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CHAPTER 6

Experiment 3: An Investigation of the Effect of Tether Length on Overall Navigational Performance

The effect of tether dynamics on local guidance performance has been investigated in

Experiment 2. It is the purpose of the current experiment to complement the earlier

experiments, according to the dynamic tether space framework shown in Figure 3.9, by

investigating the effect of tether length on navigational performance.

6.1 OBJECTIVES AND HYPOTHESES

The length of a tether determines the distance between the display viewpoint and the

avatar under the control of a user. It affects a tethered viewpoint display in several ways.

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Firstly, the length of a tether affects the relative egocentricity of a display. As discussed

before, an egocentric frame of reference is characterised by a self-centred local frame of

reference, which is often achieved by placing the display viewpoint at the avatar’s

nominal viewing position. In a tethered viewpoint display, when the length of a tether is

reduced to zero, the information presented on the display is essentially egocentric.

Secondly, the tether length affects the spatial resolution of a display. This is because a

longer tether means a greater distance between the viewpoint and the avatar. Therefore,

in terms of computer graphics, a smaller number of pixels is used to render the avatar and

its immediate surrounding environment. Thirdly, the length of a tether also affects the

amount of preview information that is available to the user. Given the same field of view,

a longer tether allows the viewpoint to cover more surrounding environment than a short

tether. It is suggested that providing more environmental information will facilitate users’

guidance performance, since it allows the user to detect changes in direction earlier.

In an experiment Wickens and Prevett conducted in 1995, a medium length (rigidly)

tethered viewpoint display was reported to support superior local tracking performance

compared with a long and a short length tethered display. However, the global awareness

measurements did not yield any significant results for the tested display conditions.

It was the goal of the current experiment to address this question systematically by

quantitatively investigating the effect of tether length on navigational performance. Two

hypotheses were formulated:

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1. Global awareness performance will improve with increase of tether length; however,

the margin of performance improvement will be reduced after the length reaches a

certain threshold.

If a maximum tether length is defined as the one which will allow the viewpoint to cover

the whole virtual world, it is obvious that any attempt to increase its length beyond this

maximum will not help to improve global awareness performance. In this study, we

believe that an optimal tether length can be found before it reaches the maximum tether

length and this optimal tether length is associated with the amount of information needed

to perform both local and global navigational tasks.

2. Due to the trade-off between preview information and display spatial resolution, both

very short and very long tethered displays will affect local guidance performance

detrimentally, with the result that optimal local guidance will occur with "medium"

length tethered displays.

In other words, it is believed that local guidance performance can be enhanced by either

providing more preview information or increasing the display spatial resolution. Both of

these factors are affected by the viewing distance, which in turn is determined by the

length of a tether. Elongating a tether will increase the amount of preview information

available to the user, however, will reduce the display spatial resolution at the same time.

On the other hand, reducing the length of a tether will increase the display’s spatial

resolution while limiting the amount of preview information. The result is a trade-off

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between the advantages and disadvantages of short and long tethers. Hypothesis 2 reflects

this tradeoff, therefore, by postulating that maximal local guidance performance will

occur for "medium length" tethered displays.

6.2 SPATIAL ABILITIES AND THEIR MEASUREMENT

One of the main goals of Experiment 3 was to investigate how users’ global awareness

performance would be affected by the viewpoint distance vector, i.e. the length of a

dynamic tether. Theoretically, however, as discussed here in Section 2.3, it is reasonable

to believe that global awareness performance may depend to a great extent also on

individual abilities with respect to factors such as spatial mapping and spatial memory

capabilities. Therefore, in an attempt to account for potential variability in global

awareness performance introduced by these underlying individual differences in spatial

abilities, if such differences do indeed exist, two evaluations were conducted at the start

of the experiment trials.

Spatial ability refers in reality to a set of abilities, including flexibility of closure, speed

of closure, visual memory, perceptual speed, spatial orientation, and visualization ability.

Many studies have shown that large individual differences exist. (Thorndyke and Stasz,

1980; Thorndyke and Goldin, 1983). In order to correctly interpret the present

experimental results, two spatial ability tests were administered to participants before the

start of the test trials. From among the available spatial ability test packages, the spatial

orientation and spatial visualization tests from the Guilford-Zimmerman Aptitude Survey

(GZAS) battery were selected. The Guilford-Zimmerman Aptitude Survey (distributed by

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the Sheridan Supply Company, Beverly Hills, California) is a result of early research

done by Guilford with aircraft personnel during World War II (Guilford and Zimmerman,

1948). The battery consists of a total of seven tests. Among them, the spatial orientation

test is designed to measure the subject’s awareness of spatial relations, with an emphasis

on the direction of movement. The spatial visualization test is designed to measure one’s

ability to mentally rotate an object in 3D space. These two tests were selected due to their

obvious relevance to the global awareness test used in the present experiment.

The spatial orientation package comprises 60 questions, a sample of which is shown in

Figure 6.1a. Each question presents two pictures to the participant. The first picture

displays the initial positional relation between a boat and its surrounding environment

(e.g. the bank, other boats, etc.). The second picture shows a subsequent positional

relation between the boat and the environment, after the boat has experienced some

change of its position and/or orientation. The participant’s task is to identify the particular

change of the boat’s position and/or orientation relative to the environment by picking

one answer from the five available choices. In the example shown in Figure 6.1a, for

instance, the correct answer is D.

The spatial visualization package comprises 40 questions, a sample of which is shown in

Figure 6.1b. Each question starts by showing an initial orientation of a clock. Following a

rotational instruction presented by arrows of different lengths on a spherical surface,

participants are asked to figure out the final orientation of the clock and pick an answer

from five possible choices. The direction of the arrow on the sphere indicates the change

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of clock orientation, while the length of the arrow indicates the amount of angular change.

There are three possible arrow lengths in the tests: 45, 90 and 180 degrees. The number

of orientation changes (arrows) in each question varies from one to three. In the example

shown in Figure 6.1b, for instance the correct answer is B.

6.3 METHOD 6.3.1 Participants

The participants were 12 undergraduate and graduate students from the University of

Toronto (8 women, 4 men). None of them had participated in the previous experiments in

this study, and thus had no experience with either the experimental platform or the

procedure. Eight participants ranged in age from 20 to 29, three participants from 30 to

Figure 6.1 Sample questions from Guilford-Zimmerman Aptitude Survey. Top: spatial orientation test (top); Bottom: spatial visualization test. See text for explanation.

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39, and one participant was younger than 20. All participants had normal or corrected-to-

normal vision, and satisfied a standard Randot test of stereoscopic acuity. All

participants were predominantly right-handed. Two participants had some limited

experience (i.e. less than 5 hours) with using a Spaceball. Four participants had some

limited experience (i.e. less than 5 hours) in playing aircraft simulation games. None of

the participants had previous experience in flying an aircraft. Participants were paid

$10/h, with a $10 bonus for completing the full experiment.

6.3.2 Apparatus

The hardware setup of this experiment was identical to that used in Experiments 1 and 2.

In order to maintain consistency in reporting the current experiment, key apparatus

features are repeated here.

A Silicon Graphics O2 workstation (1.195 MHz CPU, 224 Mb memory), with a 20-inch

(51-cm) colour monitor with 10241280× pixels of screen resolution, was used to run the

experiment. The monitor was placed approximately 50 cm away from the participants’

eye position. A pair of IMAX stereoscopic shutter goggles was used to provide a

stereoscopic view to the participants. Room lighting was adjusted to reduce the glare on

the monitor. A Spaceball was used as the input device, with only three rotational degrees

of freedom: pitch, roll, and yaw, employed.

The Dynamic Tether Simulator (DTS) was again used as the testing software platform.

Similar to the environmental models used in Experiment 1, the virtual environment

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defined in Experiment 3 consisted of a cubic space with a virtual tunnel transversing it.

The size of the cubic space was 101010 ×× graphical units. The inside of the virtual

tunnel was depicted using wire frames with a distinctive upright direction defined by a

coloured floor and open ceiling. The centre line of the tunnel was depicted by a red line.

Eight tunnel configurations were used in the experiment. These tunnels were different

from those used in Experiment 1. Each tunnel had a unique shape and orientation. The

start and end points of the tunnels were coincident with one of the eight vertices of the

cubic space.

A miniature model of each virtual tunnel was built using wood frames and pipe cleaners

for the subsequent global awareness test. Figure 6.2 is a photo of the eight physical tunnel

models. These models were randomly labelled in the testing.

Figure 6.2 Miniature of eight physical tunnel models used for global awareness measure in Experiment 3.

#2 #1 #3 #4

#5 #6 #7 #8

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6.3.3 Displays

Six critically damped dynamically tethered displays with different tether lengths, ranging

from 0.5 to 12 graphical units, were compared in Experiment 3. Figure 6.3a and 6.3b

show the screen views from the two extreme length tethered displays. Obviously,

considering the fact that the size of the virtual environment was 101010 ×× , the longest

tether depicted in Figure 6.3b, with a length of 12, could be regarded as a ‘very long’

tether. The other four displays had varying tether lengths between the two extreme

conditions, with the specific parametric values listed in Table 6.1. All six tethers were

critically damped, with the values for tether spring constant (K) and damping coefficient

(C) based on the optimal configuration identified in Experiment 2.

Table 6.1 Parameters configurations of six tethers compared in Experiment 3.

Display Code

Spring constant (k)

Damping coefficient (c)

Tether length Damping ratio (ξ)

Dynamic Response

D1 900 60 0.5 1 Critically-damped D2 900 60 1 1 Critically-damped D3 900 60 2 1 Critically-damped D4 900 60 4 1 Critically-damped D5 900 60 8 1 Critically-damped D6 900 60 12 1 Critically-damped

(a) (b) Figure 6.3 Screen views from the shortest tethered display (a) and the longest tethered display (b) used in Experiment 3.

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6.3.4 Tasks

The participants’ primary task was identical to the active flying task tested in Experiment

1 and 2. They were required to control an avatar, represented by an airplane, flying along

the centre of a virtual tunnel, while mentally keeping track of the shape of the tunnel at

the same time. Before the start of each trial, the airplane was situated at the start point of

one of the virtual tunnels. Following the on-screen instructions, a participant would start

a trial by pressing the space bar on the keyboard. Once a trial was initiated, the airplane

began to fly forward at a constant velocity. The initial part of the tunnel was straight for

all tunnel configurations. The change of orientation of the tunnel was introduced into the

simulation at around 5 seconds after the trial had started. The participant was then

required to maintain the flying trajectory inside the tunnel. In order to define unique

optimal flying performance, participants were instructed to fly the airplane along the

centre line of the tunnel and keep the two wings of the airplane parallel to the tunnel floor.

A trial was completed when the end of the tunnel had been reached. Each trial lasted

approximately 1.5 minutes.

After a trial was finished, participants were presented with a set of eight miniature tunnel

models. (see Figure 6.2) One among those eight tunnel models had the same shape and

orientation as the virtual tunnel used in the just completed trial. Participants were

required to recall the shape of the tunnel they had just flown through and pick it out from

the physical models. Participants had to rely solely on their memory for this judgement;

no further referring to the screen view was allowed.

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6.3.5 Experimental Design

The experiment was a 6×8 two-factor within-subjects design, comprising 6 tether lengths

and 8 tunnels, with each treatment presented twice to each subject. Display conditions

were counterbalanced across participants. All eight tunnel configurations were presented

for each tether length display condition and were randomly distributed throughout the

experiment.

6.3.6 Procedure

Participants were tested individually over a three-day period and completed six 1-hour

sessions.

Upon arrival at the first session, participants read and signed the informed consent form

(see Appendix 1.3), filled in a demographic questionnaire (see Appendix 2.1), and were

then given the experimental instructions to read (see Appendix 1.2). The experimenter

remained in the room and answered general questions where necessary. Once the

participants understood the experimental task, they were given 20 minutes of training on

the use of the Spaceball. Spaceball demonstration software was used and the training

focused on how to control the Spaceball using three rotational degrees of freedom. After

the participants were comfortable with the Spaceball usage and had successfully

accomplished an unrelated task involving the manipulating of a 3D tetrahedron to four

specific orientations (Zhai, 1995), participants proceeded to perform six experimental

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trials (one for each tether length). All the hardware and software used during the training

trials were identical to those of the real testing trials, except that a simplified tunnel was

used for the training. The experimenter sat beside the participants during the training and

pointed out incorrect manoeuvres, if there were any.

The second session consisted of the spatial ability examination. Participants were tested

individually using the GZAS spatial orientation and visualization tests. Before the start of

each test, participants were given 20 minutes to read the instructions. The experimenter

remained in the room and answered any question participants might have. It was clearly

explained to participants that they were required to finish each question set as quickly as

possible and that their final scores were calculated by the number of correct answers

minus a fraction of the number of wrong answer. The duration of each test was 10

minutes, for a total duration of 40 minutes for the session. Participants’ answer sheets

were collected for later analysis.

In the ensuing four sessions, the participants completed four blocks of trials. Within each

block there were 24 experimental trials. Root Mean Square (RMS) tracking errors were

used to measure performance on the local guidance subtask. (see Appendix 6) Tunnel

shape recognition was performed at the end of each trial and the accuracy of these

judgments was used as an indication of the completeness of the cognitive map developed

by the participants (Golledge, 1999), and thus as a measure of global awareness

performance.

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6.4 RESULTS

During the two-week testing period, twelve participants finished a total of 1152 (6 tethers

× 8 tunnels × 12 subjects × 2 repetitions) trials. Raw data were tabulated and analyzed

using Minitab. The analysis focused on two main components of the data: (1) overall

RMS errors produced by each display condition, and (2) tunnel shape recognition scores.

Since the effect of tether length on global awareness was the primary concern in

Experiment 3, a second method was adopted in analyzing the tunnel shape recognition

score, in addition to the same percentage of correct recognition scores used in Experiment

1 and 2. Based on information channel theory, each display was regarded as an

information channel and the amount of information transmitted through each channel (i.e.

each display) was calculated and contrasted with respect to the different tether lengths.

6.4.1 Local Guidance The overall RMS error scores generated are summarized in Table 6.2 and plotted in

Figure 6.4. (See Table 6.1 for an explanation of the display codes, D1 to D6.) An analysis

of variance (see Table 6.3) showed that there was a significant main display effect (F(5,

55) = 8.484, p=0.0005), a significant tunnel effect (F(7, 77)=2.563, p=0.02), and a

significant interaction between the display and tunnel factors (F(35, 385)=2.093,

p<0.0001).

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Table 6.2 Overall RMS errors across six displays.

Display N MEAN SD D1 192 0.30 0.56 D2 192 0.23 0.36 D3 192 0.15 0.13 D4 192 0.20 0.18 D5 192 0.33 0.42 D6 192 0.53 1.22

Judging from the mean error scores, the “medium length” tethered viewpoint display D3

(l = 2) produced the smallest amount of error. A Tukey pair-wise comparison (p<0.05)

showed that D6 (l = 12) produced significantly more errors than the other five displays,

and D3 (l = 2) generated less error than D1 (l = 0.5), D5 (l = 8), and D6 (l = 12). In

addition, D4 (l = 4) generated less error than D5 (l = 8). (see Table 6.4) It is thus apparent

that at some point the increases of tether length will cause a deterioration in local

guidance performance.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Overall RMS error

D1 D2 D3 D4 D5 D6 Display

Figure 6.4 Local guidance performance scores across six tethered displays. Horizontal axis is in increasing order of tether length, see Table 6.1.

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Table 6.3 ANOVA table for overall RMS error across six tethered displays. FACTOR : subjects tunnel display rms LEVELS : 12 8 6 1152 TYPE : RANDOM WITHIN WITHIN DATA SOURCE SS df MS F p =============================================================== mean 96.43 1 96.43 109.603 0.000 *** s/ 9.68 11 0.88 tunnel 5.90 7 0.84 2.563 0.020 * ts/ 25.32 77 0.33 display 7.09 5 3.42 8.484 0.000 *** ds/ 22.16 55 0.40 td 24.39 35 0.70 2.093 0.000 *** tds/ 128.15 385 0.33

Table 6.4 Tukey pair-wise comparisons for overall RMS error score among six tethered displays

Display D1 D2 D3 D4 D5 D6 D1

---

D2 -0.05 0.19

---

D3 0.03* 0.27

-0.04 0.20

---

D4 -0.02 0.22

-0.08 0.16

-0.17 0.07

---

D5 -0.16 0.08

-0.22 0.02

-0.30* -0.06

-0.26* -0.02

---

D6 -0.35* -0.11

-0.41* -0.17

-0.49* -0.25

-0.45* -0.21

-0.31* -0.07

---

The eight tunnels used in this experiment were originally designed in such a way that the

difficulty level of each tunnel was comparable to each other (see Figure 6.2). Therefore,

the significant tunnel effect (p=0.02) was not previously expected. A follow-up Tukey

pair-wise comparison on tunnel factors revealed that tunnel #6 generated significantly

more amount of RMS errors than tunnel #2 and #4. No significant performance

difference was found among any other tunnel pairs. (see Table 6.5) Detailed

examinations of the raw data revealed that the poorer performance of tunnel #6 could be

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attributed to results from a few trials. However, there was not enough evidence to reject

these data.

Table 6.5 Tukey pair-wise comparisons for overall RMS error score among eight tunnels Tunnels #1 #2 #3 #4 #5 #6 #7 #8

#1

---

#2 -0.15 0.29

---

#3 -0.19 0.25

-0.26 0.18

---

#4 -0.15 0.29

-0.22 0.22

-0.1764 0.2580

---

#5 -0.25 0.18

-0.32 0.11

-0.2799 0.1545

-0.32 0.11

---

#6 -0.38 0.06

-0.45* -0.01

-0.4071 0.0273

-0.45* -0.01

-0.34 0.09

---

#7 -0.28 0.15

-0.35 0.08

-0.3122 0.1222

-0.35 0.08

-0.25 0.18

-0.12 0.31

---

#8 -0.22 0.21

-0.29 0.14

-0.2508 0.1836

-0.29 0.14

-0.19 0.25

-0.06 0.37

-0.16 0.28

---

To interpret the significant interaction between the display and the tunnel factors, the

overall RMS error scores generated by each display were broken down and plotted

against tunnel settings in Figure 6.5. It is apparent that performance from D2, D3, D4

showed relative consistent transition pattern across six tunnels. Performance transition

from D1, D5, and D6, however, showed a more irregular pattern. Theoretically, there is

not enough evidence to explain this significant interaction. An analysis into the frequency

domain might shed some light on this issue. However, due to the constraints currently

imposed by the DTS software, the frequency feature of each tunnel was not significantly

distinctive enough to elicit some meaningful results. With improvements on tunnel

generating algorithms, further experiments are expected to provide more insight into this.

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6.4.2 Global Awareness

Participants’ tunnel recognition scores are summarized in Table 6.6 and plotted in Figure

6.6. The mean scores showed an apparent improvement in global awareness with the

increase of tether length. Approximately only half the recognitions (55%) were correct

for the shortest tethered viewpoint display D1 (l = 0.5). In contrast, the longest tethered

viewpoint display D6 (l = 12) produced better scores (83%). An analysis of variance

showed a significant main display effect (F(5, 55) = 15.479, p<0.001). A post hoc Tukey

pair wise comparison (p<0.05) showed that D1 (l = 0.5) and D2 (l = 1) produced

significantly lower scores than the rest four displays, D3 (l = 0.5) produced significantly

lower score than D6 (l = 12). A significant tunnel effect (F(7, 77) = 3.662, p=0.002) and a

significant interaction between the display and tunnel (F(35, 385) = 1.759, p=0.006) were

also found. Results of ANOVA and Tukey test are summarized in Tables 6.7 and 6.8

respectively.

Figure 6.5 Overall RMS errors produced by each display across tunnel conditions

Overall RMS error

Tunnel

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

D1 D2 D3 D4 D5 D6

#1

#2

#3

#4

#5

#6

#7

#8

Display

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Table 6.6 Tunnel shape recognition scores across six displays.

Display N MEAN SD D1 192 0.55 0.50 D2 192 0.55 0.50 D3 192 0.69 0.47 D4 192 0.70 0.46 D5 192 0.79 0.41 D6 192 0.83 0.38

Table 6.7 ANOVA table for overall RMS error across six tethered displays. FACTOR : subjects tunnel display global LEVELS : 12 8 6 1152 TYPE : RANDOM WITHIN WITHIN DATA SOURCE SS df MS F p =============================================================== mean 539.01 1 539.01 266.645 0.000 *** s/ 22.24 11 2.02 tunnel 6.93 7 0.99 3.662 0.002 ** ts/ 20.82 77 0.27 display 13.01 5 2.60 15.479 0.000 *** ds/ 9.24 55 0.17 td 11.13 35 0.32 1.759 0.006 ** tds/ 69.62 385 0.18

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Path recognition score

D1 D2 D3 D4 D5 D6 Display

Figure 6.6 Tunnel shape recognition scores across six tethered displays. Horizontal axis is in increasing order of tether length, see Table 6.1.

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Table 6.8 Tukey pair-wise comparisons for tunnel shape recognition score among displays. Display D1 D2 D3 D4 D5 D6

D1

---

D2 -0.14 0.13

---

D3 -0.28* -0.01

-0.27* -0.01

---

D4 -0.28* -0.02

-0.28* -0.01

-0.14 0.13

---

D5 -0.37* -0.11

-0.37* -0.10

-0.23 0.04

-0.22 0.04

---

D6 -0.41* -0.15

-0.41* -0.14

-0.27* -0.01

-0.26 0.01

-0.17 0.09

---

6.4.3 Analyzing Tunnel Shape Recognition Score Using Information Channel Theory The tunnel shape recognition score was a binary measure in which a correct judgment

yielded a score of one, whereas a mistaken judgment yielded a score of zero. One

shortcoming with this method is that it does not distinguish between situations where

participants were totally disoriented and those that they were only partially disoriented.

For example, in some cases, participants were able to recognize certain feature of the

tunnel, but failed to make the correct judgment. These situations could be descried as

being partially disoriented. The previously calculated tunnel shape recognition scores did

not consider these situations. To address this problem, participants’ responses were re-

analyzed using the information channel theory (see Sheridan and Ferrell, 1974 for a

discussion of information channels). Each display was regarded as an information

channel. The amount of input information was determined by the number of tunnel

configuration. The amount of output information was decided by participants’ responses.

A diagram illustrating an information channel is shown in Figure 6.7.

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A contingency table is commonly used for displaying the statistical relationships of an

information channel. It is a matrix in which the rows correspond with inputs, the columns

with outputs, and the elements are probabilities indicative of the association. In this

experiment, eight tunnel configurations (input) were used in the testing and the

participants were instructed to pick one out from a set of eight miniature tunnel models

(output). Participants’ choices were calculated as the elements in the matrix. Results are

shown in Table 6.9. Detailed contingency table calculations are listed in Appendix 4.

Table 6.9 Information (input, output, equivocation, noise, and transmitted) associated with each information channel (i.e. display). Unit: bit.

Display Input Transmitted Information

Equivocation Noise Output

D1 3 1.1 1.9 1.8 2.9 D2 3 1.2 1.8 1.7 2.9 D3 3 1.6 1.4 1.4 3.0 D4 3 1.7 1.3 1.3 3.0 D5 3 1.9 1.1 1.1 3.0 D6 3 2.1 0.9 0.9 3.0

The trend across displays is better shown in Figure 6.8. With the increase of tether length

(from left to right along the display axis, there is a steady trend of increasing information

transmission and decreasing equivocation (information loss) and noise. This finding is

consistent with the previous finding using incorrect judgment scores and confirms the

conclusion that global awareness performance improves with an increase of tether length.

Transmitted Information

Input Output Equivocation

Noise

Figure 6.7 Diagram of an information channel. (Adapted from Sheridan and Ferrell, 1974).

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6.4.4 Individual Differences in Spatial Abilities

An analysis of participants’ spatial orientation and spatial visualization scores revealed a

large individual difference. Test scores are summarized in Table 6.10. A regression

analysis between the each participant’s spatial abilities score and their navigational

performance was performed. However, no significant correlation between participants’

spatial ability scores and their navigational performance was identified. The sample

coefficient of determination, R2, represents the proportion of variation in response

explained by a straight line linear regression. A perfect match of a linear regression

model will give a R2 value of 100%. The computed R2 are summarized in Table 6.11.

Minitab output is included in Appendix 5.

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3 4 5 6

Input

Transmitted Information

Equivocation

Noise

Output

Information (bit)

D1 D2 D3 D4 D5 D6 Display

Figure 6.8 The amount of information (input, output, equivocation, noise, and transmitted) associated with each information channel (i.e. display). Horizontal axis is in increasing order of tether length, see Table 6.1.

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Table 6.10 Participants’ spatial orientation and spatial visualization scores using Guilford-

Zimmerman Aptitude Survey. Participant Spatial orientation score Spatial visualization score

s1 8.3 19.3 s2 24.0 25.5 s3 13.8 18.3 s4 33.8 19.8 s5 30.0 20.0 s6 18.0 16.3 s7 34.3 23.5 s8 30.3 19.5 s9 20.5 16.0 s10 31.0 19.0 s11 13.0 12.3 s12 18.0 22.3

Table 6.11 Sample coefficient of determination, R2, obtained from the regression analysis.

R2 Spatial orientation score Spatial visualization score Local guidance 12.7% 3.4%

Global awareness 4.8% 2.1%

6.5 DISCUSSION OF RESULTS

6.5.1 Major Findings

1. Comparing tethered viewpoint displays with the same dynamic properties, global

awareness improves and local guidance performance deteriorates with the increase of

tether length.

2. Tethered viewpoint display with extreme length conditions (i.e. zero or very long

length) fail to support overall navigation. The overall best navigational performance is

obtained by a medium length tethered viewpoint display.

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6.5.2. Spatial Abilities and Their Relations to Global Awareness

Theoretically, participants’ navigational performances (especially, global awareness) are

influenced by their individual spatial abilities. However, the experiment results failed to

reveal any significant correlation between participants spatial ability test scores and their

performance scores. Similar results were also reported in several other studies (e.g.

Satalich, 1995; Chen, 2000).

There could be two reasons for accounting this finding. (1) Spatial ability is a generic

term used to describe a set of human abilities. Besides visualization and orientation

ability, it also includes speed of closure, flexibility of closure, perceptual speed etc. The

two tests used in this study were mainly focused on two aspects of spatial ability. As

Istance and Hand (1998) pointed out, “it remains to be demonstrated that performance on

a particular single test can adequately characterise the component spatial abilities used

when completing tasks requiring the acquisition of navigational knowledge from virtual

environments.” This partial measurement of participants’ spatial ability might be the

reason why there was no significant correlation between participants’ spatial ability

scores and their awareness performance. (2) The Guilford-Zimmerman tests itself was

originally designed for aircraft personnel working in aviation scenario. Like many of

spatial ability test packages, the GZAS tests were validated with subjects’ navigational

performance in real geographical environments. Since the simulation used in this study

was carried out in a software simulation, in other words, in a virtual environments. It is

possible that the tests themselves are not a good representation of user’s spatial ability in

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virtual environments. No empirical data is available to address this right now. Further

research is required.

6.5.3 Experiment 2 Results Revisited

The findings in Experiment 3 provided additional context for interpreting the results in

Experiment 2. A constant tether length (2 graphical units) was adopted for all tethered

displays in Experiment 2. Participants’ tunnel shape recognition scores did not reveal any

significant performance differences across all tethered viewpoint displays. Due to the

high performance scores, it was suggested that a ceiling effect was observed in

participants’ global awareness performance.

In the current Experiment, display D3 had the same tether length as those displays tested

in Experiment 2. As manifested in the results of Experiment 3, a tether length of 2

graphical units is the threshold for supporting optimal global awareness under the

simulation task used in this study. In other words, a tethered display with a length of 2

graphical units is long enough to support optimal global awareness performance.

Elongating the tether length beyond this threshold will not significantly improve global

awareness, as indicated in the results. This confirms the ceiling effect claimed in the

global awareness performance in Experiment 2.

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6.5.4 Optimal Tether Length

The performance trade-off between the local guidance and global awareness tasks

showed that the optimal tethered display for the current task simulation was display D3

which had a length of 2 graphical units. It was claimed in the experimental conclusion

that best overall navigational performance was supported by a medium length tethered

display. The use of the word medium here was trying to emphasize the fact that the

optimal tether length does not coincident with extreme tether length conditions. This is

also an indication of the trade-off between display preview information and its spatial

resolution.

Considering the fact that the possible tether lengths for the current simulation ranged

from 0 (i.e. the egocentric case) to 15 (i.e. the exocentric case, in which the viewpoint can

survey the whole cubic environment) graphical units. An optimal tether length of 2

graphical units lies in the short tether range. As manifested in the RMS error diagram (see

Figure 6.4), the optimal tether length was mainly decided by the local guidance task

performance. Difficulties in guidance task were reported by participants during the

experiment, in other words, the local guidance task was the bottleneck in the testing

scenario. On the basis of the navigation framework proposed by Wickens and Prevett

(1995) (see Chapter 2 for detailed descriptions), it is predictable that an optimal display

for supporting the current experimental tasks shall lie on the egocentric end of the display

centricity continuum. The current finding of a short optimal tether confirms the validity

of the framework.

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Following the same principle, further predictions of optimal tether length can be made

with respect to the task difficulties. For example, the optimal tether length will increase if

the difficulties of local guidance tasks reduce (e.g. slow down the constant airplane flying

speed) or if the difficulties of global awareness tasks increase (e.g. more complicated

environments, harder awareness tasks etc.). The shift of task difficulties between the local

guidance and global awareness tasks imposes a change of requirements on the integrating

of information from the egocentric and exocentric frames of references. Dynamic

viewpoint tethering has shown its flexibility in supporting the achievement of

maximizing navigation efficiency.