The role of strategic visibility in shaping wayfinding behavior in multilevel buildings

In this paper, we explore the mutual effect of prior background expectations and visibility afforded by the 3D configuration of the physical environment on wayfinding efficiency and strategy in multilevel buildings. We perform new analyses on data from 149 participants who performed six unaided and directed wayfinding tasks in virtual buildings with varying degrees of visibility. Our findings reveal that the interaction between visibility and prior background expectations significantly affects wayfinding efficiency and strategy during between-floor wayfinding tasks. We termed this interaction effect strategic visibility, which emphasizes the importance of the strategic allocation of visibility towards actionable building elements in promoting efficient wayfinding and shaping wayfinding strategy. Our study highlights the significance of strategic visibility in promoting inclusive and accessible built environments for neurodiversity. Finally, we provide an open-source dataset that can be used to develop and test new wayfinding theories and models to advance research in the emerging field of human-building interaction.


Column Name Description
task A semantically defined destination to be reached (i.e., roof-terrace, patio, office, auditiorium, reading area, study area) task_order The chronological order in which this task was executed time_since_start_of_1st_trial Elapsed Table S1.Overview of all columns in the dataset.The dataset was generated on the basis of the VR experiment by 1 .This dataset contains 890 rows × 53 columns and is available at SSRN.

(a)
For the VR study, a model of the Zollverein building was used as the Base-case building (top).This building was manipulated through changing the first floor or the staircase shafts.In the Atria condition, the floor of the first floor was interspersed with atria.In the Glass condition, the concrete shafts for the staircases were replaced with glass.
(b) An exemplary instruction screen provided to participants during the VR study.The instruction screen shows the progression through the tasks (counter at the top), the current instructions, the color associated with the goal (e.g. a blue sphere), and a hint to solve the task quickly.Participants can proceed at any time by clinging the button at the bottom.

Figure S1
. Details of the VR experimental design.In Subfig.S1a, an overview of the building conditions is given.In Subfig.S1b, the instruction screen for the participants is shown.

S2/S15
The variables of interest for this study are reported in Tab.S3.A Tukey's range test 2 was used for a pairwise comparison for the ANOVA results to understand the difference between treatment groups.The mean age across conditions is very similar (B = 33.75 ± 8.07 years, A = 33.43 ± 6.13 years, G = 33.80 ± 6.07 years) with a slightly stronger spread in age in the control group.The average speed across conditions appears very similar (B = 1.17 ± 0.13 m/s, A = 1.20 ± 0.12 m/s, G = 1.12 ± 0.20 m/s) but the Glass treatment differs significantly from the others.The total distance moved per trial varies more visibly per condition (B = 168.72 ± 191.19 m, A = 154.85± 144.16 m, G = 104.31± 114.92 m) with Glass treatment resulting in the significantly shorter time spend per trial than the other conditions.The total time spend per trial appears more similiar per condition (B = 149.27± 177.11 s, A = 131.41± 124.04 s, G = 105.2± 161.99 s) with Glass treatment only resulting in a significantly shorter time spend per trial than the control group.The average view volume varies very strongly across treatments (B = 1060.18± 476.36 m 2 , A = 1196.95± 545.96 m 2 , G = 1583.87± 362.54 m 2 ) with all conditions differing significantly from each other and the Glasscondition resulting in the highest mean view volume and the lowest variation across trials.The percentage of the trajectories between floors is very similar between the control and the Atria treatment but significantly differs for the Glass treatment (B = 29.63 ± 23.43 %, A = 28.20 ± 22.28 %, G = 42.29 ± 29.45 %).Lastly, the time participants take to move up from the ground floor to the first is significantly shorter in the Glasscondition (B = 25.45 ± 30.43 s, A = 24.13 ± 28.12 s, G = 14.86 ± 18.27 s).Table S4.Preview of data.The format of the Zollverein summary data set 1 is shown.Here, each row corresponds to a single wayfinding task performed by one participant in one of the three building conditions.

S2 Model Comparisons
To compare our models we apply anovas to identify with models fit best.First, we compare with linear models in Tab.S7.We observe that LMER significantly performs better than the linear model for every variable except 'Distance'.Furthermore, we note that the linear model with covariates does not improve the model quality significantly.Second, we compare the LMER models to discern whether covariates improve our models in Tab.S8.We observe that for velocity and the 'time to move up', the models with covariates significantly improve the model fit.
To overcome interpretability issues of complex models, we opt to represent results as marginal effects which are ill-defined 3 and therefore need to be clearly defined and used acknowledging known biases to be used for triangulation 4 .We opt for Average Marginal Effects (AME) 5 and Marginal Effects at the Mean (MEM) 6 because both are common in different disciplines.MEM is simpler as predicted values for task and visibility treatment are compared to the average response.However, it is noted that the average respond may not exist in real data 7 and is therefore rather abstract in its implication to the real world.AME tries to improve this by calculating a model prediction for all real inputs and averaging over task and visibility treatment.We compare AME and MEM for our wayfinding efficiency measures in Fig. S2 and our wayfinding strategy measures in Fig. S3.First, we notice that the overall pattern between visibility treatments remains visually similar across AME and MEM.However, there is a slight difference in values that is visually notable for time and velocity.Nonetheless, the type of marginal effects does not impact the overall outcome.Lastly, for the models with a significant improved fit with covariates, we investigate the marginal effects and observe, that only for velocity under AME we find a large substantial impact of covariates.
Finally, we are comparing our triangulation measures to determine whether our effects are robust to differences in measurement.First, for wayfinding efficiency, we find that distance and total time have very similar patterns at different scales.Velocity has a different pattern but also shows that glass is different.Distance produces the substantially largest difference between treatment conditions and is selected for the main text.Second, for wayfinding strategy, we find all measures produce a similar pattern (with Time to move up being on an inverted scale).The ratio measure has a lower response strength for one task (Reading Area) but stronger responses for other tasks (Office, Patio, and Roof Terrace).We find that the Percentage measure has the smallest confidence intervals and select it for the main text.We believe that across measures and methods we can show robust results for our main claims.
For wayfinding efficiency, we use distance (Eq.??), time (Eq.S1), and average velocity (Eq.S2) as three distinct triangulating 4 measures.For wayfinding strategy, we use the percentage of time spend between floors (Eq.??), the ratio of distance between floors and within floors (Eq.S3), and the time to move up (Eq.S4) the first floor 1 as three distinct triangulating 4 measures.Furthermore, we compare linear models and LMER and check for the impact of gender and age, see Tab.S5 for wayfinding efficiency and Tab.S6 for wayfinding strategy. 1For each trial, the time taken to reach from the same starting position to the first step of the staircase in the ground floor (in either of the two circulation cores) was calculated by evaluating participants' camera height (set by default to 1.7 meters).and Marginal Effects at the Mean (MEM) 6 are calculated to robustly show the model outcomes.

S9/S15
time since the start of the first task (excludes registration and practice time) total_distance Distance walked by the participant total_time Total time taken to complete the task building Building condition in which this task was executed age Age of the participant gender Gender reported by the participant average_speed Average participant movement speed inside the VR environment time_of_target_first_seen Time since the start of the task when the target is first observed total_distance_deviation Total distance walked minus the distance of a straight line to the target percentage_distance_deviation Total distance deviation divide by he distance of a straight line to the target vertical_head_movement Average camera elevation change horizontal_head_movement Average camera azimuth change visibility_sum Sum of rays within the field of view that hit the target visibility_avgerage Rays within the field of view that hit the target averaged along the path view_volume_sum Sum of camera view volumes minus obstacles limiting this view along the path view_volume_average Camera view volume minus obstacles limiting this view volume averaged along the path cosine_similarity_sum Sum of cosines between the walking vectors at each step and the vector pointing to the final position cosine_similarity_average extttcosine_similarity_sum divided by the number of measurements [after/before]_target_seen_[MEASURE] [MEASURE] in the time window [after/before] the target has been seen at_target_seen_view_volume View volume at the moment the target is first seen at_seen_[x,y,z] [x,y,z] coordinate at the time the target was first seen participant Anonymized unique participant identifier experimental_session Instantiation of the experiment; data collection session distance_inside Walked distance inside the vertical circulation, stairs distance_percentage_between_floors distance_inside divided by total_distance time_to_stairs Time of the first arrival to the stairs time_inside Time the participant spent inside the vertical circulation, stairs time_percentage_between_floors time_inside divided by total_time Total Time ∼ Visibility Treatment * Task + Age + Gender + (1|Participant) (S1) Average Velocity ∼ Visibility Treatment * Task + Age + Gender + (1|Participant) (S2) Ratio Between/Within Floor ∼ Visibility Treatment * Task + Age + Gender + (1|Participant) (S3) Time To Move Up ∼ Visibility Treatment * Task + Age + Gender + (1|Participant) (S4)

Table S2 .
Counts of trials and participants.Trials and participants are ordered by treatment and gender distribution.
Note: †:A Tukey's range test was used to perform a pairwise comparison for ANOVA 2 .

Table S3 .
Distribution of variables.Distributions of variables used in this study from the summary dataset 1 .

Table S5 .
Model Comparison of Wayfinding Efficiency.

Table S6 .
Model Comparison of Wayfinding Strategy.

Table S7 .
ANOVA with linear model as base line.

Table S8 .
ANOVA with LMER as base line.
Figure S2.Comparison of measurements of marginal effects of visibility and tasks on wayfinding efficiency.Average Marginal Effects (AME)