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1 IntroductionArchitecture and urban forms are usually created in a relatively contingent and intui-tive way in large-scale urban design processes. They sometimes lack a systematicanalysis of visual and environmental effects, which may result in an urban project ofthe wrong scale, or unpredictability in the environmental impact of site development.In this paper we focus on developing a tool of GIS-based visibility analysis with thetheoretical proposition that we can analyze urban open space in a 3D way. We arguethat the visibility analysis of (3D) urban space can be regarded as one of the funda-mental aspects of urban design evaluation or urban form impact analysis. Througha review of the recent development of urban visibility analysis, some significant2D and 3D approaches of visibility analyses are examined and a new proposition ofGIS-based 3D visibility analysis called Viewsphere is taken and discussed. Through theuse of Singapore's urban space, and an urban design competition of the SingaporeManagement University (SMU) city campus plan as a test case, the proposed Viewsphereanalysis is tested. We discuss the issue of effectiveness of the Viewsphere 3D visibilitytool to the urban design evaluation.

2 A review of approaches of 2D and 3D visibility analyses in urban space2.1 Visibility analysis in urban design traditionThe idea that the human perception of urban space is structured by urban form orurban spatial configuration has been a common proposition taken by urban research-ers and urban designers for decades (Appleyard, 1976; Batty, 2001; Benedikt, 1979;Fisher-Gewirtzman et al, 2003; Hillier, 1996; Llobera, 2003; Lynch, 1976; Rana and Batty,2004; Teller, 2003; Turner, 2003). It has been suggested that complex human percep-tion, cognition, or spatial behavior may be related to some simple physical propertiesof the environment. The proposition implies that human perception is influenced and toa certain extent can be manipulated by reconfiguring physical urban form. It suggests

Viewsphere: a GIS-based 3D visibility analysis for urbandesign evaluation

Perry Pei-Ju Yang, Simon Yunuar Putra, Wenjing LiDepartment of Architecture, School of Design and Environment, National University ofSingapore, 4 Architecture Drive, Singapore 117566; e-mail: [email protected],[email protected], [email protected] 26 September 2005; in revised form 9 August 2006; published online 17 August 2007

Environment and Planning B: Planning and Design 2007, volume 34, pages 971 ^ 992

Abstract. Previously, GIS-based visibility analysis has been conducted mainly in two dimensions,based on the concept of an isovist in the built environment or the concept of a viewshed in terrainand landscape analysis. The Viewsphere, a GIS approach towards 3D visibility analysis is proposedfor measuring visible urban space quantitatively in a way that is different from its predecessors, theisovist and the viewshed. A test case of Singapore's urban space was conducted by evaluatingthe visibility of three alternative urban design scenarios and their potential impacts on the visualquality of open space. Both directional and nondirectional approaches were applied to the mapping ofvisibility based on the 2D and 3D indices. The proposition that 3D visibility indices are moreeffective than 2D indices was verified. The findings show that the 3D indices are sensitive to the changesof z-dimension.

DOI:10.1068/b32142

the importance of evaluating potential visual impacts of the existing and proposedurban form before urban design decisions are made.

In some traditional practices the views of pedestrians walking in the urban openspace were recorded through photographs or sketches in order to understand the visualeffects. The mapping techniques of visibility analysis in urban space can be traced backto the city design tradition (Bosselmann, 1998; Cullen, 1961; Lynch, 1976). Cullen (1961)proposed the recording of the sequential order of visual experience, focusing andstudying particularly on the town scale. A similar study of sequential visual analysiswas conducted along highways, while putting Lynch's five visual elements into practice(Lynch et al, 1964). Subsequently, Lynch expanded the approach further through avariety of experiments and suggested that we should prepare a framework plan thatlocates major viewpoints, corridors, and view fields with the specification of theirdesired quality, and that shows what is to be saved and what is to be created. Lynchrealized that there is a need of computer systems for delineating view fields, creatingdiagrams of intervisibility and view access, and defining the classification of districtsthrough the relative eye range' (Lynch, 1976). However, the lack of computing powerand tools in the 1970s limited the development of Lynch's analytical techniques, whichmade most of the traditional analytical tools or mapping techniques qualitative ratherthan quantitative. In urban design practices those techniques of visual analysis are stillnot fully utilized (Bosselmann, 1998).

2.2 Isovist and viewshed analysesThere have been other efforts to compute the visibility of urban space in a 2D waysince the 1970s and the attempts have been extended to a 3D approach recently. The 2Dtradition has been dominated by two types of analyses, the concept of an `isovist' inarchitecture and urban space, and the concept of a `viewshed' in terrain and landscapeanalysis. The notion of isovists was first mentioned by Tandy in 1967, and was furtherdeveloped computationally by Benedikt. The isovist or isovist plane is defined as set ofpoints in 2D space that are visible from a vantage point. With a different researchagenda from Lynch's urban design tradition, Benedikt suggested an easily quantifiableand susceptible way to scientific study (Benedikt, 1979). He developed the way ofmeasuring the shape of isovists through calculation of the area, perimeter, occlusivity,variance, skewness, circularity, and other indicators. Some recent research has appliedsimilar ideas to the analysis of architecture and urban space, such as a gallery, housestreets, or town center (Batty, 2001; Turner et al, 2001). These recent studies showedthat the idea of an isovist can be applied to the `enclosed' architecture and urbanspace appropriately, although it is simplified by taking a 2D `horizontal slice' of theviews. In the case of Batty a cumulative isovist analysis was performed, with the useof an agent-based simulation `StarLogo' from the Media Lab at MIT to `mimic'isovist radial arrays.

Batty raised a fundamental question on the motivation of conducting visibilityanalysis research. He argued that the issues such as `how far can we see', `how muchcan we see', and `how much space is enclosed' are the keys to developing good urbandesign (Batty, 2001). Batty's agent-based approach in isovist computation is compar-able to the GIS-based `line of sight' analysis, which is a visual line between two pointsthat shows the parts of the surface along the line that are visible to or hidden from anobserver, and which makes up a viewshed analysis when the line of sight moves acrossthe entire surface (Bratt and Booth, 2002).

The viewshed analysis is another traditional way of analyzing a visibility field; itcan be described as the terrain visible from a major viewpoint, and is basically appliedto the landscape with terrain and topographic differentiation (Lynch, 1976). In recent

972 P P-J Yang, S Y Putra, W Li

GIS applications the viewshed can also be defined as the grid cells in a digitalelevation model that can be connected by means of line of sight to a viewpoint withinany specified distance. Those cells or points that are not obstructed by topographywill be visible and highlighted by mapping (Llobera, 2003). The GIS-based viewshedanalysis provides a full 3608 horizontal view orientation, and 08 to 908 vertical vieworientation. The view angles of the viewshed can be set accordingly, based on humaneyesight capability.

Compared with the isovist, which is usually a 2D bounded polygon, the GIS-basedviewshed analysis is a 2.5D concept. It sometimes generates fragmented pieces ofpatches on a surface, because the terrain may block the views in between two mutuallyvisible points or in the middle of the line of sight. Viewshed analysis in GIS is rarelyapplied to urban settings because the operation is based on raster data or TIN(triangular irregular network) data structure, which have problems of accuracy inrepresenting complex 3D geometry of urban form. There is still an absence of a GISprocedure which can integrate terrain and the built environment (Llobera, 2003). Forthe intensive urban environment with complicated terrain, the 2D visual analysis mayneed to cover both the isovist and viewshed approaches.

2.3 3D spherical approachSome efforts have been made to provide better solutions in the form of 3D analysesfor urban settings. The spherical analysis of urban geometry was originally applied toenergy-related analyses (Bosselman, 1998). We discovered that there was no practicalcomputational application of full 3D visual analysis that had been successfullydeveloped or tested until the spherical-based analyses were introduced. Among theanalyses, the sky view factor (F ) is one of the well accepted methodologies appliedmostly to the energy analysis (Bosselman, 1998; Ratti, 2002). It was developed as aGIS tool for operating the automatic delineation of the visible sky and obstructions(Souza et al, 2003). Another approach similar to sky view factor computation wasproposed by Teller's sky opening indicator, which requires double projections of itsspherical surface for its visual indicator (Teller, 2003). However, the second projectionmakes the original 3D spherical surface distorted and deformed, and easily inducesincorrect calculation.

The spatial openness index (SOI), an approach to measuring 3D visible spatialinformation was proposed by Fisher-Gewirtzman et al with the development of com-puterized tools (Fisher-Gewirtzman and Wagner, 2003; Fisher-Gewirtzman et al, 2003;2005). Compared with the sky view factor and the sky opening indicator, the SOIemphasizes the computation of volumetric space and functions like a `3D isovist'.It was developed for measuring urban open space from both inside out (where theobserver is inside a building viewing outdoor space) and outside in (where the observeris `in-between' spaces). The SOI was derived from the ratio of built volume to itsenvelope area', where a volume with a larger envelope area would potentially invitegreater interaction with the surrounding environment in terms of several components,such as fresh air, natural light, and view. Through a questionnaire to a small group ofparticipants on spatial openness, Fisher-Gewirtzman et al argued that the SOI canpredict the `perceived density' better than the traditional 2D density measurements(Fisher-Gewirtzman and Wagner, 2003; Fisher-Gewirtzman et al, 2003). These spher-ical approaches have extended the analysis of visibility from 2D to 2.5D to 3D.However, few of the 3D visibility approaches are GIS-based analyses or have beentested in real urban fabrics. We argue that a GIS environment will provide advan-tages of integrating geographic data both of a 3D built environment and of a naturallandscape with the variation of terrain.

Viewsphere: a GIS-based 3D visibility analysis 973

What do we learn from those approaches in 2D, 2.5D, and 3D visual analyses, andhow de we make use of the concepts and make better propositions? We share with theprecedent research findings and agree with the proposition that the human perceptionsof urban space should be better described and analyzed through the computation of3D visual effects of urban form. The changes of human perception can be manipulatedthrough the reconfiguration of urban form, where the consequences of urban designactions can be predicted quantitatively by the 3D visibility analysis of the pedestrians'view, which is closely related to human perception.We are also aware of a critical needof a paradigm shift from 2D to 3D analysis, from traditional Euclidean geometricanalysis to a Gibsonian spherical approach, and from the city as a top-down objectto the city as a landscape. Previous 2D Euclidean analyses have always been con-strained by certain presumed urban geometry, such as the infinite street canyon, sincethey will face irregularity and continuity problems when complex urban geometry isintroduced. A pedestrian-oriented 3D visibility analysis is needed and the computingsolutions are to be improved.

3 Development of Viewsphere visibility analysisThe conceptual and computational development of Viewsphere analysis is grounded onthe visual perception theory of the ambient optic array, Gibson's theory of directecological perception, which focuses on direct spatial experience through physicalsenses. Information and knowledge of the visible environment are gained directly byperceiving the ambient optic array. With the movement of eyes, head, body, or `bodilyexperience', we can perceive and explore new details of the environment (Gibson,1986). In the context of the urban environment we argue that the spatial propertiesof `visible space' can be defined and measured from the collective amount of geometricCartesian space occupied by ambient optic arrays that are reflected by physical sur-faces and visually perceivable from a particular vantage point. This definition impliesthe potential of developing an approach of quantitative visibility analysis in a 3D way.

The Viewsphere analysis is defined as a 3D visibility analysis by calculating thevisible `volume' that is filled with the ambient optic array, which is constructed bythe view from a specific observation point to the surrounding environmental obstruc-tion points through the `scanning' of the visual line or line of sight (figure 1). TheGIS-based Viewsphere analysis was developed and customized on the ArcGIS ver-sion 8.3 platform (ESRI Inc., Redlands, CA) using component object model-basedArcObjects and Visual Basic language version 6 (Microsoft). The Viewsphere analysisis designed especially for the analysis of 3D urban massing or landscape form, inwhich the urban built environment and terrain landscape are integrated and modelledin TIN or raster data.

To run the Viewsphere analysis, the user is required to input several basic data,such as a set of Zi values of the TIN or raster surface and a set of observation pointsOi from which the visibility analysis is operated. The vertical offset of the Cartesian `z 'value can be given to raise or offset the position of the observer point Oi and thetarget points Ti j . The z offset of 1.5m is usually given to the observer point Oi tosimulate the position of human eyes. The mathematical development is described inthe following stages.

3.1 Construction of the line of sightThe Viewsphere analysis originates from the concept of the line of sight, which is abasic tool of visibility analysis in GIS. A line of sight is not a straight line. The pointsalong the line of sight might have different z values, which are defined according tospatial reference Zi . The raster dataset Zi is defined as an extruded 2.5D model, in


which an urban geometric setting is represented in TIN or raster format in GIS. Forexample, a vector-based 3D city model was combined with a 2.5D topographic modeland was then converted to a raster-based 2.5D surface using a GIS script Add buildingto TIN'. The Viewsphere analysis can operate 3D volumetric computation on the 2.5Draster surface or dataset Zi . However, it cannot be applied to the vector data structurebecause it lacks the spatial reference that is useful for identifying the topology andtopography of a 3D urban environment. The data format of 2.5D raster surface limitsits applicability to a truly 3D environment. The current Viewsphere analysis is not ableto deal with a real 3D object or space that contains points (x, y) with multiple z values,such as a cantilever structure, a bridge, a shopping mall, or a subway station.

Several observation or vantage points Oi can be assigned in order to generate theline of sight Li j , from any observation point Oi to the target points Ti j . Assuming apoint P is the function of coordinates (xi , yi , zi ). Oi can be expressed as:

Oi � P�xi , yi , zi � , Oi 2 Zi , i � 1, 2, . . . , n . (1)

Ti j as a point T, the function of coordinates (xi j , yi j , zi j ), can be expressed as:

Ti j � T�xi j , yi j , zi j � , Ti j 2 Zi , i � 1, 2, . . . , n , j 2 �08, 3608� ; (2)

T�xi j , yi j , zi j � � P��xi � rn cos aj �, �yi � rn cos aj �, zi j � . (3)

In the GIS computation, the line of sight Li j is actually a collection of segments orpolylines between the observer Oi and the target Ti j . Li j is an optic ray projectedfrom Oi and ending on Ti j , which is derivable from a user-defined radial length rn .The visible and invisible segments of Li j indicate the visible and invisible portions ofthe sight line along the surface, as well as the location of the obstruction point Qi j

if the target Ti j is obstructed. When the target Ti j is visible, Li j will not contain any

Figure 1. The Viewsphere analysis in operation.


obstruction point Qi j , and Ti j will be the horizontally farthest visible point. In thiscase we assume that the farthest visible point from Oi is the obstruction point Qi j

(figures 2 and 3). Qi j as a point Q, the function of coordinates (xi j , yi j , zi j ), can beexplained in the form:

Qi j �Q�xi j , yi j , zi j � , if Ti j is visible, where Qi j 2 Zi , i � 1, 2, . . . , n ,

j 2 �08, 3608� ,0 , otherwise ;

8<:Q�xi j , yi j , zi j � �

P��xi � ri j cos aj � , �yi � ri j sin aj � , zi;j � , if Ti j is visible ;0 , otherwise :

�(5)

The radial length ri j can be calculated as the Pythagorean distance from Oi to everyQi j within a visible segment of Li j .

TargetTi j

ObstructionQi j

Visible

Invisible

Invisible

Visible

OriginOi

Figure 2. The line of sight Li j and its components: Oi , Ti j , and Qi j .

Figure 3. Invisible and visible parts of the line of sight Li j .


3.2 Transforming the line of sight to the Viewsphere arrayThe line of sight Li j is then transformed to the 3D Viewsphere array Si j by extrudinga 3D segment `slice of pie' from the visible 2D segment of Li j and calculating its3D properties (figure 4). The 3D segment Si j is composed of slices of verticallystacked `optic rays', in which the line of sight Li j between Oi and all visible pointsstretches to the horizontally farthest visible point Qi j [figure 4(a)]. Because of thesaturated nature of stacked optic rays, we define the 3D segment Si j as an opera-tional approach to the 3D volumetric computation of the accumulated ambientoptic arrays.

The azimuthal angle an decides the depth or Pythagorean distance between Q 0i j andQ 0i � j� 1� of each Si j segment. With the depth jQ 0i j Q 0i � j� 1� j, vertical height zi j , and theradial length ri j , the `slice of pie' or the Viewsphere array segment Si j can be computed[figure 4(b)]. The construction of the total Viewsphere array Si is defined as theaccumulation of all Viewsphere array segments Si j by 3608 rotation. It simulates a3608 view of the collective ambient optic arrays visible from the observer point Oi

towards all possible obstruction points Qi j .

3.3 Volume of sight: a 3D volumetric computation of the ambient optic arraySimilar to a 2D isovist, which is defined as the space directly visible or accessible froma specific observer point and is often taken as the entire space viewed when movingthrough 3608 or 2p radians (Batty and Rana, 2004), the total Viewsphere array Vi canbe taken as a specific form of 3D isovist which uses 3608 of 3D sight lines from aspecific observation point. It can be generated by the customized GIS-based View-sphere Analyst, an extension to the GIS software ArcGIS, developed by the authors.The 3D representation of the total Viewsphere array Si in 3D GIS appears like acollection of triangular array fans originated from an observer point in the center(figure 1). We argue that the total Viewsphere array Si as a 3D spatial representationis much closer to Gibson's concept of an ambient optic array than the 2D isovist,simply because the computation includes ambient optic arrays from all possible anglesbased on 3D environmental surfaces. The visibility structure of a Viewsphere array iscloser to a 3D spherical field than to a 2D plane surface.

Qi j

Li j

anbi j

Oi

Qi j

Qi � j� 1�

Q 0i j

Q 0i � j� 1�

Y

r

Z

X

Oi

(a) (b)

Figure 4. 3D transformation from (a) 2D line of sight Li j to (b) 3D Viewsphere array Si j byadding an and bi j .


We define the volume of sight Vi j as the 3D volumetric property of the 3D segmentSi j . The Vi j can be computed from the origin Oi , target Qi j , radius ri j , and elevationangle bi j (figure 4). Vi j can be defined in the form:

Vi j � volume �Si j � �2

3� an2p

pr 2i j zj �1

3an r

3i j tan bi j . (6)

We define that the accumulation of Vi j through 3608 or 2p rotation will constitutethe total volume of sight Vi . Let Vi be the sum of all Vi j from the origin Oi towards allpossible j, in the form:

Vi �X2pj� 0

Vi j . (7)

The volume of sight provides a GIS-based visibility measure in a 3D way. However,can we use it to understand further the 3D spatial characteristics of urban spaces?How do we transform the GIS operation of 3D visibility to effective urban formindices for measuring and comparing the degree of visibility and spatial perceptionsamong different urban configurations?

3.4 Viewsphere operation for 2D urban form indicesBefore we elaborate on the application of Viewsphere analysis to 3D urban formindices, some 2D urban form indices can be derived from the Viewsphere, such asthe visible area Ai , the visible perimeter pi , and the visible distance ri j . We define thevisible area of urban space visible from Oi (each array segment) as Ai j , in the form:

Ai j �an2p

pr 2i j . (8)

The cumulative visible area Ai represents the total 2D area visible, derivable from thesum of each segmented area Ai j from the single vantage point Oi covering 2p radians.The visible perimeter pi is the horizontal perimeter acting as the boundary of thevisible area. The visible perimeter pi can be derived from the sum of polyline seg-ments between horizontally projected Q 0i j and Q 0i � j� 1� , which can be described in theform:

pi �X3608j� 08

Q 0i j Q0i � j� 1�

�� X3608j� 08

�xj ÿ xj� 1 �2 � � yj ÿ yj� 1 �2� �1=2

. (9)

On the basis of the horizontal length of line of sight Li j collected from all angles,we can deduct statistical inferences of visible radius ri j , including maximum radius(rmax ) and minimum radius (rmin ). The maximum radius rmax is the horizontal distancefrom the vantage point Oi to the farthest visible vertical surface. The minimum radiusrmin is the shortest horizontal distance from the vantage point to the closest visiblesurface. We can then define the longest axis l as the distance of the longest possiblecontinuous axial line that is generated from the vantage point. The longest axis lconsists of two combined radii which are back to back to each other, with 1808difference. It can be expressed in the form:

l � ri j � ri � j� 1808��

max, 2�rmin � < l < 2�rmax � . (10)

The idea of longest axis l was discussed extensively in previous works related to theissues of isovists and space syntax (Batty, 2001; Batty and Rana, 2004; Benedikt, 1979;Hillier, 1996; Turner et al, 2001). Batty and Rana proposed procedures for generatingaxial lines which can lead to unique and reproducible results. A similar formula for


longest axis, or maximum `axial lines' was offered using the isovist analysis (Batty andRana, 2004), in the form:

Dmaxi � max

j kfdi j � di kg , where jyi j ÿ yi k j � p , and j 6� k . (11)

Although they were developed on the basis of different tools and procedure, Battyand Rana's axial lines can also be generated from the Viewsphere analysis, where themaximum diametric length Dmax

i is the longest axis l and can be generated fromthe observer point Oi towards obstruction points Qi j and Qik . The axial line is relatedto the whole concept of space syntax and its convex-space' generation methods. Hillierand Hanson argued that the partition of space should meet an implicit condition ofenclosure that they assume to be met by geometrically convex subspaces (Hillier andHanson, 1984). However, their method of partitioning convex spaces is not welldefined, given the continuity of space (Batty and Rana, 2004). Batty and Rana pro-posed that axial lines generated from isovists may provide a consistent method forpartitioning convex spaces, and we argue that the Viewsphere analysis provides analternative way of operation, defined by the longest axis l.

However, the establishment of axial lines can only provide partitioning of 2Dconvex spaces, and is related to 2D enclosure of spaces only. The problem comesfrom the inability of space syntax to handle the third dimension, largely because itremains a manual method in terms of its representation through axial lines (Batty andRana, 2004). We realize that there is a need to develop 3D indices of urban visibilityand to test them in the 3D urban physical environment. Based on the operation ofViewsphere analysis, 3D urban form indices I and F are proposed as in the followingdiscussion.

3.5 Viewsphere index (I )In order to compare the degree of visibility among different urban settings, we define a3D urban form indicator Viewsphere index (I ) for measuring the percentage of thevisible space that is filled up by the hypothetical spherical view area. The Viewsphereindex is defined as the 3D visible volume based on the operation of the total volume ofsight (Vi ), divided by the volume of hemisphere Hi j with the optional radius of any ri jchosen by the user, such as rmax , rave , or rmin , where,

Hi j �2

3p r 3i j . (12)

The Viewsphere array Si j and its properties (radius line ri j , area Ai j , elevation anglebi j , volume Vi j ) are defined as being inside the hemisphere Hi j . The hemisphere Hi j isgenerated from any radius ri j , which defines a hypothetical hemispheric boundary ofthe area for analysis based on each vantage point Oi . The ri j or the radii of hemisphereare defined on the basis of the urban contexts, such as the urban form surroundingthe observation point. On the basis of the specific urban site analysis, users candefine the suitable radius ri j to provide boundary limits of visible arrays to be includedin the calculation. Figure 5 shows a section of the hypothetical hemisphere.

By computing the Viewsphere array Si j, the analysis separates the visible volume VB

from invisible volumes VC and VD . The Viewsphere index, I, can be calculated from:VA , the volume constructed from sky optic arrays inside Hi j ; VB , the visible volume Vi

constructed by visible arrays from the observation point to the obstruction point of theurban and environmental surface; VC , the invisible volume behind the obstructionpoint Qi j and inside the hemisphere Hi j ; and VD , the invisible volume in front of theobstruction point Qi j (figure 5).


The computation of the Viewsphere index I is defined as the visible volume (VB ) orthe total volume of sight Vi in proportion to the volume of hemisphere Hi j , includingVA , VB , VC, and VD , in the form:

I � VB

VA � VB � VC � VD� Vi

volume�Hi j �. (13)

Any length of radius ri j , such as its statistical inferences rmax , rave , or rmin , can beapplied as the reference for constructing hemisphere Hi j . The result of I calculationdepends much on the assigned ri j that is used to calculate Hi j . In the case of Hi min , rmin

is applied to the construction of Hi j and the values of the invisible volumes VC and VD

are 0. Imin can be described in the form:

Imin �VB

VA � VB� Vi

volume�Hi min �. (14)

In our previous studies we found that Imin can be taken as an indicator of density or`perceived density', on the basis of its strong correlation with the `planning density'indictor gross plot ratio (Putra et al, 2005; Yang et al, 2005).

In this research we limit the application of Viewsphere analysis to the context of anintensive urban environment. The operation of Viewsphere analysis requires the sightline or optic ray to meet the obstruction point. This can be computed within a confinedvisible boundary rather than an unbounded open field. The `boundary effect' thatappeared in the precedent study of 2D isovist analysis is to be resolved (Batty, 2001).We intend to minimize such an effect by selecting the test case and its dataset carefully.

Compared with other spherical approaches, the Viewsphere analysis chooses adifferent approach that can easily integrate geographic data both of the built environ-ment and of landscape terrain. For example, the Viewsphere analysis is conducted bythe GIS operation of `sight line' on a raster data surface. In the case of the SOI, thevolume of visible space is computed by subtracting the number of 3D building cells andoccluded space behind them from the volume of the hemisphere (Fisher-Gewirtzmanet al, 2005).

HemisphereHi

Origin (vantage)Oi

Target

Ti j

C

DBVi j

ObstructionQi j

ASky

Figure 5. Distribution of the ambient optic array and invisible parts in Viewsphere analysis. Thehashed area represents the invisible volume (VC � VD ) and part B represents the visible volume(VB � Vi ).


3.6 From Viewsphere index (I ) to sky view factor (F )Another reason why the minimum length of radius, rmin , and associated Viewsphereindex, Imin , are solely applied in this paper is because of their connection to theindicator sky view factor, F. This is an established indicator commonly used for urbanenvironmental and climatic studies (Oke, 1987; Ratti, 2002), which can be computed as:

F � VA

VA � VB, (15)

where VB is the visible volume that is constructed by visible arrays from an observationpoint on the ground to the urban spatial geometry, including buildings and props.Under the condition that VC and VD are 0, and Imin is calculated on the basis of theinner sphere without invisible volume inside (figure 5), Imin operates more as anangular indicator rather than as a volumetric one, as does F. This relationship canbe explained both conceptually and mathematically from equations (14) and (15):

Imin � F � 1 . (16)

This direct relationship indicates that higher perceived density (in Imin ) goes withlower solar availability or daylight quality (in F ), and vice versa. It provides aproposition that can bridge the analyses both of urban visibility and of urbanclimatology. It reveals that F can be a derivative perceptual index from I, an approachthrough the visual analysis rather than the other F calculations (Oke, 1987; Ratti, 2002).The relationship acts as a perceptual index because it is related to the dimension ofenvironmental perception.

3.7 Directional and nondirectional visibility analysis based on ViewsphereThe Viewsphere analysis is operated by generating the sight line of the viewer, based onthe user-inputted optional horizontal (a) and vertical (b) view angles in the context ofurban settings. The user-inputted angle a determines the horizontally radial scope of thesight line, ranging between 08 to 3608. The user-inputted angle b determines the verticalangular view, ranging between 08 and 908, where the default is 908 (the full hemi-sphere). A full 3608 computation of the Viewsphere is regarded as a nondirectionalvisibility analysis [figure 6(a)]. The result of nondirectional analysis will be valid forraster-based interpolation analysis. The accumulation of V or I point values cangenerate a raster field, which may be referred to as the cumulative Viewsphere,Viewsphere mapping, or Viewsphere field method. The concept is similar to theaccumulated isovist field of the 2D visibility analysis (Batty, 2001; Turner, 2003;Turner et al, 2001).

The Viewsphere analysis is also capable of performing directional visibility analysis,which is based on human eyesight capability [figure 6(b)]. By setting multiple vantagepoints along a sequential path we can compute the degree of visibility and simulate thesequential experience of pedestrians using a series of directional Viewsphere indices. Tomodel the pedestrian's eyesight in directional analysis we understand that the eyesightof viewers is limited vertically and horizontally. The investigation showed that `normal'eyesight corresponds to about 1508 ^ 1808 degrees horizontal front coverage (a) and 308downward to 258 upward vertical front coverage (b) (Dreyfuss, 1993). These angularsettings are modifiable, based on the user's own preference.

The decision of applying directional or nondirectional analysis should be takenbased on the purpose of analysis and the specific urban context. The directionalanalysis tends to be applied to the simulation of sequential experience and pedestrianmovement. It will be closer to experiential or behavior-related research if the com-putation of visibility can be set on the basis of the limitation of human visual angle.


The potential applications may include the analysis of a pedestrian's temporal perceptionbased on different travel modesöfor example, wider angles for an explorative modeand a closer angle for a rushing mode. In contrast, the nondirectional analysis hasprovision for free movement of eyes, head, and shoulder without any limitation ofvisual angle. It allows an area-based mapping of the degree of visibility in a largerurban area.

4 GIS-based 2D and 3D visibility analysis using the Singapore test case4.1 Urban context of the Singapore test caseA test case for the Viewsphere analysis was conducted on the museum district located inSingapore's capital city area. The district contains several historic buildings and openspaces such as museums, libraries, colonial buildings, and the Bras Basah Park, ahistorically significant open space of Singapore. The Singapore Urban Redevelopment

(a) (b)

Observation pointNo. of storeys

Edge type

1 ^ 56 ^ 10

11 ^ 1718 ^ 2526 ^ 50

Soft edgeHard edge

Elevation (m)

124 ^ 140109 ^ 12493 ^ 10978 ^ 9362 ^ 7847 ^ 6231 ^ 4716 ^ 310 ^ 16

Figure 6. (a) Nondirectional visibility analysis: grid-like vantage sample points for raster mapping,and (b) directional visibility analysis: sequential vantage sample points (1 ^ 10) along a pedestrianroute. The white blocks are institutional buildings, which are below five storeys.


Agency proposed a vision of a city campus for the SMU and reserved seven plots in thedistrict for the development of the new campus. The proposed new city campusinduced debates among governmental agencies and the professionals of architecturebecause the plots were part of the Bras Basah Park, which maintained the quality ofopenness and the memory of history as an urban green space in downtown Singapore.Two MRT (Mass Rapid Transport) subway stations, Dhoby Ghaut MRT and theMuseum MRT, are located at the two ending points of the proposed SMU city campus.Therefore, the quality of public open spaces along this corridor between two MRTstations and through the SMU campus and other cultural facilities became a crucial issueof urban design, and drew great attention from the public during the planning stage.

4.2 Research design and GIS data requirementHow can we evaluate the visual impact of the proposed urban design plan to theexisting open space quality? More specifically, how will the urban design proposalwith least impact be selected in the case of the SMU campus design competition, inwhich the preservation of the open space quality of the Bras Basah Park is the maindesign issue? To what extent can the open space quality be conserved if the new citycampus is a necessity?

We applied the GIS-based visibility analysis to different urban scenarios of SMU'snew campus design in order to evaluate their potential visual impact on the open spacequality of the existing Bras Brasah Park. A main corridor along the Bras Basah Parkbetween two MRT stations was selected as the testing area for simulating the sequen-tial movement of pedestrians. Three urban design scenarios were selected in order totest their various visual impacts. The `no action' alternative (proposal NA) was mod-eled according to the existing site, in which the open space of the Bras Basah Park stillremains as it was. Proposal A introduced groups of new campus buildings in themiddle of the Bras Basah Park. The pattern of previous open space has been dramat-ically changed. Proposal B introduced an alternative strategy to campus development, inwhich the preservation of existing open space is targeted. New campus buildings wereproposed along the periphery of the Bras Basah Park and the openness of Bras BasahPark was maintained and even reinforced by the proposed sunken plaza (Figure 7).

Two approaches of visibility analysis were applied to the evaluation of the visualimpact of the three urban design scenarios on the open space quality (figure 6). First,the nondirectional visibility analysis was conducted by generating the accumulatedraster field according to the three urban design scenarios. A set of vantage pointswas assigned to the raster-based urban model. Each vantage point contains the resultsor values of 2D and 3D indices of visibility, which can accumulate and constitute theraster mapping or raster field by interpolating the values of indices on individualvantage points, using the technique of spatial interpolation IDW (inverse distanceweighted) in GIS (Longley et al, 2001). IDW gives an interpolated raster that is verysensitive to drastic value change between two adjacent observation points. It has beenused to estimate the visibility index in terrain analysis.

Second, the directional visibility analysis was applied to the simulation of thesequential experience of pedestrian movement along a designated path. The directionalanalysis involves movement and time dimension. In the test case the path was set alongthe corridor of Bras Basah Road, starting from the Museum MRT station toward theDohby Ghaut MRT station. Ten vantage points were positioned along the corridor inorder to operate the Viewsphere analysis.

4.3 Applying 2D and 3D indices to the test caseTwo 2D and another two 3D indices were evaluated based on the three urban designscenarios represented by 2.5D raster-based data. The 2D indices include the visible


area A and the visible perimeter p. The 3D indices include the volume of sight V andthe viewsphere index I. The 2D indices measure the 2D shape of the isovist, whichimplies various degrees of visibility. Larger area A indicates higher visible area andbetter openness. A higher value of p shows that the visible surface of the physical spaceor building envelopes are larger, which implies a higher variety of sight lines if thesame area A of urban space is taken as the basis.

We assume that the 3D indices can better describe spatial visibility because of theconsideration of the third dimension of space. A higher value of the volume of sight Vindicates a larger volume of 3D visible space. It implies that the viewer has longer sightlines to the building and to topographic surfaces horizontally and vertically. The V is adirect measure of how much spatial volume is enclosed and visible by the viewer. TheViewsphere index, indicates the volume of 3D visible space in proportion to the volumeof a hypothetical hemisphere with its radius equal to the distance from the viewer tothe nearest building surface. We can compare the relative visibility among differenturban configurations using the I indicator.

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Figure 7. Three proposals for the Singapore Management University campus: (a) proposal NA,the existing site with `no action'; (b) proposal A; (c) proposal B.


4.4 The effectiveness of 2D and 3D indicesIn order to test the effectiveness of 2D and 3D indices, a comparative study wasconducted on two different urban models. Two alternative raster models were pre-pared, based on the same 2D building plan with different building heights. The modelH1 applied the original building height and the model H2 applied the double buildingheight of the original (figure 8).

Viewsphere analysis was operated on ten sequential vantage points and the resultsof 3D indices were generated for the models H1 and H2, respectively. For the indicatorV, we found that the average value was 1132 575 m3 for the model H1, and 1833 083 m3

for the model H2. This means that a 100% increase of the overall building height hasincreased the value of average V by 62%. For the indicator I we found that the averagevalue was 0.269390 for the model H1, and 0.356168 for the model H2. This means thata 100% increase of the overall building height has increased the average value of I by32%. Both for V and for I, the significant change can be observed from figure 9. Thevalue increases of V and I imply increases in the perception of visibility, spatial scale,openness, or density. These changes will not be observable if we apply 2D indices to thetest case.

To investigate further the differences in effectiveness between 2D and 3D indices,we applied the 2D visible area A and 3D volume of sight V to the same raster surfacemodels of each proposal: NA, A, and B (figure 10). Although it should be noted thatthe two indices have different metric units, one m2 and the other m3, we have observed

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Figure 8. 3D models of proposal NA with (a) H1: original building height (�1); and (b) H2:double building height (�2).

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Figure 9. Comparison of (a) VH1 and VH2 , and (b) IH1 and IH2 .


different patterns of the contour-like raster mapping of the 2D and 3D indices basedon the `equal interval' classification of nominal scale.

In the case of proposal NA the high values of 2D visible area A appear at twovantage points (point 1 and 2). The highest 3D volume V appears clearly at one vantagepoint (point 3). Points 2 and 3 are located at the southern part of the park, surroundedby building objects, in which both A and V reach their peak values. Point 1 at thenorthwest end of the park shows a higher value of A (or 2D isovist) and a lower value

Area A Volume of sight V

Area A Volume of sight V

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Figure 10. Comparisons of the 2D visible area A and the 3D volume of sight V for (a) proposal NA,(b) proposal A, and (c) proposal B. Numbers 1 ^ 3 label vantage points referred to in the text.


of V (or 3D visible volume). It is because the terrain at the north boundary is muchlower than the surrounding buildings that the value of V (or the 3D visible volume)that is enclosed by surrounding objects appears lower [figure 10(a)].

In the case of proposal A, both 2D and 3D visibility decreases because newcampus buildings occupy the central open space of Bras Basah Park. We can observethat both 2D and 3D mappings show a corridor with higher visibility in between theHistory Museum and Arts Museum. In SMU's campus design competition a visualcorridor between the two civic buildings was required as part of the urban designguideline in the test case [figure 10(b)].

In the case of proposal B, with the main feature of a sunken plaza, both 2D and 3Dvisibility decreases slightly. Contrary to the conventional notion that a sunken plazamay improve visibility, the vantage points in the sunken plaza show reduced 2D and3D visibility. When the viewer's position is set inside the sunken plaza, the sight linewill be confined by a vertically enclosed space. The 3D visibility mapping shows a moreradical decrease in visibility than the 2D equivalent because the sunken plaza does not

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make any difference in 2D mapping. The central points of the sunken plaza show highervisibility than the peripheral ones [figure 10(c)].

Through the mapping of 2D and 3D indices, we see that both proposal A andproposal B reduce the visibility of the existing site conditionsöthough with differentpatterns. The results show that the 3D indicator is sensitive to the changes of verticaldimension. The indicator V is particularly effective in urban open spaces surroundedby vertical walls or building frontages, which formulate a substantial visible volumefrom the viewer's position. We argue that the development of 3D visibility analysis iscrucial for understanding the urban spatial visibility in an intensive urban environmentwith the z dimension.

4.5 Viewsphere index I and its implicationsAs we have defined previously, the Viewsphere index I indicates the volume of 3Dvisible space in proportion to the volume of a hypothetical hemisphere with its radiusequal to the distance from the viewer to the nearest building surface. We operated I onthe geometries of three design proposals, which may represent different situations interms of the 3D visible volume V. The value of I ranges from 0 to 1, with `near 0'indicating a lower proportion of visible volume, and `near 1' indicating a high propor-tion. For example, lower V and higher I can be found in the vantage points located insmall open spaces and near a building frontage. Higher V and lower I can be foundin the center of a large open space surrounded by remote tall buildings.

In the case of proposal NA the points with the lowest I value, below 0.1, areobserved at the c area in the south of the plot, while the points with I value below0.2 but above 0.1 can be found both at the b area of the central space and at the aarea of the northwest corner [figure 11(a)]. Values of I as high as 0.6 can only beobserved at the spaces near the edges of tall buildings. The lower I values show ahigher degree of spatial openness. At the same time, the higher I values appear ina denser and more enclosed space. A similar observation appears in the case ofproposals A and B. In the case of proposal A, the overall I increases dramatically by100% because new campus buildings occupy the central open space of Bras BasahPark. The I points that are above 0.5 appear around those new campus building areasd, e, f, and g. Relatively low I points, below 0.3, are found between the two museums[figure 11(b)]. In the case of proposal B the overall I decreases significantly. We canobserve that the lowest values of I points are inside the sunken plaza area [figure 11(c)].

On the basis of the three urban scenarios, we also applied the directional analysisto the comparison of V and I indices using the ten sequential sample points. The chartsof figure 12 represent the sequential experience of pedestrians walking through thepath [figure 6(b)]. The pattern of V shows that the existing condition of proposal NAhas the highest value, followed by proposal A and then proposal B. It reveals that thepattern of proposal A is similar to that of proposal NA, while the pattern of proposalB differs slightly.

The pattern of I appears to be a nearly converse pattern of the V result. Proposal Ahas the highest I value, followed by proposal NA and then proposal B. It apparentlyshows that proposal A increases the visual impact and proposal B reduces it in termsof the value of I. As we observed in the nondirectional raster mapping, the pedestrianmay perceive a denser and more enclosed space in the space of proposal A, and mayexperience high spatial openness in proposal B when walking along the path. Thepatterns of I in the three proposals are identical along the path. This implies that thepedestrian may experience a similar rhythm of visual form along the sequential spacein terms of Lynch's diagrammatic analysis of visual quality (Lynch, 1976).


The previous tests imply that I may contain some specific environmental meanings.When the urban design proposal brings in more building objects and formulates spaceswith enclosure, we can find that the I values around and between building objects.If more open spaces or the sunken plaza are proposed, the I values will easily go down.We argue that the meaning of I is very close to the viewer's perception of density or`perceived density', and is related to the senses of spatial enclosure.

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Figure 11. The raster field of Viewsphere index (I) for (a) proposal NA, (b) proposal A, and(c) proposal B.


4.6 Potential application to urban design evaluationThe 2D and 3D visibility analyses can be applied to the evaluation of the alternativeurban design proposals for the SMU design competitionöif the decision is driven bythe visual impact of the new design on the existing open space quality of Bras BasahPark, a historically significant green space of downtown Singapore. The 3D visibilityanalysis reveals that proposal A will significantly reduce the degree of visibility andwill increase the perceived density of the park by introducing new campus buildingsto the center of the park. However, the result also shows that proposal A can fulfillthe requirement of the planning agency that a visual corridor is needed between thetwo museum buildings [figure 10(b) and figure 11(b)]. The analysis also shows thatproposal B has a successful design strategy by placing new campus buildings at theperiphery of the park. The lowest I implies that this proposal contains the highestvisibility or lowest `perceived density' at the sunken plaza and along the path whilewalking from point 1 to point 10 [figure 11(c) and figure 12(b)].

5 ConclusionThe concepts of an isovist, a viewshed, or the quantitative description of urban spacefrom the point of view of pedestrians have been proposed in the few decades sinceTandy and Benedikt's work. However, the third dimension of isovist or viewshedanalysis is relatively rare in the current literature. The Viewsphere analysis is developedon the basis of the scholarship of the isovist and the viewshed, as well as the sphericalapproachöincluding the sky view factor, the spatial openness index, and sky opening.We explore a GIS-based approach to the measurement of 3D urban spatial visibility.In contrast to the Euclidean analysis of the spatial shape, we propose an approachcloser to Gibsonian visual space, in which the quantitative measure of 3D visibilityresults from the interplay of urban geometry and the viewer's sight lines. We assumethat the quantitative analysis of 3D visual space is one of the keys to the understandingof architectural and urban morphology. The analytical result can help to predict thespatial consequences of the proposed design intervention or the potential changes ofthe existing urban form, which will provide supporting information to the urbandesign decision-making process. The research was intended to connect the GIStechnology, visibility analysis, and urban design evaluation. By developing a newtoolöViewsphere analysisöwe tested how a GIS-based 3D visibility analysis canbe conducted to evaluate different urban design scenarios. The proposition that 3Dvisibility indices are more affective than 2D indices was verified. The findings showthat the 3D indices are sensitive to the changes of z-dimension. It is observable that theresults of V and I sequential analysis or raster mapping tend to reveal the 3D spatialcharacteristics. Building heights make significant differences. The meanings of 3D indices

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Figure 12. Charts of 3D evaluations of three proposals (NA, A, and B) for the SingaporeManagement University campus: (a) volume of sight V and (b) Viewsphere index I.


were also discussed.We argue that I is close to the meaning of perceived density. However,further studies will be needed for other spatial characteristics such as the senses ofopenness, enclosure, and spatial scale. The development of new indices is to be connectedto the empirical studies of environmental perception.

The Viewsphere analysis relies on the dataset that is constructed based on the 2.5Draster surface, with the advantage of incorporating 3D urban form and topographiclandscape features. However, we are aware of the limitation of 2.5D raster data and itsapplicability to a truly 3D environment. It cannot deal with a real 3D object or spacethat contains the point with multiple z values such as a cantilever structure, a bridge, ashopping mall, or a subway station. Besides, the quantitative indices are not sufficientfor describing other aspects of urban spatial quality. For example, the relationshipbetween the 3D visibility indices and the social dimension of urban space, which iscritical to urban design practices, is still unclear. This will require further studies basedon cross-cultural urban settings.

Acknowledgements. This research was funded by National University of Singapore and partiallyfunded by Singapore Millennium Foundation.

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ß 2007 a Pion publication printed in Great Britain


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