(1, 11) =
3.38, MSE = 0.05, p = .05, and a significant three-way interaction, F(2, 22) = 5.52, MSE =
0.03, p = .01 (see Figure 4). A repeated measures ANOVA of the RMS deviation data
showed main effects of perception condition, F(2, 11) = 21.81, MSE = 0.04, p < .01, angle,
F(1, 11) = 192.79, MSE = 0.02, p < .01, and axis combination, F(1, 11) = 80.26, MSE = 0.01,
p < .01, and there was a significant interaction between axis combination and angle, F(1, 11)
= 5.57, MSE = 0.02, p = .04 (see Figure 5). A repeated measures ANOVA of the IDOR data
showed main effects of perception condition, F(2, 11) = 35.53, MSE = 367.80, p < .01, angle,
F(1, 11) = 20.29, MSE = 269.04, p < .01, and axis combination, F(1, 11) = 9.79, MSE =
391.79, p < .01. There was a significant interaction between axis combination and angle, F(1,
11) = 29.19, MSE = 106.80, p < .01, and a significant three-way interaction, F(2, 22) = 5.04,
MSE = 176.30, p = .02 (see Figure 6).
Discussion
As expected, in all five types of data reported above there was a main effect of
perception condition. The increase in ease with which the orientations of the objects could be
determined in the colored condition, compared with the textured condition, produced a
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
modest (14%) reduction in rotation time and a corresponding increase in rotation efficiency.
However, there was no overall change in the percentage of IDOR trials between these two
conditions, indicating that using color to identify the short and long stubs of the object had no
initial effect on the ease with which participants could determine the shortest path of rotation.
There was a large difference in performance between the observe condition and the
two instantaneous response conditions. During the 10 s of observation participants were able
to determine the relative orientation of the target and mobile objects so that their initial motor
response was almost always in the correct direction. In turn, this brought about a decrease in
rotation time and a corresponding change in efficiency of participants’ rotations. Despite this,
a sizeable amount of inefficiency remained, probably caused by difficulties in executing the
motor task of virtual rotation. Although rotation time was least in the observe condition, the
rate of rotation was slower than in the other two conditions. However, this was probably
caused by the emphasis on speed of response in those latter conditions.
General Discussion
The aim of the present study was to provide information about the manner in which
people manually rotate objects in the real world, and the extent to which they can perform
that rotation “naturally” in an immersive VE. While it is acknowledged that objects have
many properties (e.g., size, weight, and shape) and tasks have many constraints (e.g.,
precision, or maintaining something “this way up”) that affect rotation, the scope of this study
was restricted to a small abstract shape that was manipulated freely and spontaneously.
The general pattern of the data was similar in all three experiments and three main
findings should be highlighted. First, in common with simple (e.g., one-dimensional) motor
tasks but in contrast to mental rotation, the mean rate at which rotations were performed
increased with the angle between the stimuli. Second, under friendly experimental conditions
(the OVR axis combination) participants performed rotation by using a near-shortest path.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Third, when there were inefficiencies in participants’ rotations they were caused by errors in
the perception of the objects’ orientations or the motor response for rotation, rather than a
deliberate but non-optimal path. Thus, some support was found for the common processing
hypothesis (Wohlschläger & Wohlschläger, 1998) but there are also clear differences
between manual and mental rotation.
When performed under similar conditions (Experiments 1 and 2) virtual rotation was
almost twice as inefficient as manual rotation (see the PE-angle data, above). Under easier
experimental conditions (the observe condition of Experiment 3), the time required to
perform virtual rotation, and the efficiency with which it was performed, became similar to
that rotating an object manually and responding instantaneously. This shows that a large
amount of the difference between manual and virtual rotation that was observed in the first
two experiments was caused by the difficulty participants had perceiving the orientation of
the objects in the VE, and the difference was present despite the fact that the images were
displayed in stereo and standard rendering techniques (directional lighting and Phong
shading) were used. Of course, if manual rotation were studied using the observe condition
then further improvement would be likely. Therefore, some residual inefficiency remains in
the motor task of virtual rotation but this is to be expected given the differences in the shape
and inertia of the virtual objects and the prop.
The three-colored object was used to explicitly identify the short and long stubs of the
objects and, therefore, remove one source of error that occurred in the first two experiments.
It was particularly effective in increasing the efficiency of trials performed using the most
difficult combination of angle and axis (135-general), but only to the level of performance
that occurred in manual rotation. Substantial questions remain about the cause of the
perceptual problems that participants encountered during virtual rotation and further research
is required to determine the extent to which they were caused by the optical quality of the
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
HMD (substantially less than that of a computer monitor) or the limitations of computer
graphics algorithms in general (ray tracing is not possible in real-time and radiosity cannot be
applied to scenes in which objects or the viewer moves).
From an applied perspective, this study shows that a spherical prop interface only
allows virtual objects to be manipulated in a natural manner to a limited extent, even though
all three rotational degrees of freedom can be varied simultaneously. For example, virtual
object manipulation times would have to be reduced by a scale factor to provide reliable data
for method-time-motion studies of manufacturing operations, although the scale factor would
become closer to one as the operations became more repetitive and the positions and
orientations of objects became easier to predict.
Finally, three additional points need to be made. First, the prop-type interface used in
the present study is just one of many different types of interface that are used in VEs. Further
investigations are required using alternative interfaces and rotation tasks that have other types
of constraint. Second, the fine-tuning stage of the trials took substantially longer than the
rotation stage. This means that the unexpectedly long rotation times recorded in some VE
studies (e.g., Hinckley et al., 1997; Ware & Rose, 1998) were probably caused by the trial
completion criterion that were used or an increased emphasis on accuracy, rather than any
inherent difficulty in performing virtual object rotation. Third, the results help set out a
manifesto for follow-up research in this understudied area. The data processing techniques
and metrics used in the present study are well-suited for quantifying the efficiency of free-
form object rotations performed in real and virtual environments, and other versions of the
mental rotation paradigm such as successive presentation (Cohen & Kubovy, 1993) could be
used to investigate the fine tuning stage of rotation, and to distinguish between observation
time that can be used to perceive objects’ orientation or plan rotational paths.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Acknowledgements
This work was supported by grant GR/L95496 from the Engineering and Physical Sciences
Research Council. We gratefully acknowledge Raymond Nickerson and the anonymous
reviewers for their helpful suggestions.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Table 1
Mean Rotation Time and Efficiency Data for the Angles and Axis Alignments in Experiment
1.
45º 135º
OVR General OVR General
Fine tuning time (s)
10.4 10.5 9.4 9.4 Rotation stage time (s)
1.0 1.5 1.9 3.8 Rotation rate (deg/s)
56.3 54.9 91.1 81.6
Percentage extra angle (PE-angle)
25.1 56.4 21.8 112.8 RMS deviation from shortest path (deg)
9.6 13.6 14.1 38.1 % IDOR trials
12.9 9.7 13.3 43.3
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Table 2
Mean Rotation Time and Efficiency Data for the Angles and Axis Alignments in Experiment
2.
45º 135º
OVR General OVR General
Fine tuning time (s) 8.3 8.3 9.7 7.0
Rotation stage time (s) 1.9 2.2 4.0 5.6
Rotation rate (deg/s) 51.3 46.6 70.2 70.6
Percentage extra angle (PE-angle) 79.4 92.0 87.1 157.0
RMS deviation from shortest path (deg) 15.0 17.4 25.4 47.5
% IDOR trials 22.2 10.8 28.3 44.6
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Figure Captions
Figure 1.
Examples of the axis combinations used in the experiments. The right hand images show the
stimuli as they appeared in the HMD in Experiments 2 and 3, with the target object on top
and the mobile object below. The left hand images show the orientation of the target object
and the axis of the shortest path of rotation (R) between the objects, relative to the principal
axes of the viewer (Vx, Vy and Vz are rightwards, forwards and upwards, respectively). O is
the axis of the major limb of the object. From the top the images are for: rotation about the X
axis (OVR condition), Y axis (OVR condition), Z axis (OVR condition), and the general
condition. In the general condition the vector R is {0.58, 0.58, 0.58} and O is {-0.58, 0.58,
0.58}.
Figure 2.
Mean orientation error during spinning object interface training in Experiment 2 (and
standard error of the mean).
Figure 3.
Mean rotation time in Experiment 3 (and standard error of the mean).
Figure 4.
Percentage extra angle (PE-angle) the mobile object was rotated through in Experiment 3
(and standard error of the mean).
Figure 5.
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Manual And Virtual Rotation
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Mean root mean square (RMS) deviation of mobile object from the shortest path in
Experiment 3 (and standard error of the mean).
Figure 6.
Mean percentage of trials in Experiment 3 where initial rotation was away from the target
(IDOR) (and standard error of the mean).
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Manual And Virtual Rotation
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
VxOR
Vy
Vz
Vx
VyOR
Vz
Vx
Vy
VzOR
Vx
O
R
Vy
Vz
OVR-X 135°
General 135°
OVR-Z 45°
OVR-Y 45°
VxOR
Vy
Vz
VxOR
Vy
Vz
Vx
VyOR
Vz
Vx
VyOR
Vz
Vx
Vy
VzOR
Vx
Vy
VzOR
Vx
O
R
Vy
Vz
Vx
O
R
Vy
Vz
OVR-X 135°
General 135°
OVR-Z 45°
OVR-Y 45°
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Trial block
1 2 3 4 5
Mean o
rie
nta
tion e
rror
(de
g)
0
25
50
75
100
125
90 deg/sec
60 deg/sec
30 deg/sec
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Textured Colored Observe
Tim
e (
s)
0
1
2
3
4
5
6
7
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Textured Colored Observe
% e
xtr
a a
ngle
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Textured Colored ObserveRM
S a
ngula
r de
via
tion
(d
egre
es)
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10
20
30
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Ruddle, R. A., & Jones, D. M. (2001). Manual and virtual rotation of a three-dimensional object. Journal of
Experimental Psychology: Applied, 7, 286-296.
Textured Colored Observe
% I
DO
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rials
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