CSIS Discussion Paper No. 42

Direction judgment in a corridor containing a single turn

Naohide Yamamoto and Atsuyuki Okabe
University of Tokyo
Tokyo, Japan

November 15, 2001

Center for Spatial Information Science, University of Tokyo
4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, JapanAbstract
This experiment investigated direction judgment in a corridor containing a single
turn. The turn degree of the corridor ranged from 0° to 90° with 15° intervals. A direction
was presented to subjects at the entrance of the corridor and subjects were asked to point
this direction at the exit of the corridor. Considering the fact that subjects had to judge
directions in the featureless corridor, two hypotheses were proposed: (a) subjects tend tojudge directions by eight categories of egocentric directions (front, back, left, right, andfour diagonals); (b) subjects tend to estimate angular distance from their front to the direction which they try to judge. The result supported both hypotheses. The effects of vestibular and kinesthetic information as well as visual information obtained by subjects are discussed.

Author Note
Naohide Yamamoto, Department of Urban Engineering; Atsuyuki Okabe, Center for
Spatial Information Science.
The authors would like to thank Yasushi Asami and Yukio Sadahiro for their helpfulcomments. Thanks are also due to Toru Ishikawa for his valuable critiques on the earlier
draft of this article.
Correspondence concerning this article should be addressed to Naohide Yamamoto,Department of Urban Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo
113-8656, Japan. Electronic mail may be sent to naohide@ua.t.u-tokyo.ac.jp.

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The objective of this study is to experimentally investigate direction judgment in acorridor which has a single turn. Stated a little more explicitly, subjects in our experimentare firstly presented a direction at the entrance of a corridor; they secondly walk throughthe corridor to the exit; they are finally asked to point the target direction which waspresented at the entrance (see Figure 1). The corridor is a featureless space except for aturn, and so subjects rely on an egocentric reference system to judge direction. That is,they judge direction with respect to their own body (e.g., now that I take a right turn in thecorridor, the target direction comes to the front of my body).
Given this experimental environment, our first hypothesis is that subjects tend tojudge direction by eight categories of egocentric directions (i.e., front, back, left, right,
and four diagonals). An underlying model of our first hypothesis is that subjects use eightdirection reference axes in the eight egocentric directions (see the left panel of Figure 2)
for judging direction. Subjects judge that the target direction belongs to which of eight
directional categories by estimating the closest reference axis to the target direction. We
call this model the eight-direction model.
Our second hypothesis is that subjects tend to make a judgment on which reference
axis is the closest to the target direction by estimating angular distance from their front
The Correct Answer

Exit

A Presented Direction
Entrance
Figure 1.
1. An example of a presented direction at the entrance of the corridor and the correct
answer for the presented direction.

2

reference axis to the target direction. Because the front reference axis has the greatest
saliency among reference axes, subjects use only their front axis as the basis of their judgment. This hypothesis is based on a model that the front axis predominates over the other
axes.
Many experimental studies have been conducted concerning reference axes. Most ofthese studies focused on two topics. First topic is the existence of diagonal axes; the second topic is predominance of the front axis over the other axes. Rosch (1975) conducted
two experiments in which subjects judged the angular orientation of lines. One experiment used a linguistic hedge task and the other experiment used a spatial task in which
subjects estimated the psychological distance between two stimuli. Data from the linguistic hedge task supported the eight-direction model. On the other hand, data from the spatial task were against the existence of diagonal axes. In other words, the data supported thefour-direction model that subjects’ reference axes consist of four orthogonal axes (front,
back, left, and right), as is shown in the right panel of Figure 2.

Eight-direction Model

Four-direction Model

Front

Front
Diagonal

Left

Right

Left

Back

Right

Back

Figure 2.
2. Eight-direction model and four-direction model of reference axes for direction judgment.

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While Rosch (1975) used the linguistic hedges and the psychological distance between stimuli, some studies used reaction time for the analysis of reference axes. Loftus(1978) examined subjects’ comprehension of compass directions. Reaction time supported
the four-direction model, and showed that subjects used four reference axes equally fordirection judgment. This result suggested that there was no predominance among reference axes. Franklin and Tversky (1990) also used reaction time to investigate predominance of the front axis. In their experiment, objects in front of subjects were judged mostquickly, followed by objects in back, in left or in right. From this result, Franklin andTversky concluded that the front axis predominated over the other axes.
Franklin, Henkel, and Zangas (1995) used errors in judgment for the analysis of reference axes. The errors showed that directions which were close to the front axis wererecalled most accurately. On the other hand, directions which were close to the diagonalaxes were recalled most inaccurately. This result supported the four-direction model.
Montello, Richardson, Hegarty, and Provenza (1999) also used errors in judgment for the
analysis of reference axes. In case that subjects used a manual pointer to judge direction,
their data supported the four-direction model and showed that there was no predominanceamong reference axes.
While the experiments of the above studies were conducted on the subjects whostood at a point or took their seats, Sadalla and Montello (1989) conducted an experiment
which required subjects to traverse pathways, each of which had a single turn. The subjects judged the angular size of the pathway turn by pointing the original direction of
traverse at the end of the pathway. The errors in the judgment became the greatest when
the turn degree was 45° and 135°. This result supported the four-direction model. Montello
and Frank (1996) extended the analysis of Sadalla and Montello by computer simulation.

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Montello and Frank hypothesized not only the four-direction model but also the eightdirection model. The result of the simulation showed that the eight-direction model accounted for the pattern of the data of Sadalla and Montello better than the four-direction
model.
In summary, many previous studies supported the four-direction model, but somestudies supported the eight-direction model. Many previous studies supported the predominance of the front axis, but some studies showed that there was no predominanceamong reference axes. Thus, it is still an open question that reference axes for direction
judgment consist of either four or eight directions. Predominance of the front axis is also
controversial. Because there is room for further discussion on these matters, the present
study is designed to examine the existence of diagonal axes and predominance of the frontaxis.
By integrating our two hypotheses mentioned above, we expected the variation ofabsolute errors in judgment as is shown in Figure 3. By the first hypothesis, we expectedthat absolute errors in judgment would increase as a function of angular distance fromevery reference axes. In particular, we were concerned with absolute errors for the direction of 45° and 135°. If subjects used eight-direction reference axes, absolute errors for the
directions would be small, as is shown in the left panel of Figure 3. On the other hand, if
subjects used four-direction reference axes, absolute errors for the directions would belarge, as is shown in the right panel of Figure 3. By the second hypothesis, we expectedthat absolute errors in judgment would increase as a function of angular distance from thefront axis to the target direction that subjects tried to judge. If the front axis predominatedover the other axes, that is, if subjects estimated an angular distance to the target direction
from their front axis, absolute errors would become larger in proportion to the angular5distance extended, as is shown by the broken line of Figure 3.

MethodSubjects
Seventy subjects consisted of 12 females and 58 males, ranging from 20 years to 33
years (mean age = 21.9 years). Subjects were undergraduates at the University of Tokyo,
who attended an introductory urban analysis class and participated in partial fulfillment ofa course requirement.

Materials
The experiment took place in a corridor which was temporarily constructed in a hallfor this experiment. The walls of the corridor were made of plain white plates, which were
2 m high. The corridor was 1.5 m in width and 6 m in length. A blue sheet with no texture
covered the floor of the hall in order to provide the subjects with no directional cues. A
partition was placed around the corridor in order to prevent subjects from looking theAbsolute Error in Judgment

Eight-direction Model

0

4545

90 90

Four-direction Model

135 135 180 180

0

4545

90 90

135135180180Angular Distance from the Front Axis to the Target Direction in Degrees

Figure 3.
3. Eight-direction model and four-direction model of the expected variation of absolute
errors in subjects’ judgment.

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corridor from the outside.
An angular turn was in the middle of the corridor, i.e., 3 m from the entrance (seeFigure 4). The degrees of the turn ranged from 0° to 90° with 15° intervals. The corridor
was used from both ends, and so the angular turn became both a left-hand turn and a righthand turn. We considered that the difference between left and right would not affect direction judgment, because some previous studies (Franklin et al., 1995; Franklin & Tversky,
1990; Sadalla & Montello, 1989) found no significant difference between left and right inregard to direction judgment with an egocentric reference system.
A circular measuring device, an 18 cm diameter circle with a rotating pointer, wasused for both presenting a direction to subjects at the entrance of the corridor and subjects’making direction judgment at the exit. The device was mounted horizontally on a stand 70
cm high.

Procedure
The experiment was administered individually. After receiving a brief instruction
concerning the tasks to be performed, a subject was led to the entrance of the corridor. Oneof five directions (see Figure 5) was presented to the subject at the entrance. After memo-Turn Degree

3m

3m

Figure 4.
4. A bird’s-eye view of the corridor for the experiment.

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rizing the presented direction, the subject proceeded to walk along the corridor. The subject was asked to walk as usual. The subject was also asked not to look back and track
back. On arriving at the exit of the corridor, the subject turned the pointer of the circularmeasuring device to make the pointer point the direction which was presented at the entrance (see Figure 1). Unlimited time was provided for this task. When this task was done,
an experimenter turned the pointer randomly so that the subject could not utilize her/his
previous answer for direction judgment.
After completing this task, the subject went out the corridor once. The experimenter
asked to the subject whether or not she/he could maintain sense of orientation during thetask.
After a short interval, the subject was asked to reenter the corridor. At this time, thesubject traversed the corridor to the opposite direction. One of the other directions, as isalso shown in Figure 5, was presented to the subject at the entrance, and then the subject
performed the task in the same manner. This procedure was repeated five times to complete the tasks for all directions shown in Figure 5. After five tasks were finished, the turndegree of the corridor was changed to another one, and the same tasks were performed in
the same manner. Every subject traversed four out of seven angles: half of the subjects
walked the corridor which had an angular turn of 0°, 15°, 45°, and 75°; the other half

Direction

A

C

B

D

E

Figure 5.
5. Directions which were presented to the subjects at the entrance of the corridor.

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walked the corridor which had an angular turn of 0°, 30°, 60°, and 90°. The experiment
took approximately 30 minutes for a subject. The order of the presented directions and theturn degrees was randomized for each subject.

Results
The answers of the subjects were examined both as absolute errors and as signed
errors. Note that in signed errors, overestimation of the angular distance from the front
reference axis to the target direction was defined as positive value, and underestimation of
the angular distance was defined as negative value.
We eliminated 86 data points, because the subjects reported that they lost sense oforientation and gave up answering in these trials. These eliminated data points were approximately 6 % of the whole data. In addition, two data points were lost because of theexperimenter’s error.
To test our model of the variation of absolute errors in judgment (see Figure 3), we
primarily examine the answers of the subjects as absolute error in three steps. First, weinvestigate subjects’ perception of the direction that was presented to subjects at the entrance of the corridor. Second, we investigate subjects’ perception of the turn degree of thecorridor. Third, we test both the four-direction model and the eight-direction model toaccount for the variation of absolute errors by using the results obtained in the former two
steps.

Perception of the Direction That Was Presented to Subjects at the Entrance
Errors for the 0° turn was examined in order to investigate perception of the directionthat was presented at the entrance. Because the corridor became complete straightaway

9when the turn degree was 0°, the errors showed how subjects perceived the presented
direction at the entrance. The mean errors are plotted in Figure 6.
If subjects perceived the presented directions accurately, all the mean errors for eachpresented direction would be approximately equal to 0. The errors were analyzed by arepeated-measures ANOVA with the presented direction (direction A, B, C, D, and E; see
Figure 5) as within-subjects factor. The result of the ANOVA revealed that all the presented directions were not perceived equally (F(F (4, 268) = 8.46, p < .001). To find thepresented directions which were not perceived accurately, we applied a two-sided t test to
the errors under the null hypothesis that the mean error for each presented direction was
equal to 0. The result of the t test showed that the errors for the direction B and D weresignificantly less than 0 (for the direction B, t (69) = -2.93, p < .01; for direction D, t (68)20Mean Error in Degrees

-2

-4

A

BB

C C

D

D

E

E

The Presented Direction
Figure 6.
6. Mean errors and 95 % confidence intervals for the presented direction when the turndegree was 0°.

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= -4.82, p < .001). The errors for the direction A, C, and E were not significantly different
from 0.

Perception of the Turn Degrees of the Corridor
Figure 7 shows the mean errors for each turn degree when the direction C (see Figure5) was presented at the entrance. In these cases, subjects tried to estimate angular distances from their front axis to the target direction so that the angular distances became
equal to the turn degrees of the corridor. Thus the mean errors plotted in Figure 7 shows
how subjects perceived the turn degrees of the corridor.
The mean errors indicated that turn degrees between 0° and 45° were all overesti-

10

Mean Error in Degrees

0

-10

-20
00

15
15

3030

4545

60 60

75 75

90 90

The Turn Degrees of the Corridor
Figure 7.
7. Mean errors and 95 % confidence intervals for the turn degrees of the corridor when
the direction C was presented.

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mated, while turn degrees between 45° and 90° were all underestimated. The mean errors
also indicated that turns of 0°, 45°, and 90° were accurately perceived. This fact was
confirmed statistically by a two-sided t test under the null hypothesis that the mean error
for each group of the presented directions was equal to 0: for the turn degrees less than45°, t (67) = 3.47, p < .01; for the turn degrees greater than 45°, t (64) = -12.9, p < .001.
Thus, all turn degrees were distorted in the direction of 45°.

Variation of Absolute Errors
The mean absolute errors are shown in Figure 8. This figure illustrates that the abso-

20

Mean Absolute Error in Degrees

15

10

5

0

0

15 30 45 60 75 90 105 120 135 150 165 180

The Angular Distance from the Front Reference Axis
to the Target Direction
Figure 8.
8. Mean absolute errors and 95 % confidence intervals for the angular distance from thefront axis to the target direction.

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lute errors were small when the angular distance from the front axis to the target direction
was 0°, 45°, 90°, 135°, and 180°. This fact was confirmed statistically, t (1310) = -18.1, p< .001. This result supported the eight-direction model of the variation of absolute errors,
which is shown in the left panel of Figure 3. We hereby examined both the four-direction
model and the eight-direction model by estimating two parameters of the model: a slope
and an intercept of the broken line in Figure 3. These two parameters can determine thestructure of the model, because our model considered that middle directions of two adjoining reference axes (e.g., the direction of 22.5° in the eight-direction model) gave the peaksof the graph. This meant that our model considered that egocentric space would be divided
homogeneously into four or eight categories. On the other hand, Franklin et al. (1995) andMontello and Frank (1996) showed that egocentric space was divided heterogeneously(e.g., front category have wider range than the other categories). Further examination on
this matter would be required in the future.
To estimate these two parameters, the true angular distance from the front axis to thetarget direction was transformed into subjective angular distance. To make this transformation, both the subjects’ perception of the presented direction and the subjects’ perception of the turn degrees was used in the following manner. When the direction B or D waspresented at the entrance, the error for each direction was subtracted from the true angulardistance. In a similar manner, the error for each turn degree was add to or subtracted fromthe true angular distance. Thus, the true angular distance was transformed to the subjective angular distance. We used this subjective angular distance hereafter.
The parameters were estimated by the least square method, and the results are tabulated in Table 1. Comparing the values of the determination coefficient in Table 1, theeight-direction model fitted to the data better than the four-direction model. This result

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showed that the eight-direction model accounted well for the variation of the absolute
errors. Moreover, values of the slope were significantly greater than 0 (for the four-direction model, t (1310) = 6.54, p < .001; for the eight-direction model, t (1310) = 8.86, p <.001). This result showed that the subjects estimated the angular distance from their front
reference axis.

Clockwise or Counterclockwise Error
As we have seen in the above examination, the eight-direction model could accountfor the variation of the absolute errors well. The absolute errors, however, do not haveanother important information; whether the answer of the subjects appeared on the clockwise side or counterclockwise side of the correct answer. We therefore examined both thefour-direction model and the eight-direction model whether or not the answer predicted by
the model and the answer made by the subjects was on the same side of the correct answer.
The investigation was conducted by the following steps.
First, the mean direction of the subjects’ answers for each trial was calculated bycircular statistics (Fisher, 1993). Second, the subjects’ judgment that the target direction
belonged to which directional categories was predicted by the subjective angular distance.
Third, the answer predicted by the model was fixed by the reference axis which was in the

Table 1
Values of Parameters and Determination Coefficient

ModelIntercept

Slope

Determination
Coefficient

Four-direction model

8.50

0.03850.390

Eight-direction model

12.1

0.05300.661

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directional category chosen by the former step. Fourth, the mean direction and the predicted value were examined with regard to whether or not these two directions were on thesame side of the correct answer. Note that 15 trials in which the turn degree of the corridor
was 0°, 45°, and 90° were excluded from the investigation, because it could not be determined that the predicted value was on which side of the correct answer in these trials.
The result of the above investigation also revealed that the eight-direction model was
more advantageous to account for the data than the four-direction model. The eight-direction model explained well that the subjects’ answer appeared on which side of the correct
answer, z = 3.35, p < .001 (by a binomial test). The 18 predicted values from the eightdirection model and the corresponding mean directions of the subjects’ answers were on
the same side of the correct answer. On the other hand, the same test conducted on thepredicted values from the four-direction model was not significant. The 8 predicted values
from the four-direction model and the corresponding mean directions were on the sameside of the correct answer.

Discussion
The present study tested two hypotheses regarding direction judgment with an egocentric reference system. The first hypothesis is that subjects tend to judge direction by
eight categories of egocentric directions (i.e., front, back, left, right, and four diagonals).
An underlying model of the first hypothesis is the eight-direction model in which subjects
judge directions by using eight-direction reference axes. This model was compared withthe four-direction model in which subjects’ reference axes consist of only front, back, left,
and right axis. The result of the present study supported the eight-direction model. The
second hypothesis is that subjects tend to estimate angular distance from their front refer-15

ence axis to the target direction in order to make a judgment on which reference axis is theclosest to the target direction. The second hypothesis is based on the model that the front
axis predominates over the other axes. The result of the present study also supported thismodel. Our results, however, were not always consistent with the results of the previous
studies referred to in the introduction.
As compared with the experiments of the previous studies, the present experiment
had two distinctive features. The first feature was that there was no restriction on thesubjects’ vision; the second feature was that the subjects walked through the corridor. In
contrast with the first feature of the present experiment, Montello et al. (1999) and Sadalla
and Montello (1989) restricted subjects’ vision partially or completely. This difference
implies that the subjects of the present study obtained more visual information than thesubjects of their studies. In contrast with the second feature of the present experiment,Franklin and Tversky (1990), Franklin et al. (1995), Loftus (1978), Montello et al., andRosch (1975) conducted the experiment on subjects who stood at a point or took theirseats. This difference implies that the subjects of the present study obtained more vestibular and kinesthetic information than the subjects of their studies. These two differencessuggest that vestibular and kinesthetic information as well as visual information obtainedby the subjects affected the results of the present study.
The first result of the present study was that the subjects used eight-direction reference axes, as mentioned previously. As compared with the subjects of the previous studies(Franklin & Tversky, 1990; Franklin et al., 1995; Loftus, 1978; Sadalla & Montello, 1989)
who used four-direction reference axes, the subjects of the present study had four morecategories in their egocentric space. Dividing egocentric space into eight categories would
require more information than dividing it into four categories.

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In the present study, the subjects were provided with more information than the previous studies. The subjects saw an angle made by the walls of the corridor and received an
optic flow in the course of walking. Because these visual cues were sufficient to construct
eight categories within egocentric space, the subjects of the present study could use eightdirection reference axes. This inference was evidenced from the fact that Sadalla andMontello (1989), which required subjects to walk pathways, supported the four-direction
model. In their experiment, the subjects’ forward vision was restricted to 0.5 m and their
peripheral vision was completely restricted. Thus the subjects of their experiment hadvestibular and kinesthetic information but had little visual information. The lack of visual
information led to the result that subjects used four-direction reference axes.
Vestibular and kinesthetic information also affected the first result in conjunction
with spatial updating. When locomotion involved rotational body movement, vestibular
and kinesthetic information enhanced the accurate updating of self-position and traveling
direction (Chance, Gaunet, Beall, & Loomis, 1998; Klatzky, Loomis, Beall, Chance, &Golledge, 1998; Presson & Montello, 1994). Differently from the experiments of the previous studies, the present experiment required subjects to walk through the corridor. Since
walking through the corridor provided vestibular and kinesthetic information for perceiving change in the traveling direction, the subjects could update the perceived traveling
direction more accurately. This allowed subjects to use eight-direction reference axes.
The second result of the present study was predominance of the front reference axis.
Because egocentric directions typically serve for guiding travel, the front axis should intrinsically be predominant when people walk. Moreover, visual information in the environment of the present experiment helped the subjects perceive their traveling direction.
Thus the fact that the subjects of the present study walked through the corridor with suffi-17cient visual information elicited the intrinsic predominance of the front axis. This inference was supported by the fact that Sadalla and Montello (1989) found no predominanceamong reference axes. In their experiment, subjects received a partial optic flow due to acomplete blockage of peripheral vision, and so it was difficult for them to perceive theirtraveling direction after taking a turn. This difficulty led to the result that there was no
predominance among reference axes.
Lastly, we should note the possibility that the subjects of the present study did notcompletely rely on an egocentric reference system. Although the corridor for the experiment was a featureless space, the subjects might have formed representation of geometryof the corridor, and might have used this representation to judge directions (Shelton &McNamara, in press; Wang & Spelke, 2000). If we completely prevented the subjects
from looking the corridor by asking them to wear a blindfold or a hood, we could havecompletely precluded this possibility. Nevertheless we did not use a blindfold or a hood,because we aimed to make our experimental environment as natural as possible. Walking
without vision is not a natural experience for sighted people. On the contrary, walking
through a featureless corridor with vision is a common behavior in our everyday lives.
This was the very reason that we used the corridor for the experiment. Thus using thecorridor was an appropriate method for the present study, although it might make possiblethat subjects used non-egocentric information for direction judgment.

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References
Chance, S. S., Gaunet, F., Beall, A. C., & Loomis, J. M. (1998). Locomotion mode
affects the updating of objects encountered during travel: The contribution of vestibularand proprioceptive inputs to path integration. Presence
Presence,, 7, 168-178.
Fisher, N. I. (1993). Statistical analysis of circular data.
data. Cambridge, UK: Cambridge
University Press.
Franklin, N., Henkel, L. A., & Zangas, T. (1995). Parsing surrounding space into
regions. Memory & Cognition,
Cognition, 23
23,, 397-407.
Franklin, N., & Tversky, B. (1990). Searching imagined environments. Journal of
Experimental Psychology: General,
General, 119
119,, 63-76.
Klatzky, R. L., Loomis, J. M., Beall, A. C., Chance, S. S., & Golledge, R. G. (1998).
Spatial updating of self-position and orientation during real, imagined, and virtual locomotion. Psychological Science,
Science, 9, 293-298.
Loftus, G. R. (1978). Comprehending compass directions. Memory & Cognition,
Cognition, 6 ,416-422.
Montello, D. R., & Frank, A. U. (1996). Modeling directional knowledge and reasoning in environmental space: Testing qualitative metrics. In J. Portugali (Ed.), The construction of cognitive maps (pp. 321-344). Dordrecht, The Netherlands: Kluwer Academic.
Montello, D. R., Richardson, A. E., Hegarty, M., & Provenza, M. (1999). A comparison of methods for estimating directions in egocentric space. Perception
Perception,, 28
28,, 981-1000.
Presson, C. C., & Montello, D. R. (1994). Updating after rotational and translational
body movements: Coordinate structure of perspective space. Perception
Perception,, 23
23,, 1447-1455.
Rosch, E. (1975). Cognitive reference points. Cognitive Psychology,
Psychology, 7, 532-547.
Sadalla, E. K., & Montello, D. R. (1989). Remembering changes in direction. Envi-19

ronment & Behavior,
Behavior, 21
21,, 346-363.
Shelton, A. L., & McNamara, T. P. (in press). Systems of spatial reference in humanmemory. Cognitive Psychology.
Psychology.
Wang, R. F., & Spelke, E. S. (2000). Updating egocentric representations in humannavigation. Cognition
Cognition,, 77
77,, 215-250.

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