Sign Oclusion in Buildings and Urban Spaces Dynamic TRB

8/6/2019 Sign Oclusion in Buildings and Urban Spaces Dynamic TRB

1/15

USING THE SOCIAL FORCE MODEL TO OPTIMIZE SIGN LOCATION FOR PEDESTRIAN1TRAFFIC2

3Khaled Nassar4American University in Cairo5

Department of Construction and Architectural Engineering6PO Box 74 New Cairo7Cairo, Egypt8

9Telephone: +2016709413810FAX: +2016709413811

[email protected]

1415

1st

August 20101617

4971 words + 10 figures = 7,471 words1819

ABSTRACT20

Locating the best place for signage in large buildings such as airports, railway stations or large academic21buildings is an important aspect of facility management and design which has a significant impact on the22usability of the building as well as having a beneficial effect on the way-finding characteristics of the23pedestrian in these environments. This paper presents an approach for evaluating the effect of placement24on the sign occlusion in public spaces. The approach models the dynamics of occupant movement in25space and its relation to the sign location as well the occupant flow characteristics and its direction.26Occupant movement is simulated using the social force model. The criteria used for optimizing sign27

location is the likelihood of an occupant/pedestrian missing the sign based on the minimum distance28 required for that occupant/pedestrian to detect, recognize and read the sign. The simulation model allows29the designers to identify optimum location for signs in a space to maximize visibility and minimize30occlusion under certain space design and geometric conditions. The model takes into account the31geometric configuration of the space, the occupant/pedestrian travel flow patterns, and the location of32obstructions as well as the legibility distance. The model also accounts for variables like the location of33obstructions, sign design, and the primary and secondary travel paths of occupants/pedestrians.34

KEYWORDS:Architecture Design, Signs Occlusion, Discrete event Simulation, Design, Space design35


2/15

Khaled Nassar Page 2

USING THE SOCIAL FORCE MODEL FOR OPTIMIZING SIGN LOCATION FOR36PEDESTRIAN TRAFFIC37

1. INTRODUCTION38The location of signs in large public buildings such as airports, railway stations or large academic39

buildings will have a significant impact on the usability of the building or urban setting as well as having40 a beneficial impact on the way-finding characteristics of the pedestrian in these environments. It is no41surprise therefore that the location of the signs in large buildings and urban spaces is an important part of42the successful design of these places especially if there are flaws in the underlying design. Signing43provides pedestrians/occupants with clear instructions for easy progress to their destinations. With the44advent of more sophisticated and costly signage and announcement boards (such as Liquid Crystal45Displays, LCD), the optimum placement of these signs to maximize visibility by occupants/pedestrians46and minimize occlusion has gained an increased importance. Moreover, sign installations should be an47integral part of the space design and therefore are best planned in tandem with the design of the space48itself.49

A good sign placement plan is one that results in the signs being visible to the largest number of the50buildings occupants during their movements in the spaces. This placement should also take into51

consideration the direction of traffic flow of the building occupants. Currently however, the factors to be52considered for the installation of signs and displays have not been defined in specific numerical terms and53this leaves much of this decision to engineering judgment. There is a lack of systematic and methodical54models or techniques for optimized sign placement in spaces. There are basic guidelines on sign design55such as font, text and, lighting, however tools that aid in the sign placement are virtually inexistent. The56most detailed sign placement guidelines are for the placement of exit signs which outline the exact size57and location of sign placement in basic corridor-type layouts. On the other hand, the placements of other58wall-mounted or ceiling-mounted directional signs and announcement boards have not been studied. In59absence of such design tools, the location of the signs is often left to professional judgment or experience.60

This paper presents research efforts aiming at exploring and assessing the effect of the different space61configurations and geometry, and sign placement on the occlusion of ground-mounted and ceiling62mounted signs. This paper presents an approach that could be used for studying the location of signs and63displays in buildings and public spaces. The approach considers movement of occupants and pedestrians64in the spaces and locates the signs to optimize the probabilities of spotting the sign. The social force65model is used to simulate the occupant/pedestrian dynamics in the space. The social force has been able66to accurately model various phenomena associated with occupant movement with a relatively simple67formulation. One of the limitations of the initial formulation of the social force model is the lack of group68aggregated behavior, which was studied later by Helbing et. al. (2001). Previous research addressing69sign placement and occlusion is presented next.70

2. PREVIOUS RESEARCH71Review of previous research suggests that there is little information in the literature that addresses the72

issue of sign visibility and optimum placement of signs based on scientific models. Basic guidelines on73the placement of signs and especially way-finding and emergency egress signs have been presented in the74literature (International Code Council 2006, Arthur and Romedi 1992, Colin 1984, Follis and Hammer751979, McLendin and Blackistone 1982, Romedi 1984).These deal primarily with size of the signs, font76and text size to use (Figure 1), location of emergency exist signs, as well as lighting and materials used.77

Research on signage for emergency egress has also been carried out where the goal was to simulating the78interaction of occupants with Ssgnage systems (Filippidis et al 2008) and to study the influence of79signage on evacuation behavior within an evacuation model (Filippidis et al 2006). In addition, Filippidis80


3/15


et al (2001) studied the catchments area of exit and exit signage during emergency evacuation. Hui et al81(2009) conducted an experimental study of the effectiveness of emergency signage. In the field of traffic82engineering, a study by McDonald et al. (1988) investigated the obstruction of ground-mounted and83overhead signs by heavy vehicles using two different approaches. In addition Al Kaisy et al (Al Kasiy et84al 2003) developed a simulation model for assessing the large vehicles occlusion of signs on the85passenger cars.86

0

20

40

60

80

100

120

140

160

0 30 60 90 120

Distance Between Viewer and Sign Face (m)

CaptialLetterHeight(mm

87

Figure 1: Acceptable Legibility (adapted from Dines and Brown 2001)88

In addition to the above two directions, some governmental guidelines exist for sign placement with the89aim of aiding the public to clearly recognize activities in public buildings and spaces (Treasury Board of90Canada, 1992). These guidelines provide means of consistent sign identification to improve the service to91

the public by facilitating access and way-finding. However, these guidelines also are focused on the92physical properties of the sign itself (size, illumination, etc) and provide very little in terms of93placement location within a facility. Signage legibility distances as a function of observation angle was94studied by Hui et. al. (2007a) and verified through an experimental study. In addition, Hui et. al. (2007b)95provided a theoretical analysis of signage legibility distances as a function of observation angle.96

When planning sign placement one should consider the physical characteristics of the building or site, the97direction and volume of pedestrian/occupant traffic flow, the type of sign used, as well the placement and98design of the sign. In general, correct sign placement involves two main aspects; firstly, placing them in a99manner to minimize occlusion and maximize visibility. This involves choosing the best location in the100space to increase the number of occupants/pedestrians that can see the sign during their regular traveling101routes and minimize sign occlusion by the obstacles in the space. Secondly, correct sign placement102involves sign-specific variables such as using appropriate material, legible font and the type of sign used.103The sign design itself is an underlying input variable of the model as will be explained below.104

3. THE PROPOSED APPROACH105In this section we present the proposed approach for locating signs in public spaces considering occupant106movement. Firstly, the variables affecting visibility are identified. Next details of the social force model107implementation are presented. Thirdly, we describe how visibility was modeled and integrated with social108force model. Finally simulations using the proposed model are presented.109

AcceptableLegibility


4/15


3.1VARIABLES AFFECTING VISIBILITY110Many variables are believed to affect the occlusion of ground-mounted and ceiling signs by obstacles in111architectural and urban spaces, such as building elements (columns, stairs, street furniture, cars, other112pedestrians, etc) and therefore should be accounted for in modeling this effect. These variables include:113

Legibility distance: this is the maximum distance along the occupant/pedestrian sightline from the114subject sign where the occupant/pedestrian is able to read the sign (Figure 2). It is mainly a115function of sign design (e.g. letter size, font, color contrast, etc) and human vision characteristics116particularly vision acuity. Displacement on the other hand is the distance between the centre of a117sign and an observers central line of vision (measured at a right angle to the central line of118vision). The angle of displacement should fall between 5 and 15 degrees in order to optimize119legibility, e.g., 0.25 m of displacement per 1.00 m of viewing distance provides an angle of120approximately 15 degrees at the eye of an observer (Treasury Board of Canada, 1992). The signs121legibility and ultimate size are determined form the viewing distance and character size.122

Dis

pla

cem

ent

WidthW

123

Figure 2, Variables affecting visibility124

Divergence angle : this is the angle between the occupant/pedestrians sightline and the125centerline of the direction of travel (Figure 2).126

Legibility zone: this is an imaginary zone upstream of the sign where the occupant/pedestrian is127able to read the sign. This zone is delineated by the legibility distance along the pedestrians128sightline and the line that represents the maximum divergence angle .This zone is represented by129the shaded area in Figure 2. Note that the legibility zone is a function of the location of the130occupant and not the sign and therefore emanates from the occupant as he/she travels in the131space. As such, it may or may not intersect with the actual sign. In the sections below, we132investigate the various geometric relationships between the legibility zone and the sign location.133


5/15


The space design and the obstructions within the space: for example in building spaces, the size134of columns, walls, stairs, or any other architectural element that may hinder the visibility of the135sign.136

Occupant/pedestrian traffic volumes, walking speeds and directions of travel. This is determined137in terms of the arrival rate in occupants/hour. Expected walking speed of occupant/pedestrian:138

this variable determines the time spent by the occupant/pedestrian within the legibility zone139 described earlier. The viewing distances referred to in Figure 1 are for normal140occupant/pedestrian who is standing or walking towards a sign.141

Given these variables the goal is to develop a simulation model that can account for them in the most142realistic method. This is described next.143

3.2 MODELING OCCUPANT DYNAMICS USING THE SOCIAL FORCE MODEL144To account for variable 5 above we need to be able to simulate the occupant/pedestrian movement in145space accurately to ensure the best location of the sign. In our approach we used the social force model to146simulate occupant movement. The social force model was first introduced by Helbing and Molnr147

(Helbing and Molnr 1997, Helbing et al 2001) and has been expanded to include physical contact forces148(with similarities to granular flows) for panic situations.149

150

Figure 3: Parameters of the Social Force Model151

The model simulates the movement of each pedestrian in terms of three kinds of forces that act on the152pedestrians/occupants in space as they move (Figure 3); firstly, there are forces pushing them forward to153

their destinations. Secondly, there are forces pushing them away from obstaclew, iwf

and thirdly there154

are forces pushing pedestrian i away from pedestrian j, ijf

for all N pedestrians. The forces are all given155physical real world quantities (in Newtons for example). The model has elements which enable walkers156


6/15


to self-organize as well as learn from their geometric experiences. We first outline the structure of the157social force model, and then illustrate how it can be used to model visibility.158

Each i of the N pedestrians has mass mi has a desired speed at time t equal to)(tv

o

i and a desired159

direction,)(te

o

i . Pedestrian i therefore needs to change his current velocity)(tvi at certain rate governed160

by a constant characteristic time for each pedestrian i

. The change in velocity is therefore,161

++

=

w

iw

N

ij

ij

i

i

o

i

o

ii

ii ff

tvtetvm

dt

dvm

)(

)()()(

(1)162

The change in position is therefore given by163

dttvdr ii )(= (2)164

The forces between each two pedestrians ijf

is given by165

[ ]{ }ij

t

jiijijijijijiijijiij tvdrgndrkgBdrAf ++= )()(/)(exp (3)166

Where the first term, ijiijijinBdrA /exp

, represents the repulsive force between each two pedestrians167

i and j. This force increases exponentially governed by two constants iA iB , as the distance between them168

)ijij dr decreases ( jiij

rrr +=, where i

rand j

rare the radii of the two pedestrians and169

jiij rrd =). ij

nis the normalized vector pointing from pedestrian i to pedestrian j and is given by170

ijji drrnn ijij /)(),(

21==

. In the cases where ijd is less than jiij rrr += , two new terms are added,171

ijijij ndrkg )( and ijt

jiijij tvdrg )( , representing a foci counteracting body compression and another172

for sliding friction respectively.)( ijij drg is a function that returns 0 if ijij

dr and ijij

dr otherwise.173

Therefore, if the two pedestrians are not touching each other, these two last terms are zero otherwise these174

forces come into play. The body compression force ( ijijijndrkg )(

) is a function of the normalized175

vector pointing from pedestrian i to pedestrian j as well as the constant k. The sliding friction force176

( ijt

jiijij tvdrg )( ) is a function of the tangential direction,),( 12

ijijnntij =

, the tangential velocity177

difference, ijijt

ji tvvv = )( and the constant . The forces between the pedestrians and obstacles is178similarly given by179

[ ]{ } iwiwiiwiiwiwiiiwiiiw ttvdrgndrkgBdrAf ))(()(/)(exp += (4)180

Computer simulations of crowds of interacting pedestrians using the above model show that it can181describe several observed collective effects of pedestrian behavior very realistically and simulate182occupant traffic streams during high flow densities. In our application we are able to simulate occupant183


7/15


movement in building spaces by defining a set of predefined movement directions in the space under184consideration as will be described below. Given the above model for the movement of occupants, the next185step is the definition of visibility criteria for the sign.186

3.3 MODELING VISIBILITY OF THE SIGN187In order to evaluate the location of a certain sign, one could run a simulation of occupant movement188according to the model described above and at each time step check to see if the sign is within the189legibility region of the respective occupant/pedestrian. A cumulative sum or frequency of hits could be190used as a measure of sign visibility during the simulation. However we need to also account for the191distance to the sign and the location of the sign within the legibility zone as this is an important factor in192the visibility of the sign. Therefore we need to consider the sign as a stimuli and accordingly develop a193model where seeing the sign itself is the perception of that stimuli. The seminal theory here is that of194Weber-Fechner Law (Longo and lourenco 2007). The WeberFechner law attempts to describe the195relationship between the physical magnitudes of stimuli and the perceived intensity of the stimuli. This196law states that the smallest noticeable difference in perception is proportional to the starting value of the197stimuli. This kind of relationship can be described by a differential equation as,198

S

Skp

= (5)199

wherep

is the differential change in perception, S is the differential increase in the stimulus and S is200the stimulus at the instant. A constant factor k is to be determined experimentally. Integrating the above201equation and solving for the constant yields,202

=

oS

Skp ln (6)203

204

Figure 4, the effect of distance and displacement angle on sign visibility205


8/15


Therefore the relationship between stimulus and perception is logarithmic and applies to the visibility of206the sign. We assume that each of the i occupants/pedestrian described above has a cone of vision, i.e. the207legibility region. This describes how much of a scene shows up in an image, for any given eye point,208direction of vision, and picture plane. The wider the cone of vision, the more of the periphery is seen. If a209person's eye is looking at an object, it also sees allother objects without difficulty that are less than 30210from the direct line of sight. This cone of vision is therefore defined by two parameters, the angle of211

divergence as well as the legible viewing distance. The angle of divergence for the cone of vision and has212been reported to be about 30 degrees. The viewing distance in our model is a variable that is defined by213the size of the sign or display or by the size of the actual text on the display. Values for the viewing214distance may be derived from Figure 1. The displacement angle on the other hand accounts for the fact215that signs that are seen head on are easier to spot and read than those which are viewed at an angle.216Although the subtended angle (or solid angle in three dimensions) may be the same for different viewing217distances the angle of incidence of the center of vision line may be different. Therefore equation 6 above218needs to account for both of these stimuli; the viewing distance as well as the displacement angle, Figure2194. Furthermore, we need to account for the fact that not the whole sign may be visible from the vantage220point. Thus we could rewrite equation 6 as,221

ad PPp = (7)222

Where,223

Pd= k1 ln di/doandPa=k2 ln Cos () X Wv/W (8)224

Where Pd is the sign perception as affected by the distance stimulus and Pa is the sign perception as225affected by the visible width Wv of the entire sign width W. k1 and k2 are constants, di is the distance of226the sign from the occupant, do is the initial distance (which could be taken as 1 meter) and, is the angle227of incidence. This equation gives a value that can be used to estimate the perceived effect of the sign228(stimulus) given its relationship to the legibility zone of the occupant and pedestrian at any certain point229in time during the simulation. Various objectives can now be formulated for the visibility of the sign. The230simplest of which is minimizing the probability of missing the entire sign for all occupants in the231simulation. This entails calculating the weak visibility region of the sign placed either on the boundary or232any where in the middle of the space polygon. Alternatively we may be interested in maximizing the233probability of missing a portion of the sign for occupants coming from a certain direction. This entails234calculating the strong visibility region ofthe sign.235

During the simulation, the sign can be either completely or partially within the legibility zone.236Alternatively, the sign can be outside the legibility zone altogether. In order to calculate the visible width237of the sign Wv, we need to consider the relationship between the two edge of the legibility zone L1 and238L2 (figure 5) and the sign. If no intersection occurs then the sign could be either completely inside the239zone or completely outside the zone. On the other hand if only one line intersects the sign then the sign is240partially visible. The following algorithm could be used;241

For each t to SimTime242For each occupant i243

If AND(L1 intersects S, L2 intersects S)244Case A calculate Wv\\ signpartially visible245Else246


9/15


IF OR((L1 intersects S, L2 intersects S)247Case A calculate Wv\\ signpartially visible248Else249If OR(S1 > polar angle of L1> S2)250Case B\\ signcompletely visible251Else252

Case C\\ signcompletely invisible253Next i254Calculate P255

Next t256257258

259

260261

Figure 5, Various cases of sign visibility in relation to the legibility zone262

The visible width of the sign can be calculated from the geometrical relationship of the legibility zone and263the sign (figure 6). At each time step during the simulation and for a given sign location, we need to264calculate the total perception strength of the sign P, which is the aggregated value for all the occupants265during the simulation. This is given by,266

= =SimT

t

N

i

it

a

it

d PPP 0,, (9)267

Given the above formulation, we are able to run simulations of the occupants/pedestrians where an268accurate estimate of the visibility perception of the sign can be evaluated taking into consideration the269various variables defined above. In the next section we present an example using the developed model.270

271


10/15


272

Figure 6, Geometric variable for calculating the visible width of the sign273

274

4. AN EXAMPLE USING THE MODEL275In order to verify the model, an actual building was used to run the simulation. The space used for the276application of the model is an exhibition hall located in a large museum. The space consists of multiple277subspaces and has four different entrances and exits. The goal is determine the best place to install an278LCD that posts announcements and information about the various exhibits in the gallery. In this example279we are only considering wall-mounted LCD and therefore we want to determine the location on any of the280walls in the gallery. The design of the spaces where the major occupant traffic is expected is represented281in Figure 7. Input to the model includes the possible locations of signs, space and obstruction boundaries282and dimensions as well as occupant/pedestrian traffic flow directions. The traffic flow directions are283inputted to the model in the form of centerline for the main pathways. Each traffic flow direction is284assigned an arrival rate based on the expected number of occupants traveling. There rates assume a285Poisson distribution as explained earlier.286

287

Figure 7, the Example Building and the visibility polygon area field288


11/15


289

The expected traffic patterns are defined in a pair wise fashion between the various exits and entrances.290Four different alternate locations were investigated as shown in Figure 8. As an initial analysis the291visibility polygon from each point in the gallery is plotted as shown in figure 7. The visibility polygon292represents the visible area from a certain point in the space and this is repeated for each point in a square293

grid that covers the entire space. The area of the visibility polygon in then calculated and plotted as a field294using an iso-color scheme. The best location to place the sign would obviously be the portion of the space295with the highest visibility polygon area since this part of the space would be seen the most. However, we296need to consider pedestrian traffic patterns in order to get a more accurate picture.297

298

Figure 8, the Simulation after 5 minutes299

A tool called Right Place was developed to run the simulation. The tool is built using VBA on top of300Visio, which is a commercial charting and graphing tool. The various variables defined above are301incorporated into the developed tool. Users then define the space in the Visio interface and import the302

spaces and boundaries into RP. After defining the traffic patterns in a separate layer and inputting other303model parameters such as various constants, occupant speed, possible sign locations, etc the users can304run the simulation. Figure 8 shows the main interface of theRP. Although it may seem clear, in the case305study presented here, that the location of the sign should be placed so that is perpendicular to the line of306sight of the main flow direction, the varying occupant traffic patterns and flow directions complicate the307problem. The simulation was therefore run by means of generating occupants traveling along the flow308directions. At each time step the model checks the line of site of the occupants and sign occlusion using309the procedure described in the above section and the two measures, Pa and Pd are calculated accordingly.310


12/15


13/15


329

Figure 10, Comparison of Sign locations330

331

5. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH332Correct sign placement is a very important aspect of urban and architectural design. However, the333location of signs in architectural spaces is often left to engineering judgment. Not withstanding a few334basic guidelines on the placement of signs, there is currently no developed models for the placement of335signs to maximize visibility and minimize occlusion, even though the correct placement will have a great336impact on the usability and functionality of the building or urban context being designed. This paper337presented a discrete event simulation model that evaluates the effect of placement on the sign occlusion in338architectural spaces. The model utilized two measures: the first measure is the probability of a sign being339occluded under certain space design and geometric conditions. The second measure estimates the340likelihood of an occupant/pedestrian missing the sign based on the minimum time required for that341occupant/pedestrian to detect, recognize and read the sign.342

The model at the current stage has some limitations. For example the model does not account for waiting343areas or areas of congregations e.g. next to elevators. In addition, occupants currently do not occlude344other occupants and therefore the importance of relative speed is not accounted for. Suggestions for future345research includes expanding the model to more accurately model urban spaces and modeling the effect of346

occlusion by dynamic obstructions in the urban environment such as vehicles or other pedestrians. Also,347another direction for future research is developing an optimization routine that searches for the best348location in the space for the sign. It may also be wise to assign relative importance of certain vantage349points or to certain flow directions or for signs to be seen from one point and not others. Also, validation350of the model can be conducted though experimental analysis.351


14/15


6. REFERENCES352Ahmed Al-Kaisy, Jigar Bhatt, and Hesham Rakha (2005), Modeling the Effect of Heavy Vehicles on Sign353Occlusion at Multilane Highways, J. Transp. Engrg., Volume 131, Issue 3, pp. 219-228354

Arthur, Paul and Passini, Romedi (1992), Wayfinding: People, Signs, and Architecture,McGraw Hill,355

Inc., New York356

D. Helbing and P. Molnr (1995) Social force model for pedestrian dynamics. Physical Review E 51,3574282-4286.358

D. Helbing, P. Molnr, I. Farkas, and K. Bolay (2001) Self-organizing pedestrian movement.359Environment and Planning B 28, 361-383.360

Federal Highway Administration (2000). Manual on Uniform Traffic Control Devices FHWA, U.S.361Department of Transportation, Washington, D.C.362

Filippidis L, Galea E, Gwynne S, Lawrence P. (2006), Representing the Influence of Signage on363

Evacuation Behaviour within an Evacuation Model, Journal of Fire Protection Engineering, Vol 16,364No1, pages 37-73, 2006. DOI: 10.1177/1042391506054298365

Filippidis, L., Lawrence, P., Galea E.R., Blackshields, D. (2008), Simulating the Interaction of366Occupants with Signage systems. Proceedings of 9th IAFSS Symposium Karlsruhe, Germany, 2008,367ISNN 1817-4299, pp 389-400. DOI:10.3801/IAFSS.FSS.9-389368

Follis, J., and Hammer, D. (1979), Architectural Signing and Graphics,Whitney Library of Design, New369York370

Helbing I. J. F. D., Moln P. r and Bolay K. (2001). Self-organizing pedestrian movement. Environment371and Planning B: Planning and Design, 28:361383, 2001372

Hui X, Filippidis L, Gwynne S, Galea E.R., Blackshields, D., and Lawrence P. (2007a), "Signage373Legibility Distances as a Function of Observation Angle, Journal of Fire Protection Engineering, Vol 17,374No1, pages 41-64, 2007. DOI: 10.1177/1042391507064025.375

Hui X, Filippidis, L., Galea E.R., Gwynne S., Blackshields, D. (2007b), Experimental Study and376theoretical analysis of signage legibility distances as a function of observation angle. Proc Pedestrian and377Evacuation Dynamics 2005, Ed: N.Waldau, P.Gattermann, H.Knoflacher, M.Schreckenberg, Springer,378Germany, ISBN 878-3-540-47062-5, pp131-143, 2007.379

Hui X, L Filippidis, E R Galea, D Blackshields, P J Lawrence (2009), "Experimental Study of the380Effectiveness of Emergency Signage". Proceedings of the 4th International Symposium on Human381

Behaviour in Fire, Robinson College, Cambridge, UK, 13-15 July 2009, pp. 289-300, ISBN 978-0-382 9556548-3-1.383

International Code Council (2006), Uniform Building Code, Washington DC384

L.Filippidis, E.R.Galea, P.Lawrence and S.Gwynne. (2001), Visibility Catchment Area of Exits and385Signs", Proceedings of the 9th International Fire Science and Engineering Conference: Interflam '01, Vol.3862, pp 1529-1534, Edinburgh, Scotland, Sept 17-19 2001, published by Interscience Communications Ltd,387London, UK, 2001. ISBN 0 95323129 1 (vol2).388


15/15


Longo, M. R. & lourenco, S. F. (2007), Spatial attention and the mental number line: evidence for389characteristic biases and compression, Neuropsychologia, 45, 1400-1406390

McDonald, M., Starkey, O., and Rutley, K. S. (1988). Obstruction of Traffic Signs and Signals391Transport and Road Research Laboratory, Contractor Report 100, Department of Transport, United392Kingdom.393

Nicholas Dines and Kyle Brown (2001), Landscape Architects Portable Handbook, McGraw-Hill, New394York395

Passini, Romedi (1984), Wayfinding in Architecture,Van Nostrand Reinhold Company Inc., New York396

Treasury Board of Canada (1992), Signage: System overview and Implementation, Government of397Canada, Toronto, Canada398

Documents

Sign Oclusion in Buildings and Urban Spaces Dynamic TRB