Geometric cues, reference frames, and the equivalence of experienced-aligned and novel-aligned views in human spatial memory

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Geometric Cues 1
Running head: GEOMETRIC CUES IN HUMAN SPATIAL MEMORY
Geometric Cues, Reference Frames, and the Equivalence of Experienced-Aligned and Novel-
Aligned Views in Human Spatial Memory
Jonathan W. Kellya1, Lori A. Sjolunda, & Bradley R. Sturzb1
aIowa State University
bGeorgia Southern University
1Corresponding Authors:
Jonathan W. Kelly, Ph.D. Bradley R. Sturz, Ph.D.
Department of Psychology Department of Psychology
Iowa State University, Georgia Southern University
W112 Lagomarcino Hall, P.O. Box 8041
Ames, IA 50011-3180. Statesboro, GA 30460
USA USA
Phone: (515) 294-2322 Phone: (912) 478-8539
E-mail: jonkelly@iastate.edu Email: bradleysturz@georgiasouthern.edu

Geometric Cues 2
Abstract 1
Spatial memories are often organized around reference frames, and environmental shape 2
provides a salient cue to reference frame selection. To date, however, the environmental cues 3
responsible for influencing reference frame selection remain relatively unknown. To connect 4
research on reference frame selection with that on orientation via environmental shape, we 5
explored the extent to which geometric cues were incidentally encoded and represented in 6
memory by evaluating their influence on reference frame selection. Using a virtual environment 7
equipped with a head-mounted-display, we presented participants with to-be-remembered object 8
arrays. We manipulated whether the experienced viewpoint was aligned or misaligned with 9
global (i.e., the principal axis of space) or local (i.e., wall orientations) geometric cues. During 10
subsequent judgments of relative direction (i.e.,participants imagined standing at one object, 11
facing a second object, and pointed toward a third object), we show that performance was best 12
when imagining perspectives aligned with these geometric cues; moreover, global geometric 13
cues were sufficient for reference frame selection, global and local geometric cues were capable 14
of exerting differential influence on reference frame selection, and performance from 15
experienced-imagined perspectives was equivalent to novel-imagined perspectives aligned with 16
geometric cues. These results explicitly connect theory regarding spatial reference frame 17
selection and spatial orientation via environmental shape and indicate that spatial memories are 18
organized around fundamental geometric properties of space. 19
(216 words) 20
21
Keywords: Spatial Memory, Reference Frames, Geometric Cues 22

Geometric Cues 3
Geometric Cues, Reference Frames, and the Equivalence of Experienced-Aligned and Novel-23
Aligned Views in Human Spatial Memory 24
Spatial memories are critical to everyday navigation. For example, finding a detour to 25
avoid campus construction requires a navigator to retrieve a memory of the surrounding space, 26
determine his or her current location within that remembered space, and then plan an appropriate 27
alternative route based on the retrieved memory. Imagining different perspectives within the 28
remembered environment, as one might do when comparing potential routes, typically reveals 29
preferred access to a small number of specific perspectives (Greenauer & Waller, 2008, 2010; 30
Hintzman, O’Dell, & Arndt, 1981; Kelly, Avraamides, & Loomis, 2007; Kelly& McNamara, 31
2008, 2012; Marchette, Yerramsetti, Burns, & Shelton, 2011; Mou & McNamara, 2002; Shelton 32
& McNamara, 1997, 2001; Werner & Schmidt, 1999; Yamamoto & Shelton, 2005), and such 33
orientation-dependence is thought to reflect the reference frame structure of spatial memories 34
(Klatzky, 1998; Shelton & McNamara, 2001). Perspectives aligned with a reference frame are 35
directly represented in memory, and are therefore relatively easy to retrieve, whereas misaligned 36
perspectives must be inferred, and this inference process results in longer latencies and larger 37
errors (see Shelton & McNamara, 2001). 38
Reference frame selection has been found to depend on a combination of experienced 39
views and environmental structure. Shelton and McNamara (2001, Exp 1) conducted a 40
paradigmatic study in which participants studied a layout of seven objects placed on the floor of 41
a rectangular room. Participants experienced the layout from multiple views, two of which were 42
aligned and one misaligned with the wall surfaces of the surrounding room. After learning, 43
participants performed judgments of relative direction (JRD) in which they imagined standing at 44
the location of one object, facing a second object, and pointed toward a third object from the 45

Geometric Cues 4
imagined perspective. Pointing performance was best when imagining experienced perspectives 46
aligned with the room walls. Performance when imagining the misaligned-experienced 47
perspective was no better than imagining non-experienced perspectives. The authors interpreted 48
these findings as evidence that participants remembered the object locations using a reference 49
frame, and that reference frame selection was determined by a combination of experienced views 50
and environmental structure. 51
The salience of environmental structure in reference frame selection has been repeatedly 52
demonstrated in studies investigating spatial memory organization (Hintzman et al., 1981; 53
Marchette et al., 2011; Yamamoto & Shelton, 2005; McNamara, Rump, & Werner, 2001; 54
Montello, 1991), and room shape has been shown to be a particularly powerful environmental 55
cue to reference frame selection such that performance is best when imagining experienced 56
perspectives aligned with the room walls (Kelly & McNamara, 2008; Shelton & McNamara, 57
2001; Valiquette & McNamara, 2007; Valiquette, McNamara, & Labrecque 2007). To date, 58
however, the specific environmental cues represented in memory that influence reference frame 59
selection remain relatively unknown. 60
In contrast, research in the area of spatial orientation has long been interested in the 61
environmental cues responsible for the determination of heading (Cheng, 1986; Gallistel, 1990; 62
Hermer & Spelke, 1994). Extant literature suggests that fundamental geometric properties of 63
space are responsible for successful orientation with respect to the environment (Cheng, 2005, 64
Lee, Sovrano, & Spelke, 2012; for a review, see Cheng & Newcombe, 2005). For example, 65

Geometric Cues 5
orientation may be accomplished by global geometric cues, such as the principal axis of a space, 66
and/or local geometric cues, such as the length and orientation of a single wall surface or the 67
angle formed by the intersection of two wall surfaces (Bodily, Eastman, & Sturz, 2011; Cheng & 68
Gallistel, 2005; Lubyk, Dupuis, Gutiérrez & Spetch, 2012; McGregor, Jones, Good, & Pearce, 69
2006; Pearce, Good, Jones, & McGregor, 2004; Sturz, Gurley, & Bodily, 2011). For 70
clarification, the principal axis of space is a summary parameter of the entire shape that passes 71
through the centroid and approximate length of the entire space (for a detailed mathematical and 72
mechanical definition, see Cheng, 2005, Cheng & Gallistel, 2005). 73
In orientation tasks, after learning to locate a goal situated in one corner of an otherwise 74
featureless rectangular room, a disoriented navigator appears to attempt to return to the goal by 75
relying on its location relative to geometric cues (e.g., the trained egocentric side of the principal 76
axis of space) or by relying on its location relative to features that define the corner (e.g., the 90° 77
corner formed by a short wall on the left and a long wall on the right). Using these global and 78
local geometric cues leads to equivalent (above chance) performance in these orientation tasks 79
conducted in rectangular environments (for a review, see Cheng & Newcombe, 2005). 80
Transformations (i.e., manipulations) of environmental shape has allowed researchers to 81
delineate the relative contributions of global and local geometric cues and indicate that incidental 82
encoding of environmental geometry is a fundamental and ubiquitous component of orientation 83
(Cheng, 1986; Bodily et al., 2011; Gallistel, 1990; for a review, see Cheng & Newcombe, 2005; 84
Sturz et al., 2011). 85

*Research on reference frame selection has often described the environmental axis of symmetry as the relevant cue
(Mou & McNamara, 2002; Kelly, McNamara, Bodenheimer, Carr, & Rieser, 2008), whereas research on orientation
has often described the principal axis as the relevant cue (Cheng, 2005,Cheng & Gallistel, 2005; Sturz & Bodily,
2011, 2012; Sturz, Forloines, & Bodily, 2012; Sturz, Gurley, & Bodily, 2011). The axis of symmetry and the
principal axis are often identical in built environments. Herein we refer exclusively to the principal axis, which was
identical to at least one symmetry axis in the environments used in the current studies.


Geometric Cues 6
Despite recent advances in identifying the contributions of global and local geometric 86
cues to reorientation, less is known about the relative influences of these geometric cues on 87
reference frame selection and, ultimately, the organization of spatial memories. One intriguing 88
possibility is that the geometric cues responsible for successful orientation are also the geometric 89
properties of room shape that are directly represented in memory. As a result, these are the 90
environmental cues that influence reference frame selection. A few recent studies provide 91
promise for such a possibility – for example, spatial memory research showing the influence of 92
layout axes on reference frame selection. After learning a layout of objects with a bilateral 93
symmetry axis, the selected reference frame often corresponds to the symmetry axis of the layout 94
(Greenauer & Waller, 2012; Kelly & McNamara, 2010; Mou & McNamara, 2002; Mou, Liu, & 95
McNamara, 2009; Mou, Zhao, & McNamara, 2007) . The influence of object layout axes 96
suggests that global geometric cues, such as the principal axis, might be primarily represented in 97
memory and, therefore, responsible for reference frame selection. However, commonly used 98
experimental environments investigating reference frame selection often contain redundant 99
global and local geometric cues. For example, past research on the role of room shape in 100
reference frame selection has shown that spatial memories acquired within a rectangular room 101
are organized around a reference frame selected from experienced views parallel to room axes 102
and wall surfaces (Hintzman, et al., 1981; Kelly & McNamara, 2008; Shelton & McNamara, 103
2001; Valiquette & McNamara, 2007; Valiquette et al, 2003, 2007). However, the global cue 104
defined by the principal room axis and the local cue defined by the wall surface orientations are 105
redundant (i.e., confounded) in a rectangular room. Therefore, it is unclear to what extent global 106
and local geometric cues (such as axes and wall surfaces) are represented in memory and 107
influence reference frame selection. The current studies used immersive virtual reality to 108

Geometric Cues 7
evaluate the relative saliencies of global and local geometric cues in memory and their relative 109
influence on reference frame selection. 110
The current experiments were motivated by a desire to connect the literature of reference 111
frame selection with that of orientation via environmental shape by evaluating the relative 112
saliencies of global and local geometric cues in memory and hence their influences on reference 113
frame selection. Using a virtual environment equipped with a head-mounted-display, we 114
presented participants with to-be-remembered object arrays. In viewing the object arrays, we 115
manipulated whether the experienced viewpoint was aligned or misaligned with global (i.e., the 116
principal axis of space) or local (i.e., wall orientations) geometric cues. Participants then 117
performed a sequence of eight JRDs. 118
To the extent that global and local geometric cues are incidentally encoded and 119
represented in memory, they should influence reference frame selection. Specifically, 120
participants’ JRD performance should reflect superior performance for imagined views aligned 121
with these geometric cues and inferior performance with imagined views misaligned with these 122
geometric cues. Moreover, to the extent that spatial memories are organized around these 123
incidentally encoded geometric cues, performance from experienced and novel imagined views 124
aligned with these fundamental properties of space should be equally available in memory. As a 125
result, performance for imagined views that were experienced should be equivalent to 126
performance for imagined views that were novel. Should performance for experienced and novel 127
perspectives aligned with geometric cues be equivalent and superior to performance for 128
experienced and novel perspectives misaligned with geometric cues, it would provide converging 129
evidence that geometric cues are the salient environmental cues involved in reference frame 130

Geometric Cues 8
selection and that spatial memories are organized around these fundamental geometric properties 131
of space. 132
Experiment 1 133
Experiment 1 was designed to evaluate whether a global geometric cue defined by the 134
principal axis of space is sufficient to influence reference frame selection and/or whether local 135
geometric cues defined by straight wall surfaces parallel and orthogonal to the principal axis are 136
necessary to induce a preferred reference frame. Participants studied object locations within a 137
virtual room. Room shape (Figure 1, 1st and 2nd panels) was either rectangular (containing a 138
principal axis and straight walls) or elliptical (containing a principal axis but no straight walls). 139
Because the elliptical and rectangular rooms both contain a principal axis, but only the 140
rectangular room contains straight wall surfaces parallel to the principal axis, comparison of 141
reference frame selection in the rectangular and elliptical rooms can be used to evaluate whether 142
local straight wall surfaces parallel to the global principal axis are a necessary condition for 143
reference frame selection. All participants studied the objects from two views, separated by 135°, 144
in a fixed order. Furthermore, room orientation was manipulated such that the principal axis was 145
aligned with the first experienced view and misaligned with the second experienced view or vice 146
versa. Participants then made JRDs from eight imagined perspectives in increments of 45°. 147
Based on previous work on reference frame selection (Shelton & McNamara, 2001), we 148
expected participants in the rectangular room to select a reference frame parallel to the studied 149
view aligned with the wall surfaces (and the principal axis), regardless of whether the aligned 150
view was experienced first or second. Therefore, manipulation of the orientation of the 151
rectangular room should affect reference frame selection and subsequent JRD performance. If 152
global and local cues are equally and independently represented in memory (that is, if both cue 153
types exert similar influence over reference frame selection and neither cue type requires the 154

Geometric Cues 9
presence of the other cue in order to exert such influence), then reference frame selection in the 155
elliptical room should be identical to that in the rectangular room. However, if these geometric 156
cues are not equally or independently represented in memory, then participants in the elliptical 157
room should select a reference frame from the initial study view (similar to past work using 158
circular rooms; Kelly et al, 2007; Shelton & McNamara, 2001), and JRD performance should 159
therefore be unaffected by manipulation of room axis orientation. 160
Should participants select reference frames aligned with these geometric cues, it would 161
provide evidence that not only were these cues incidentally encoded but also equally and 162
independently represented in memory. As a result, we expected that if participants were 163
incidentally encoding these fundamental geometric properties of space and representing them in 164
memory, then performance for imagined views that were experienced should be equivalent to 165
imagined views that were novel. In short, if reference frames are selected on the basis of 166
incidentally encoded geometric cues, then performance aligned with these cues should be equally 167
available in memory and performance from these views should be equivalent regardless of 168
whether they were experienced or novel. 169
Method 170
Participants. Forty-nine undergraduate students at Iowa State University participated in 171
exchange for course credit. One participant was removed due to average pointing errors larger 172
than 65° (a predetermined performance criterion). The remaining forty-eight participants were 173
randomly assigned to each of four conditions: Rectangle 0°-180°, Rectangle 135°-315°, Ellipse 174
0°-180°, or Ellipse 135°-315° (with room shape and room orientation, respectively, see below). 175
Participant gender was balanced across condition. 176

Geometric Cues 10
Stimuli and Design. The virtual environment was viewed on a head-mounted display 177
(HMD; nVisor SX111, NVIS, Reston, VA), which presented stereoscopic images of the virtual 178
environment at 1280 × 1024 resolution within a 102° (horizontal) × 64° (vertical) field of view. 179
Images viewed in the HMD were refreshed at 60 Hz and reflected moment-to-moment changes 180
in the participant’s head position and orientation. Graphics were rendered using Vizard software 181
(WorldViz, Santa Barbara, CA) on a desktop computer with Intel Core2 Quad processors and 182
Nvidia GeForce GTX 285 graphics card. 183
The virtual environment consisted of eight objects (cup, car, plant, lamp, hat, ball, apple, 184
and train) placed on the floor of a room. Objects were scaled to fit within a 30 cm3 volume. The 185
object layout was similar to that used in previous research (Mou & McNamara, 2002). The 186
surrounding room shape was rectangular or elliptical (see Figure 1, 1st and 2nd panels), and room 187
shape was manipulated between participants. The surrounding room, regardless of shape, was 8 188
meters long by 3.5 meters wide by 2.5 meters tall. Room walls were covered with a repeating 189
brick texture. Room orientation was manipulated between participants, such that the principal 190
axis was parallel to 0°-180° or 135°-315° (Figure 1, 2nd panel). 191
All participants studied the object layout from two views: first from the 135° view and 192
second from the 0° view (Figure 1, 2nd panel, shows the 0° view of the rectangular and elliptical 193
rooms with principal axes parallel to 0°-180°). After learning, participants were led to another 194
room where they were tested on their memory for object locations by performing JRDs displayed 195
on a desktop computer. JRDs required participants to imagine standing at one object, facing a 196
second object, and point toward a third object from the imagined perspective using a joystick 197
(e.g., “Imagine standing at the plant, facing the hat. Point to the ball.”). The first two objects 198
established the imagined perspective and the third object served as the pointing target. JRDs 199

Geometric Cues 11
tested eight different imagined perspectives spaced every 45° from 0° to 315°. For each 200
imagined perspective, eight unique trials were constructed requiring correct egocentric pointing 201
responses spaced every 45° from 0° to 315°. Each participant completed 64 JRDs. The 202
dependent measure for JRDs was absolute pointing error (defined by the angular distance 203
between indicated position and actual position). 204
Procedure. Participants donned the HMD and were led to the 135° view. Once the 205
participant was in position, the objects appeared on the floor and the experimenter named each 206
object in a random sequence. Participants were given 30 seconds to study the object locations, 207
after which the objects disappeared and the participant attempted to point toward each object in a 208
random order determined by the experimenter. Pointing accuracy was visually evaluated by the 209
experimenter. However, because the experimenter was unable to see the virtual objects to which 210
the participant was pointing, the experimenter focused on the overall pattern of pointing 211
judgments rather than using a criterion based on angular pointing error. After completing the 212
study-then-point procedure three times, the objects were hidden from view and the participant 213
was led to the 0° study view where the learning procedure was repeated. The HMD was 214
removed after learning was complete. 215
Following the study-then-point procedure, participants were led to another room to 216
perform JRDs. Participants first performed three practice JRDs using the locations of buildings 217
on campus, which allowed the experimenter to verbally verify that participants understood the 218
task. Participants then completed 64 JRDs in a random sequence. Pointing responses were 219
recorded when the joystick was deflected by approximately 30° from vertical. 220

Geometric Cues 12
Results 221
Theory on reference frame selection fundamentally makes predictions regarding the 222
pattern (or allocation) of errors such that participants (regardless of their magnitude of error) 223
should prefer certain perspective relative to others (Shelton & McNamara, 2001). However, to 224
date, analyses regarding preferred perspectives have typically made direct comparisons only of 225
the magnitude of absolute pointing error at one perspective to the magnitude of absolute pointing 226
error at another (or other) perspectives (Kelly et al., 2007; Kelly& McNamara, 2008, 2012; 227
Marchette et al., 2011; Mou & McNamara, 2002; Shelton & McNamara, 1997, 2001; Werner & 228
Schmidt, 1999; Yamamoto & Shelton, 2005; however, see Greenauer & Waller, 2008). To 229
evaluate performance in the current task, we conducted two types of analyses on pointing errors. 230
First, we utilized a standard method of analysis for JRDs based upon absolute pointing error 231
(Shelton & McNamara, 2001). Specifically, we evaluated absolute pointing error as a function of 232
room shape, room orientation, and imagined perspective. Second, we adopted a novel analytic 233
approach to evaluate the allocation of pointing error. Specifically, we calculated the proportion 234
of total pointing error allocated to each of the imagined perspectives separately for each 235
participant. The result of this calculation is that patterns of errors across imagined perspectives 236
are more evenly weighted across participants. Such a calculation is advantageous because error 237
patterns are the primary source of evidence used to infer reference frame organization, and 238
analyses based upon proportion of total error allowed for meaningful determination of the 239
distribution of errors across perspectives and the direct comparisons of isolated perspectives. 240
One potential disadvantage of analyzing the proportion of total error, as compared to absolute 241
error, is that it removes individual differences. Although the removal of individual differences 242
prevents analysis of main effects for between-participant variables, interactions involving 243

Geometric Cues 13
between-participant variables are still valid, as they reveal differences in error patterns across 244
between-participant variables. 245
Absolute pointing error. Figure 1 (3rd panel) shows that absolute pointing errors, 246
regardless of room shape, were smaller when imagining the experienced perspective aligned with 247
the principal axis (M = 26.02°, SEM = 2.57°) compared to imagining the experienced perspective 248
misaligned with the principal axis (M = 39.14°, SEM = 3.22°). This conclusion was supported 249
by statistical analyses. A three-way mixed analysis of variance (ANOVA) on absolute pointing 250
error with Room Shape (Rectangle, Ellipse), Room Orientation (0°-180° or 135°-315°), and 251
Imagined Perspective (every 45° from 0°-315°) as factors revealed a main effect of Imagined 252
Perspective, F(7, 308) = 2.87, p < .01, and a significant Room Orientation x Imagined 253
Perspective interaction, F(7, 308) = 3.99, p < .001. The interaction contrast between the two 254
studied perspectives (0° and 135°) and Room Orientation was also significant, F(1, 44) = 12.00, 255
p < .001. 256
Proportion of total pointing error. It should be noted that our conversion to proportion 257
of total pointing error resulted in equivalence for the between subject factors when analyzing all 258
eight imagined perspectives. However, the within-subject factor of Imagined Perspective, all 259
interactions, and the custom interaction contrasts were statistically meaningful. Moreover, the 260
conversion to proportion of total pointing error provided an a priori value for the meaningful 261
determination of whether errors were allocated equivalently across imagined perspectives (i.e., 262
proportion of total error/eight imagined perspectives = 0.125). 263
Figure 1 (4rd panel) shows the mean proportion of total pointing error plotted by imagined 264
perspective for both the Rectangle and the Ellipse. Consistent with the absolute error analysis 265
reported above, pointing error, regardless of room shape, was allocated less to the experienced 266

Geometric Cues 14
perspective aligned with the geometric cues (M = .09, SEM = .007) compared to the experienced 267
perspective misaligned with the geometric cues (M = .13, SEM = .009). This conclusion was 268
supported by statistical analyses. A three-way mixed ANOVA on proportion of total pointing 269
error with Room Shape (Rectangle, Ellipse), Room Orientation (0°-180° or 135°-315°), and 270
Imagined Perspective (every 45° from 0°-315°) as factors revealed a main effect of Imagined 271
Perspective, F(7, 308) = 2.83, p < .01, and a significant Room Orientation x Imagined 272
Perspective interaction, F(7, 308) = 4.58, p < .001. The interaction contrast between the two 273
studied perspectives (0° and 135°) and Room Orientation was also significant, F(1, 44) = 12.06, 274
p < .01. 275
Evaluation of equivalence between experienced and novel perspectives aligned with 276
geometric cues. Isolating and comparing specific perspectives that are theoretically relevant 277
among the range of imagined perspectives is not unprecedented (Shelton & McNamara, 2001). 278
As a result, we isolated analysis to four perspectives that were theoretically relevant: 1) 279
experienced-aligned (i.e., the perspective that was experienced during the study phase and was 280
aligned with both the principal axis and the long-wall orientation), 2) novel-aligned (i.e., the 281
perspective that was not experienced during the study phase and was the 180° rotationally 282
equivalent perspective from the experienced-aligned view), 3) experienced-misaligned (i.e., the 283
perspective that was experienced during the study phase and misaligned with both the principal 284
axis and the long-wall orientation), and 4) novel-misaligned (i.e., the perspective that was not 285
experienced during the study phase and was the 180° rotationally equivalent perspective from the 286
experienced-misaligned view). We excluded the other four perspectives in order to equate the 287
angular deviations among the selected comparisons. Importantly, the proportion of total pointing 288

Geometric Cues 15
error allowed the excluded perspectives to impact performance and allowed meaningful 289
comparisons across aligned and misaligned perspectives. 290
Figure 2 shows the mean proportion of total pointing error plotted by alignment type for 291
experienced and novel imagined views that were aligned and misaligned with the geometric cues 292
for both the Rectangle and the Ellipse. Consistent with absolute pointing error and proportion of 293
total pointing error reported above for all eight imagined perspectives, less pointing error was 294
allocated to perspectives that were aligned with the geometric cues (M = .10; SEM = .006) 295
compared to that of perspectives misaligned with the geometric cues (M = .13; SEM = .005). 296
Moreover, the allocation of proportion of total pointing error was equivalent for 297
experienced-imagined (M = .11; SEM = .005) and novel-imagined (M = .12; SEM = .005) views 298
that were aligned with geometric cues. These results were confirmed by a four-way mixed 299
ANOVA on proportion of total pointing error with Room Shape (Rectangle, Ellipse), Room 300
Orientation (0°-180°, 135°-315°), Alignment Type (Aligned, Misaligned), and Imagined 301
Perspective Type (Experienced, Novel) as factors which revealed only a main effect of 302
Alignment Type, F(1, 44) = 19.1, p < .001. None of the other main effects or interactions were 303
significant, Fs < 2.6, ps > .11. In addition, imagined perspective that were experienced-aligned 304
and novel-aligned were both significantly less than 0.125, one-sample t-tests, t(47) = -5.12, p < 305
.001, and t(47) = -2.5, p < .05., respectively. The imagined perspectives that were experienced-306
misaligned and novel-misaligned were not significantly different from 0.125, t(47) = 1.07, p = 307
.29, and t(47) = 1.3, p = .2, respectively. 308
Although there was no statistical difference between experienced-imagined and novel-309
imagined views aligned with the geometric cues, we acknowledge that basing theoretical 310
conclusions on empirical null effects results in statistical, conceptual, and interpretational 311

Geometric Cues 16
difficulties; however recent efforts have advocated for the importance of such effects for 312
theoretical diagnostic purposes (Gallistel, 2009). As a result, in addition to the standard null 313
hypothesis testing reported above, we also subjected these experienced-imagined and novel-314
imagined perspectives aligned with geometric cues to Bayesian analyses. Unlike standard null 315
hypothesis testing, such analyses can be used to provide evidence in support of the null 316
hypothesis (Gallistel, 2009). As shown in Table 1 (refer to Appendix A for graphical 317
representation of these analyses), results were in favor of the equivalence of performance for 318
imagined perspectives that were experienced-aligned and novel-aligned with the geometric cues. 319
Discussion 320
Memories for locations of objects learned within a rectangular or an elliptical room were 321
organized around a reference frame aligned with the principal axis, and performance was better 322
for perspectives aligned with this geometric cue compared to perspectives misaligned with this 323
geometric cue. Because straight wall surfaces were absent in the elliptical room, these results 324
indicate that a global geometric cue (i.e., principal axis of space) is independently represented in 325
memory and was sufficient to select a reference frame. 326
According to Shelton and McNamara’s (2001) theory, participants who experienced the 327
axis-aligned view first selected a reference frame aligned with that view, and they did not update 328
the reference frame upon experiencing the axis-misaligned view. In contrast, participants who 329
experienced the axis-misaligned view first also selected a reference frame parallel to the first 330
view, but they later updated to a new reference frame aligned with the principal axis because this 331
perspective provided better access to environmental cues (Valiquette et al., 2007). These 332
processes resulted in spatial memories organized around a reference frame aligned with the 333
principal axis, regardless of room shape or room orientation. Moreover, allocation of error was 334

Geometric Cues 17
equivalent for experienced perspectives and novel perspectives aligned with the principal axis.335
Collectively, these results suggest that the geometric cues were incidentally encoded and 336
represented in memory. As a result, reference frames were selected on the basis of alignment 337
with these geometric cues and performance aligned with these cues was equivalent regardless of 338
whether they were experienced or novel. 339
Although Experiment 1 indicated that a global geometric cue is independently 340
represented in memory and sufficient to influence reference frame selection, it did not 341
distinguish between the relative saliencies of global and local geometric cues in memory nor 342
their relative contributions to reference frame selection. As a result, we conducted a second 343
experiment in which the principal axis and wall surface orientations were placed in conflict in 344
order to evaluate their relative saliency in memory and their relative influence on reference frame 345
selection. 346
Experiment 2 347
Participants studied object locations within a virtual room containing a principal axis 348
diagonal (i.e., at a 45° angle) relative to the orientations of the component wall surfaces (Figure 349
3, 1st and 2nd panels). As in Experiment 1, all participants studied the object layout from two 350
views separated by 135°. Furthermore, the room orientation was manipulated such that the 351
principal axis was aligned with the first view and the wall surfaces were aligned with the second 352
view or vice versa. Participants then made JRDs from eight imagined perspectives in increments 353
of 45°. 354
If the principal axis is more saliently represented in memory compared to wall surface 355
orientations, then the principal axis should provide a more salient cue to reference frame 356
selection compared to wall surfaces. As a result, JRD performance should be best when 357

Geometric Cues 18
imagining the studied axis-aligned perspective. In contrast, if wall surface orientations are more 358
saliently represented in memory compared to the principal axis, then wall surface orientations 359
should provide a more salient cue to reference frame selection compared to the principal axis. As 360
a result, JRD performance should be best when imagining the studied wall-aligned perspective. 361
However, if the principal axis and wall surface orientations are equally represented in memory, 362
they should exert an equivalent influence on reference frame selection. As a result, participants 363
should select a reference frame from the initial study view (similar to past work with multiple 364
conflicting cues; Kelly & McNamara, 2008; Shelton & McNamara, 2001; Kelly, 2011), and JRD 365
performance should therefore be unaffected by the manipulation of room orientation. 366
Method 367
Participants. Thirty-nine undergraduate students at Iowa State University participated in 368
exchange for course credit. Three participants were removed due to average pointing errors 369
larger than 65° (a predetermined performance criterion). The remaining thirty-six participants 370
were randomly assigned to one of two room orientation conditions: 0°-180° or 135°-315° (see 371
below). Participant gender was balanced across condition. 372
Stimuli, design & procedure. Stimuli from Experiment 1 were modified by replacing 373
the surrounding room with a new room which placed the orientation of the walls in conflict with 374
the orientation of the principal axis (Figure 3, 1st and 2nd panels). Conceptually, the room was 375
composed of four square rooms, 2.5 × 2.5 meters each, which overlapped at the corners. The 376
overlapping regions of the room were removed, leaving an elongated room with two saw-tooth 377
shaped sides, each with four outer corners, or “peaks.” The resulting room is herein referred to 378
as the 4-peaks room (so as to distinguish it from the 7-peaks room used in Experiment 3). The 379
length of the room was 8.84 meters along the principal axis and the width was 3.54 meters at the 380

Geometric Cues 19
widest point in the orthogonal direction. The component walls which comprised the saw-tooth 381
sides of the room were each 1.25 meters long. Room orientation was manipulated between 382
participants, such that the principal room axis was parallel to 0°-180° or 135°-315°. All 383
participants studied first from the 135° view and second from the 0° view. Figure 3 (1st and 2nd 384
panels) shows the 0° view of the 4-peaks room with the principal axis oriented along (a) 0-180° 385
and (b) 135°-315°. The stimuli, design, and procedure were otherwise identical to those in 386
Experiment 1. 387
Results 388
Similar to Experiment 1, we conducted separate analyses regarding performance. Again, 389
we utilized a standard method of analysis for JRDs based upon absolute pointing error (Shelton 390
& McNamara, 2001), and we evaluated absolute pointing error as a function of room orientation 391
and imagined perspective. We also utilized proportion of total pointing error to evaluate the 392
allocation of pointing error by calculating the proportion of total pointing error that was allocated 393
to each of the eight imagined perspectives. 394
Absolute pointing error. Figure 3 (3rd panel, left) shows that absolute pointing errors, 395
regardless of room orientation, were smaller when imagining experienced perspectives aligned 396
with the room walls (M = 28.07°, SEM = 3.08°) than experienced perspectives aligned with the 397
principal axis (M = 39.43°, SEM = 3.94°). This conclusion was supported by statistical analyses. 398
A two-way mixed ANOVA on absolute pointing error with Room Orientation (0°-180° or 135°-399
315°) and Imagined Perspective (every 45° from 0-315°) revealed a significant Room 400
Orientation x Imagined Perspective interaction, F(7, 238) = 2.57, p < .05. The interaction 401
contrast between the two studied perspectives (0° and 135°) and Room Orientation was also 402

Geometric Cues 20
significant, F(1, 34) = 4.77, p < .05, providing further evidence that performance was best for 403
experienced perspectives aligned with the room walls. 404
Proportion of total pointing error. Figure 3 (3rd panel, right) shows the proportion of 405
total pointing error plotted by imagined perspective for each room orientation. Consistent with 406
the analyses regarding absolute pointing error reported above, pointing error, regardless of room 407
shape, was allocated less to the experienced perspective that was wall-aligned (M = .10, SEM = 408
.008) compared to the experienced perspective that was axis-aligned (M = .13, SEM = .01) This 409
conclusion was supported by statistical analyses. A two-way mixed ANOVA on proportion of 410
total pointing error with Room Orientation (0°-180° or 135°-315°) and Imagined Perspective 411
(every 45° from 0°-315°) revealed a significant Room Orientation x Imagined Perspective 412
interaction, F(7, 238) = 2.7, p < .05. The interaction contrast between the two studied 413
perspectives (0° and 135°) and Room Orientation was also significant, F(1, 34) = 4.13, p < .05, 414
providing further evidence that performance was best for experienced perspectives aligned with 415
the room walls. 416
Evaluation of equivalence between experienced and novel perspectives aligned with 417
geometric cues. To evaluate the equivalence of performance for experienced-imagined and 418
novel-imagined views aligned with geometric cues, we selected imagined perspectives that fell 419
within those categories. It is important to note, however, that unlike Experiment 1 analyses, we 420
isolated our analyses to the four perspectives that were axis-aligned or wall-aligned. Moreover, 421
we isolated the analysis for wall-aligned only to the experienced wall-aligned and its 180° 422
rotational equivalent. We excluded the other four perspectives in order to equate the angular 423
deviations among the four perspectives included for comparisons and because, unlike 424
Experiment 1, there were no perspectives that had equivalent misalignment from both the 425

Geometric Cues 21
principal axis and wall orientations. Importantly, the proportion of total pointing error allowed 426
excluded perspectives to impact performance and meaningful comparisons across axis-aligned 427
and wall-aligned perspectives. 428
Figure 4 shows the mean proportion of total pointing error plotted by alignment type for 429
experienced and novel imagined views aligned with these geometric cues for both room 430
orientations. Consistent with absolute pointing error and proportion of total pointing error 431
reported above for all eight imagined perspectives, the proportion of pointing error for Wall 432
Aligned (M = .10; SEM = .006) was significantly different from that of Axis Aligned (M =.13; 433
SEM =.007) but there was no significant difference between experienced-imagined (M =.12; 434
SEM = .005) and novel-imagined (M =.12; SEM =.005) views that were aligned with geometric 435
cues for both axis aligned and wall aligned. These results were confirmed by a three-way mixed 436
ANOVA on proportion of total pointing error with Room Orientation (0°-180°, 135°-315°), 437
Alignment Type (Axis Aligned, Wall Aligned), and Imagined Perspective Type (Experienced, 438
Novel) as factors which revealed only a main effect of Alignment Type , F(1,34) = 5.48, p < .05. 439
None of the other main effects or interactions were significant, Fs < 2.3, ps > .14. In addition, 440
experienced wall-aligned and novel wall-aligned perspective were both significantly less than 441
0.125, one-sample t-tests, t(35) = -3.38, p < .01, and t(35) = -2.66, p < .05, respectively. 442
Experienced and novel axis-aligned perspectives were not significantly different from 0.125, 443
t(35) = 0.83, p = .41, and t(35) = -0.01, p = .99, respectively; however, the average mean 444
proportion of total pointing error for the remaining four perspectives (M = .13, SEM = .003) was 445
significantly greater than 0.125, t(35) = 3.27, p < .01. 446
As with Experiment 1, there was no statistical difference between experienced-imagined 447
and novel-imagined views aligned with the geometric cues. As a result, in addition to the 448

Geometric Cues 22
standard null hypothesis testing reported above, we also subjected these experienced-imagined 449
and novel-imagined perspectives aligned with geometric cues to Bayesian analyses. As shown in 450
Table 1 (refer Appendix A for graphical representation of these analyses), results were in favor 451
of the equivalence of performance for imaged perspectives that were experienced-aligned and 452
novel-aligned with the geometric cues. 453
Discussion 454
When the principal axis was placed in conflict with (i.e., when it was oblique with respect 455
to) the local wall surfaces, memories for locations of objects within the room were organized 456
around a reference frame aligned and orthogonal to the wall surfaces. Local geometric cues 457
defined by wall surfaces were not only sufficient to influence reference frame selection but also 458
appeared capable of exerting a greater influence over reference frame selection compared to that 459
of global geometric cues. 460
Participants who experienced the wall-aligned view first selected a reference frame 461
aligned with that view, but they did not update the reference frame upon experiencing the axis-462
aligned view. In contrast, participants who experienced the axis-aligned view first also selected a 463
reference frame parallel to the first view, but they later updated to a new reference frame aligned 464
with the wall surfaces because this perspective provided better access to environmental cues 465
(Shelton & McNamara, 2001; Valiquette et al, 2007). These processes resulted in spatial 466
memories organized around a reference frame aligned with the wall surfaces regardless of room 467
orientation. However, allocation of error was equivalent for experienced perspectives and novel 468
perspectives aligned with principal axis and the wall surfaces. Collectively, these results suggest 469
that the geometric cues were incidentally encoded and represented in memory but that the 470
salience of local cues was greater than that of global cues. As a result, reference frames were 471

Geometric Cues 23
selected on the basis of alignment with wall surfaces. However, perspectives aligned with the 472
principal axis were also saliently represented in memory, and, as a result, performance for 473
experienced and novel perspectives aligned wall surfaces or the principal axis was equivalent. 474
It is unclear whether local geometric cues (i.e., wall surfaces) are always more saliently 475
represented in memory compared to global geometric cues (i.e., principal axis) and hence exert 476
relatively more influence on reference frame selection. For example, the relative physical 477
salience of the two cues may determine which is more saliently represented in memory and 478
hence utilized for reference frame selection, and in the orientation literature, cue salience has 479
been shown to be a contributing factor to which particular cues are preferred for reorientation 480
(Newcombe & Ratliff, 2007; Ratliff & Newcombe, 2008). 481
In order to further evaluate the relative saliency of the principal axis and wall surfaces in 482
memory and their relative influence of on reference frame selection, we conducted another 483
experiment in which we attempted to reduce the physical saliency of the wall surfaces relative to 484
that of the principal axis. In an attempt to reduce the physical saliency of the wall surfaces, we 485
shortened the component walls by 50% relative to Experiment 2. 486
Experiment 3 487
Experiment 3 was identical to Experiment 2 except the component wall surfaces forming 488
the saw-tooth sides of the room were reduced by 50% relative to the previous experiment. The 489
resulting 7-peaks room (Figure 5, 1st and 2nd panels) was used to compare the relative strengths 490
of global and local geometric cues in reference frame selection when those cues were placed in 491
conflict with one another. As with Experiment 2, if the principal axis is more saliently 492
represented in memory compared to wall surface orientations, then the principal axis should 493
provide a more salient cue to reference frame selection compared to wall surfaces. As a result, 494

Geometric Cues 24
JRD performance should be best when imagining the studied axis-aligned perspective. In 495
contrast, if wall surface orientations are more saliently represented in memory compared to the 496
principal axis, then wall surface orientations should provide a more salient cue to reference 497
frame selection compared to the principal axis. As a result, JRD performance should be best 498
when imagining the studied wall-aligned perspective. However, if the principal axis and wall 499
surface orientations are equally represented in memory, they should exert an equivalent influence 500
on reference frame selection. As a result, participants should select a reference frame from the 501
initial study view, and JRD performance should therefore be unaffected by the manipulation of 502
room orientation. 503
Method 504
Participants. Forty undergraduate students at Iowa State University participated in 505
exchange for course credit. Four participants were removed due to average pointing errors larger 506
than 65° (a predetermined performance criterion). The remaining thirty-six participants were 507
randomly assigned to one of two room orientation conditions: 0°-180° or 135°-315° (see below). 508
Participant gender was balanced across condition. 509
Stimuli, design & procedure. Stimuli from Experiment 2 were modified by replacing 510
the surrounding room with a new room composed of seven overlapping squares (see Figure 5, 1st 511
and 2nd panels). Room length and maximum width were the same as in Experiment 2, which 512
resulted in side walls that were half the length of those in Experiment 2. The stimuli, design, and 513
procedure were otherwise identical to those in Experiment 2. Figure 5 (1st panel) shows the 0° 514
view of the 7-peaks room with the principal axis oriented along (a) 0°-180° and (b) 135°-315°. 515

Geometric Cues 25
Results 516
Identical to Experiments 1 and 2, we conducted separate analyses regarding performance. 517
Again, we utilized a standard method of analysis for JRDs based upon absolute pointing error 518
(Shelton & McNamara, 2001), and we evaluated absolute pointing error as a function of room 519
orientation and imagined perspective. We also utilized proportion of total pointing error to 520
evaluate the allocation of pointing error by calculating the proportion of total pointing error that 521
was allocated to each of the eight imagined perspectives. 522
Absolute pointing error. Figure 5 (3rd panel, left) shows that absolute pointing errors 523
were smaller when imagining the first experienced perspective (i.e., the 135° perspective; M = 524
32.60°, SEM = 3.81°) compared to the second experienced perspective (i.e., the 0° perspective; 525
M = 38.19°, SEM = 2.32°), regardless of the room orientation. This conclusion was supported by 526
statistical analyses. A two-way mixed ANOVA on absolute pointing error with Room 527
Orientation (0°-180° or 135°-315°) and Imagined Perspective (every 45° from 0°-315°) as 528
factors revealed a main effect of Imagined Perspective, F(7, 238) = 3.69, p < .01, but the Room 529
Orientation x Imagined Perspective interaction was not significant, F(7, 238) = 0.56, p > .5. 530
Proportion of total pointing error. Figure 5 (3rd panel, right) shows the proportion of 531
total pointing error plotted by imagined perspective for each room orientation. Consistent with 532
the absolute error analysis reported above, proportion of total pointing error was smaller when 533
imagining the first experienced perspective (i.e., the 135° perspective; M = .10, SEM = .009) 534
compared to the second experienced perspective (i.e., the 0° perspective; M = .13, SEM = .008), 535
regardless of the room orientation. This conclusion was supported by statistical analyses. A two-536
way mixed ANOVA on proportion of total pointing error with Room Orientation (0°-180° or 537
135°-315°) and Imagined Perspective (every 45° from 0°-315°) revealed only a main effect of 538

Geometric Cues 26
Imagined Perspective, F(7, 238) = 4.44, p < .001, but the Room Orientation x Imagined 539
Perspective interaction was not significant, F(7, 238) = 0.62, p > .7. 540
Evaluation of equivalence between experienced and novel perspectives aligned with 541
geometric cues. Identical to Experiment 2, we evaluated the equivalence of performance for 542
experienced-imagined and novel-imagined views aligned with geometric cues. Again, we 543
selected imagined perspectives that fell within those categories. As with Experiment 2, we 544
isolated our analyses to the four perspectives that were axis-aligned or wall-aligned. Moreover, 545
we isolated the analysis for wall-aligned only to the experienced wall-aligned and its 180° 546
rotational equivalent. We excluded the other four perspectives in order to equate the angular 547
deviations among the four perspectives included for comparisons and because, unlike 548
Experiment 1, there were no perspectives that had equivalent misalignment from both the 549
principal axis and wall orientations. Importantly, the proportion of total pointing error allowed 550
excluded perspectives to impact performance and meaningful comparisons across axis-aligned 551
and wall-aligned perspectives. 552
Figure 6 shows the mean proportion of total pointing error plotted by alignment type for 553
experienced and novel imagined views aligned with these geometric cues for both room 554
orientations. Consistent with absolute pointing error and proportion of total pointing error 555
reported above for all eight imagined perspectives, the proportion of total pointing error for Wall 556
Aligned (M = .10; SEM = .006) was significantly different from that of Axis Aligned (M =.14; 557
SEM =.01) in the 0°-180° Room Orientation, but there was no significant difference between 558
proportion of total pointing error for Wall Aligned (M = .11; SEM = .01) and Axis Aligned (M 559
=.13; SEM =.006) in the 135°-315° Room Orientation. However, there was no significant 560
differences between experienced-imagined (M =.12; SEM = .005) and novel-imagined (M =.12; 561

Geometric Cues 27
SEM =.005) views that were aligned with geometric cues for both perspectives that were axis-562
aligned and wall-aligned. For axis aligned perspectives, the proportion of total pointing error for 563
those experiencing the 135°-315° room orientation (M = 0.11, SEM = 0.009) was significantly 564
less than that of those experiencing the 0°-180° room orientation (M = 0.14, SEM = 0.008), t(34) 565
= 2.79, p < .01. For wall-aligned perspectives, the proportion of total pointing error for those 566
experiencing the 0°-180° room orientation (M = .10, SEM = 0.006) was significantly less than 567
that of those experiencing the 135°-315° room orientation (M = 0.13, SEM = 0.007), t(34) = 3.12, 568
p < .01. These results were confirmed by a three-way mixed ANOVA on proportion of total 569
pointing error with Room Orientation (0°-180°, 135°-315°), Alignment Type (Axis Aligned, 570
Wall Aligned), and Imagined Perspective Type (Experienced, Novel) as factors which revealed 571
only a significant Room Orientation x Alignment Type interaction, F(1,34) = 12.71, p < .01. 572
None of the other main effects or interactions were significant, Fs < 1.9, ps > .18. In addition, in 573
the 0°-180° Room Orientation, the mean proportion of total pointing error for wall-aligned 574
perspectives was significantly less than 0.125, t(35) = 4.64, p < .001, whereas mean proportion 575
of total pointing error for axis-aligned perspectives was not significantly different from 0.125, 576
t(35) = 1.75, p = .09. In contrast, in the 135°-315° Room Orientation, the mean proportion of 577
total pointing error for axis-aligned perspectives was significantly less than 0.125 t(35) = 2.24, p 578
< .05, whereas mean proportion of total pointing error for wall-aligned perspectives was not 579
significantly different from 0.125, t(35) = 0.15, p = .88. Moreover, the average mean proportion 580
of total pointing error for the remaining four perspectives (M = .13, SEM = .003) was 581
significantly greater than 0.125, t(35) = 2.55, p < .05. 582
As with Experiments 1 and 2, there was no statistical difference between experienced-583
imagined and novel-imagined views aligned with the geometric cues. As a result, in addition to 584

Geometric Cues 28
the standard null hypothesis testing reported above, we also subjected these experienced-585
imagined and novel-imagined perspectives aligned with geometric cues to Bayesian analyses. As 586
shown in Table 1 (refer Appendix A for graphical representation of these analyses), results were 587
in favor of the equivalence of performance for imaged perspectives that were experienced-588
aligned and novel-aligned with the geometric cues. 589
Discussion 590
When the principal axis was placed in conflict with (i.e., when it was oblique with respect 591
to) the local wall surfaces, memories for locations of objects within the room were organized 592
around a reference frame aligned with the geometric cue experienced first. 593
According to Shelton and McNamara (2001), reference frame selection is based primarily 594
on environmental cues aligned with the first study view. Reference frame selection occurs from 595
a subsequent study view only when the subsequent view offers superior access to environmental 596
cues (i.e., alignment with a stronger environmental cue such as shown in Experiments 1 and 2). 597
Under this interpretation, the principal axis and wall surface were both sufficient for reference 598
frame selection. Reference frame selection occurred from the first study view, regardless of 599
which cue was aligned with that view, and the cue aligned with the second study view was not 600
sufficiently more salient than the former to cause selection of a new reference frame. These 601
processes resulted in spatial memories organized around a reference frame aligned with the wall 602
surfaces and the principal axis. Moreover, the allocation of error was equivalent for experienced 603
perspectives and novel perspectives aligned with principal axis and the wall surfaces. 604
Collectively, these results suggest that the geometric cues were incidentally encoded and equally 605
represented in memory. As a result, reference frames were selected on the basis the first 606

Geometric Cues 29
experienced perspective and performance for experienced and novel perspectives aligned wall 607
surfaces or the principal axis were equivalent. 608
General Discussion 609
Drawing from both the literature on reference frame selection and the literature on 610
orientation via environmental shape, this project evaluated the relative saliency of global and 611
local geometric cues in memory and their resulting influences on reference frame selection. 612
Previous work on the role of environmental shape in reference frame selection has shown that 613
rectangular rooms provide a powerful environmental cue (Hintzman, et al., 1981; Kelly & 614
McNamara, 2008; Shelton & McNamara, 2001; Valiquette & McNamara, 2007; Valiquette et al, 615
2003, 2007), such that memories are organized around reference frames selected from 616
experienced perspectives parallel to room axes and wall surfaces. However, room axis and wall 617
surface orientations are redundant cues in rectangular rooms, and, as a result, past work has been 618
unable to distinguish the relative saliencies in memory of global and local cues or their relative 619
contributions to reference frame selection. The current studies used immersive virtual reality to 620
evaluate relative saliencies of global and local geometric cues in memory and their relative 621
influence on reference frame selection. 622
In the first experiment, reference frame selection was compared after learning occurred in 623
a rectangular room (with aligned principal axis and wall surfaces) and an elliptical room (with 624
principal axis but no straight wall surfaces). Similar to past work (Shelton & McNamara, 2001), 625
reference frame selection in the rectangular room occurred from the experienced view aligned 626
with the principal axis and wall surfaces. Reference frame selection in the elliptical room 627
occurred from the experienced view aligned with the principal axis, despite the absence of 628
straight wall surfaces. The similarity between the reference frames selected in the rectangular 629

Geometric Cues 30
and elliptical rooms indicates that the principal axis of space is incidentally encoded and 630
independently represented in memory. As a result, it was sufficient to influence reference frame 631
selection. 632
The second and third experiments were designed to compare the relative saliencies of 633
global and local cues in memory and their resulting relative influences on reference frame 634
selection. To that end, the 4-peaks (Experiment 2) and 7-peaks (Experiment 3) rooms contained 635
principal axes that were oblique with respect to the wall surface orientations. Reference frame 636
selection in the 4-peaks room occurred from the experienced perspective aligned with the wall 637
surfaces, indicating the potential for local geometric cues to be more saliently represented in 638
memory compared to global geometric cues. As a result, local geometric cues exerted a greater 639
influence over reference frame selection compared to that of global geometric cues. Reference 640
frame selection in the 7-peaks room, which contained shorter (and therefore less salient) wall 641
surfaces, occurred from the first experienced perspective, regardless of whether it was aligned 642
with the principal axis or the wall surfaces. Similar to past spatial memory and spatial 643
orientation research using conflicting environmental cues (Kelly & McNamara, 2008; Shelton & 644
McNamara, 2001; Newcombe & Ratliff, 2007; Ratliff & Newcombe, 2008), global and local 645
geometric cues were equally represented in memory. As a result, reference frame selection 646
occurred from the first experienced perspective. 647
In all three experiments, experienced and novel views aligned with the geometric cues 648
appeared to be equally available in memory. Primarily, the allocation of error was equivalent for 649
experienced perspectives and novel perspectives whether these cues were aligned with wall 650
surfaces or the principal axis of space. In combination with the superior performance for 651
perspectives aligned with these geometric cues, our results suggest that both local and global 652

Geometric Cues 31
geometric cues are incidentally encoded and represented in memory. As a result, they both 653
influenced reference frame selection because spatial memories were independently organized 654
around these fundamental geometric properties of space. 655
To our knowledge, these are the first results to directly connect the literature on reference 656
frame selection with the literature on spatial orientation by means of environmental shape. These 657
are also the first results to show that experienced and novel views aligned with local or global 658
geometric cues are equally represented in memory. In short, our results suggest that the 659
geometric cues responsible for successful orientation (i.e., principal axis of space and wall 660
lengths) also appear to be the geometric cues responsible for the organization of spatial 661
memories about a frame of reference. 662
Such a conclusion bridges existing empirical and theoretical work in these areas and 663
provides the opportunity for novel hypothesis-driven predictions regarding spatial learning, 664
memory, and cognition. For example, environment size has been shown to differentially 665
influence the relative reliance on global and local geometric cues during orientation (Sturz et al., 666
2012; Sovrano, Bisazza, & Vallortigara, 2005), and future research could explore the extent to 667
which environment size differentially influences the relative saliency of global and local 668
geometric cues in memory by the extent to which they differentially influence reference frame 669
selection. 670
In summary, our results show that (a) global geometric cues such as the principal axis of 671
space is sufficient to influence reference frame selection, (b) local and global geometric cues can 672
exert differential influence on reference frame selection, and (c) performance from experienced 673
and novel views aligned with these geometric cues are equivalent. As a result, we conclude that 674
although the saliencies of these memories for local and global geometric cues can be 675

Geometric Cues 32
differentially influenced by physical changes to the environment, they are independently 676
represented in memory. Our results are consistent with prevailing theories in realms of reference 677
frame selection (Shelton & McNamara, 2001) and orientation via environment shape 678
(Newcombe & Ratliff, 2007), provide converging evidence that geometric cues are the salient 679
environmental cues involved in spatial memory organization, and explicitly connect these 680
theoretical realms by indicating that spatial memories are organized around these fundamental 681
geometric properties of space. 682

Geometric Cues 33
References
Bodily, K. D., Eastman, C. K., & Sturz, B. R. (2011). Neither by global nor local cues alone:
evidence for a unified orientation process. Animal Cognition, 14, 665-674.
149-178.
Cheng, K. (1986). A purely geometric module in the rat’s spatial representation. Cognition, 23,
149-178.
Cheng, K. (2005). Reflections on geometry and navigation. Connection Science, 17, 5-21.
Cheng, K., & Gallistel, C. R. (2005). Shape parameters explain data from spatial
transformations: Comment on Pearce et al. (2004) and Tommasi & Polli (2004). Journal of
Experimental Psychology: Animal Behavior Processes, 31, 254-259.
Cheng, K., & Newcombe, N. S. (2005). Is there a geometric module for spatial orientation?
Squaring theory and evidence. Psychonomic Bulletin & Review, 12, 1-23.
Gallistel, C. R. (1990). The organization of learning. Cambridge, MA: MIT Press.
Gallistel, C. R. (2009). The importance of proving the null. Psychological Review, 116, 439-453.
Greenauer, N. & Waller, D. (2008). Intrinsic array structure is neither necessary nor sufficient
for nonegocentric coding of spatial layouts. Psychonomic Bulletin & Review, 15, 1015-
1021.
Greenauer, N. & Waller, D. (2010). Micro- and macro-reference frames: Specifying the relations
between spatial categories in memory. Journal of Experimental Psychology: Learning,
Memory, & Cognition, 36, 938 - 957.
Hermer L., & Spelke E. S. (1994). A geometric process for spatial reorientation in young
children. Nature, 370, 57-59.
Hintzman, D. L., O’Dell, C. S., & Arndt, D. R. (1981). Orientation in cognitive maps. Cognitive

Geometric Cues 34
Psychology, 13, 149–206.
Kelly, J. W. (2011). Head for the hills: The influence of environmental slant on spatial memory
organization. Psychonomic Bulletin & Review, 18, 774-780.
Kelly, J. W., Avraamides, M. N. & Loomis, J. M. (2007). Sensorimotor alignment effects in the
learning environment and in novel environments. Journal of Experimental Psychology:
Learning, Memory & Cognition, 33, 1092-1107.
Kelly, J. W. & McNamara, T. P. (2008). Spatial memories of virtual environments: How
egocentric experience, intrinsic structure, and extrinsic structure interact. Psychonomic
Bulletin & Review, 15, 322-327.
Kelly, J. W. & McNamara, T. P. (2010). Reference frames during the acquisition and
development of spatial memories. Cognition, 116, 409-420.
Kelly, J. W., McNamara, T. P., Bodenheimer, B., Carr, T. H. & Rieser, J. J. (2008). The shape of
human navigation: How environmental geometry is used in maintenance of spatial
orientation. Cognition, 109, 281-286.
Klatzky, R. L. (1998). Allocentric and egocentric spatial representations: Definitions,
distinctions, and interconnections. In C. Freksa, C. Habel, K. F. Wender (Eds.), Lecture
Notes in Artificial Intelligence: Spatial Cognition (pp. 1-17). Berlin: Springer-Verlag.
Lee, S. A., Sovrano, V. A., & Spelke, E. S. (2012). Navigation as a source of geometric
knowledge: Young children’s use of length, angle, distance, and direction in a
reorientation task. Cognition, 123, 144-161.
Lubyk, D. M., Dupuis, B., Gutiérrez, L., & Spetch, M. L. (2012). Geometric orientation by
humans: Angles weigh in. Psychonomic Bulletin & Review 19, 436-442.

Geometric Cues 35
Marchette, S. A., Yerramsetti, A., Burns, T. J. & Shelton, A. L. (2011). Spatial memory in the
real world: long-term representations of everyday environments. Memory & Cognition, 39,
1401-1408.
McGregor, A., Jones, P. M., Good, M. A., & Pearce, J. M. (2006). Further evidence that rats rely
on local rather than global spatial information to locate a hidden goal: Reply to Cheng and
Gallistel (2005). Journal of Experimental Psychology: Animal Behavior Processes, 32, 314-
321.
McNamara, T. P., Rump, B., & Werner, S. (2003). Egocentric and geocentric frames of reference
in memory of large-scale space. Psychonomic Bulletin and Review, 10, 589–595.
Montello, D. R. (1991). Spatial orientation and the angularity of urban routes: A field study.
Environment and Behavior, 23, 47–69.
Mou, W., Liu, X. & McNamara, T. P. (2009). Layout geometry in encoding and retrieval of
spatial memory. Journal of Experimental Psychology: Human Perception and Performance,
35, 83-93.
Mou, W., & McNamara, T. P. (2002). Intrinsic frames of reference in spatial memory. Journal of
Experimental Psychology: Learning, Memory, & Cognition, 28, 162-170.
Mou, W., Zhao, M., & McNamara, T. P. (2007). Layout geometry in the selection of intrinsic
frames of reference from multiple viewpoints. Journal of Experimental Psychology:
Learning, Memory, and Cognition, 33, 145-154.
Newcombe, N. S., & Ratliff, K. R. (2007). Explaining the development of spatial reorientation:
Modularity-plus-language versus the emergence of adaptive combination. In J. Plumert & J.
Spencer (Eds.), The emerging spatial mind (pp. 53-76). New York: Oxford.
Pearce, J. M., Good, M. A., Jones, P. M., & McGregor, A. (2004). Transfer of spatial behavior

Geometric Cues 36
between different environments: Implications for theories of spatial learning and for the role
of the hippocampus in spatial learning. Journal of Experimental Psychology: Animal
Behavior Processes, 30, 135–147.
Ratliff, K. R., & Newcombe, N. S. (2008). Reorienting when cues conflict: Evidence for an
adaptive combination view. Psychological Science, 19, 1301-1307.
Shelton, A. L. & McNamara, T. P. (1997). Multiple views of spatial memory. Psychonomic
Bulletin & Review, 4, 102-106.
Shelton, A. L. & McNamara, T. P. (2001). Systems of spatial reference in human memory.
Cognitive Psychology, 43, 274-310.
Sovrano, V. A., Bisazza, A., & Vallortigara, G. (2005). Animals’ use of landmarks and metric
information to reorient: Effects of the size of the experimental space. Cognition, 97, 121-
133.
Sturz, B. R., & Bodily, K. D. (2011). Is surface-based orientation influenced by a proportional
relationship of shape parameters? Psychonomic Bulletin & Review, 18, 848-854.
Sturz, B. R., & Bodily, K. D. (2012). On discriminating between geometric strategies of surface-
based orientation. Frontiers in Psychology, 3, 112. DOI:10.3389/fpsyg.2012.00112
Sturz, B. R., Forloines, M. R., & Bodily, K. D. (2012). Enclosure size and the use of local and
global geometric cues for reorientation. Psychonomic Bulletin & Review, 19, 270-276.
Sturz, B. R., Gurley, T., & Bodily, K. D. (2011). Orientation in trapezoid-shaped enclosures:
Implications for theoretical accounts of geometry learning. Journal of Experimental
Psychology: Animal Behavior Processes, 37, 246-253.
Tommasi, L., & Polli, C. (2004). Representation of two geometric features of the environment in
the domestic chick (Gallus gallus). Animal Cognition, 7, 53-59.

Geometric Cues 37
Valiquette, C. M. & McNamara, T. P. (2007). Different mental representations for place
recognition and goal localization. Psychonomic Bulletin & Review, 14, 676-680.
Valiquette, C. M., McNamara, T. P. & Labrecque, J. S. (2007). Biased representations of the
spatial structure of navigable environments. Psychological Research, 71, 288-297.
Valiquette, C. M., McNamara, T. P. & Smith, K. (2003). Locomotion, incidental learning, and
the selection of spatial reference systems. Memory & Cognition, 31, 479-489.
Werner, S., & Schmidt, K. (1999). Environmental reference systems for large-scale spaces.
Spatial Cognition and Computation, 1, 447-473.
Yamamoto, N. & Shelton, A. L. (2005). Visual and proprioceptive representations in spatial
memory. Memory & Cognition, 33, 140-150.

Geometric Cues 38
Acknowledgments
Preparation of this manuscript was supported in part by funds from the Office of the Vice
President for Research and the Jack N. Averitt College of Graduate Studies at Georgia Southern
University to B.R.S. We are grateful to Andrew McKeever and Eric Pihlblad for assistance with
data collection and Kent Bodily for helpful discussions and comments.

Geometric Cues 39
Table 1.
Bayesian analyses including odds in favor of the null hypothesis and weight for the equivalence
of Experienced-Imagined and Novel-Imagined Views by Geometric Cue Alignment Type for each
Experiment. P-values from standard null hypothesis testing using paired-samples t-tests are
included.
Experiment Condition Odds in Favor of the Null Weight P-Value
Experiment 1
Aligned 4.9:1 0.69 .23
______________________________________________________________________________
Experiment 2
Axis Aligned 6.7:1 0.83 .47
Wall Aligned 4.9:1 0.69 .26
______________________________________________________________________________
Experiment 3
Axis Aligned 8.2:1 0.91 .76
Wall Aligned 3.4:1 0.53 .12
Note. Odds < 3:1 are considered "weak"; Odds between 3-10:1 are considered "substantial";
Odds between 10-100:1 are considered "strong"; Odds > 100:1 are considered "decisive".
Weights < 0.5 are considered "modest to negligible"; Weights between 0.5-1.0 are considered
"substantial"; Weights between 1-2 are considered "heavy"; Weights greater > 2 are considered
"crushing". For a review, see [37]. See Appendix A for graphical representation of these
analyses.

Geometric Cues 40
Figure Captions
Figure 1. 1st Panel. Perspective views of the virtual environments used in Experiment 1.
Images show the 0° view of the (a) rectangular room and the (b) elliptical room with the
principal room axis oriented along 0°-180°. 2nd Panel. Plan view of the virtual environments
used in Experiment 1. Object locations are represented by filled circles, and study views are
represented by arrows at 0° and 135°. The surrounding room was rectangular or elliptical, and
the principal axis of the room was oriented along 0°-180° or 135°-315°. 3rd Panel. Absolute
pointing error as a function of imagined perspective and room orientation after learning in the
rectangular room (left) and elliptical room (right) in Experiment 1. 4th Panel. Proportion of total
pointing error as a function of imagined perspective and room orientation after learning in the
rectangular room (left) and elliptical room (right) in Experiment 1. Dashed lines represent the
proportion of total pointing error expected on the basis of equivalence in distribution of error to
all eight perspectives. In the 3rd and 4th panels, imagined perspectives surrounded by a rectangle
or an ellipse represent perspectives aligned with the principal axis of the room (bold symbols
correspond to the 0°-180° room orientation; light symbols correspond to the 135°-315° room
orientation). Error bars represent ±1 standard error of the mean.
Figure 2. Mean proportion of total pointing error plotted by alignment type for
experienced and novel perspectives in the rectangle and ellipse of Experiment 1. Dashed line
represent the proportion of total pointing error expected on the basis of equivalence in
distribution of error to all eight perspectives. Error bars represent ±1 standard error of the mean.
Brackets indicate significant pairwise differences at p < .05 for the most theoretically relevant
comparisons.

Geometric Cues 41
Figure 3. 1st Panel. Perspective views of the 4-peaks virtual environment used in
Experiment 2. Images show the 0° view of the room with the room axis oriented along (a) 0°-
180° or (b) 135°-315°. 2nd Panel. Plan view of the 4-peaks virtual environment used in
Experiment 2. Object locations are represented by filled circles, and study views are represented
by arrows at 0° and 135°. The principal axis of the room was oriented along 0°-180° or 135°-
315°. 3rd Panel. Absolute pointing error (left) and mean proportion of total pointing error (right)
as a function of imagined perspective and room orientation after learning in the 4-peaks room in
Experiment 2. Dashed lines represent the proportion of total pointing error expected on the basis
of equivalence in distribution of error to all eight perspectives.Imagined perspectives surrounded
by a rectangle represent perspectives aligned with the principal axis of the room (bold symbols
correspond to the 0°-180° room orientation; light symbols correspond to the 135°-315° room
orientation). Error bars represent ±1 standard error of the mean.
Figure 4. Mean proportion of total pointing error plotted by alignment type for
experienced and novel perspectives in the 0°-180° and 135°-315° orientations of Experiment 2.
Dashed line represent the proportion of total pointing error expected on the basis of equivalence
in distribution of error to all eight perspectives. Error bars represent ±1 standard error of the
mean. Brackets indicate significant pairwise differences at p < .05 for the most theoretically
relevant comparisons.
Figure 5. 1st Panel. Perspective views of the 7-peaks virtual environment used in
Experiment 3. Images show the 0° view of the room with the room axis oriented along (a) 0°-
180° or (b) 135°-315°. 2nd Panel. Plan view of the 7-peaks virtual environment used in
Experiment 3. Object locations are represented by filled circles, and study views are represented
by arrows at 0° and 135°. The principal axis of the room was oriented along 0°-180° or 135°-

Geometric Cues 42
315°. 3rd Panel. Absolute pointing error (left) and mean proportion of total pointing error (right)
as a function of imagined perspective and room orientation after learning in the 7-peaks room in
Experiment 3. Dashed line represent the proportion of total pointing error expected on the basis
of equivalence in distribution of error to all eight perspectives. Imagined perspectives surrounded
by a rectangle represent perspectives aligned with the principal axis of the room (bold symbols
correspond to the 0°-180° room orientation; light symbols correspond to the 135°-315° room
orientation). Error bars represent ±1 standard error of the mean.
Figure 6. Mean proportion of total pointing error plotted by alignment type for
experienced and novel perspectives in the 0°-180° and 135°-315° orientations of Experiment 3.
Dashed line represent the proportion of total pointing error expected on the basis of equivalence
in distribution of error to all eight perspectives. Error bars represent ±1 standard error of the
mean. Brackets indicate significant pairwise differences at p < .05 for the most theoretically
relevant comparisons.

Geometric Cues 43

Figure 1.
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Proportion of Total Pointing Error
0.00
0.05
0.10
0.15
0.20
Rectangle 0o-180o
Rectangle 135o-315o
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Proportion of Total Pointing Error
0.00
0.05
0.10
0.15
0.20
Ellipse 0o-180o
Ellipse 135o-315o
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Absolute Pointing Error (degrees)
0
10
20
30
40
50
60
Rectangle 0
o
-180
o
Rectangle 135
o
-315
o
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Absolute Pointing Error (degrees)
0
10
20
30
40
50
60
Ellipse 0
o
-180
o
Ellipse 135
o
-315
o
0
135
0
135
0-180° axis
0
135
0
135
0-180° axis

Geometric Cues 44
Figure 2.
Alignment Type
Aligned Misaligned
Mean Proportion of Total Poining Error
0.00
0.05
0.10
0.15
0.20
0.25
0.30 Experienced Rectangle
Novel Rectangle
Experienced Ellipse
Novel Ellipse
*

Geometric Cues 45

Figure 3.
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Absolute Pointing Error (degrees)
0
10
20
30
40
50
60
4-Peak 0
o
-180
o
4-Peak 135
o
-315
o
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Proportion of Total Pointing Error
0.00
0.05
0.10
0.15
0.20
4-Peak 0
o
-180
o
4-Peak 135
o
-315
o
0
135
0-180° axis
5

0
135

Geometric Cues 46
Figure 4.
*
Alignment Type
Axis Aligned Wall Aligned
Mean Proportion of Total Pointing Error
0.00
0.05
0.10
0.15
0.20
0.25
0.30 Experienced 0
o
-180
o
Novel 0
o
-180
o
Experinced 135
o
-315
o
Novel 135
o
-315
o

Geometric Cues 47

Figure 5.
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Absolute Pointing Error (degrees)
0
10
20
30
40
50
60
7-Peak 0
o
-180
o
7-Peak 135
o
-315
o
Imagined Perspective (degrees)
0 45 90 135 180 225 270 315
Mean Proportion of Total Pointing Error
0.00
0.05
0.10
0.15
0.20
7-Peak 0
o
-180
o
7-Peak 135
o
-315
o
0
135
0-180° axis
3
5
0
135

Geometric Cues 48
Figure 6.
Alignment Type
Axis Aligned Wall Aligned
Mean Proportion of Total Pointing Error
0.00
0.05
0.10
0.15
0.20
0.25
0.30 Experienced 0
o
-180
o
Novel 0
o
-180
o
Experinced 135
o
-315
o
Novel 135
o
-315
o
*
*

Geometric Cues 49
Appendix A: Figure Caption
Figure 1. Graphical representation of the Bayesian analyses comparing experienced-aligned
perspectives to novel-aligned perspectives for Experiment 1 (1st panels), Experiment 2 for both
axis-aligned and wall-aligned perspectives (2nd and 3rd panels) and Experiment 3 for both axis-
aligned and wall-aligned perspectives (4th and 5th panels). (a) The likelihood function for the
mean of the experienced-aligned perspective (dashed curve) and two prior probability functions
for to two different hypotheses: the null hypothesis (solid curve), which is that the experienced-
aligned data were drawn from the same distribution as the data from the novel-aligned
perspective, and the alternative hypothesis (dotted curve) that the experienced-aligned and novel-
aligned perspectives differ. The prior probability distributions are plotted on the left axis. The
likelihood function is plotted on the right axis. (b) The odds in favor of the null as a function of
the assumed lower and upper limit on the possible size of the effect (log-log scale). The dashed
line at 1 is where the odds are equivalent for favoring the null to favoring the alternative. The
odds in favor of the null and the associated weights are also included. Odds < 3:1 are considered
"weak"; Odds between 3-10:1 are considered "substantial"; Odds between 10-100:1 are
considered "strong"; Odds > 100:1 are considered "decisive". Weights < 0.5 are considered
"modest to negligible"; Weights between 0.5-1.0 are considered "substantial"; Weights between
1-2 are considered "heavy"; Weights greater > 2 are considered "crushing". For a review, see
(Gallistel, 2009).

Geometric Cues 50
Probability Density
0
20
40
60
80
100
Proportion of Total Pointing Error
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Likelihood
0.0
0.2
0.4
0.6
0.8
1.0
Odds in Favor = 4.9
Null Prior
Likelihood
Alt Prior
Weight = 0.69
Proportion of Total Pointing Error
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Likelihood
0.0
0.2
0.4
0.6
0.8
1.0
Probability Density
0
10
20
30
40
50
Axis Aligned
Odds in Favor = 6.7
Null Prior
Likelihood
Alt Prior
Weight = 0.83
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Likelihood
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Proportion of Total Pointing Error
Probability Density
0
10
20
30
40
50
60
Wall Aligned
Odds in Favor = 4.9
Null Prior
Likelihood
Alt Prior
Weight = 0.69
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Likelihood
0
1
2
3
4
5
Proportion of Total Pointing Error
Probability Density
0
10
20
30
40
50
Axis Aligned
Odds in Favor = 8.2
Null Prior
Likelihood
Alt Prior
Weight = 0.91
0.00 0.05 0.10 0.15 0.20 0.25
Likelihood
0.0
0.5
1.0
1.5
Proportion of Total Pointing Error
Probability Density
0
10
20
30
40
50
60
Wall Aligned
Odds in Favor = 3.4
Null Prior
Likelihood
Alt Prior
Weight = 0.53
Lower/Upper Limit on Increment Prior
0.0001 0.001 0.01 0.1 1
Oddis in Favor of the Null
0.01
0.1
1
10
100
Even Odds
Lower/Upper Limit on Increment Prior
0.0001 0.001 0.01 0.1 1
Oddis in Favor of the Null
0.01
0.1
1
10
100
Even Odds
Lower/Upper Limit on Increment Prior
0.0001 0.001 0.01 0.1 1
Oddis in Favor of the Null
0.01
0.1
1
10
100
Even Odds
Lower/Upper Limit on Increment Prior
0.0001 0.001 0.01 0.1 1
Oddis in Favor of the Null
0.01
0.1
1
10
100
Even Odds
Lower/Upper Limit on Increment Prior
0.0001 0.001 0.01 0.1 1
Oddis in Favor of the Null
0.01
0.1
1
10
100
Even Odds
Appendix A
Experiment 1
Experiment 2
Experiment 3
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