This paper proposes the application of some well known two-dimensional
geometrical shape descriptors for the visualisation of the structure of
architectural open spaces. The paper demonstrates the use of visibility
measures such as distance to obstacles and amount of visible space to calculate
shape descriptors such as convexity and skeleton of the open space. The aim of
the paper is to indicate a simple, objective and quantifiable approach to
understand the structure of open spaces otherwise impossible due to the complex
construction of built structures.Comment: 10 pages, 9 figure

Batty, M

Rana, S

English

arXiv

UCL Discovery

Visualising the Structureof Architectural OpenSpaces Based on ShapeAnalysisSanjay Rana and Mike Batty123 issue 01, volume 02 international journal of architectural computingIJAC 2-1_2 proof  14-4-04  2:46 pm  Page 123Visualising the Structure of Architectural OpenSpaces Based on Shape AnalysisSanjay Rana and Mike BattyThis paper proposes the application of some wellknown two-dimensional geometrical shape descriptorsfor the visualisation of the structure of architecturalopen spaces.The paper demonstrates the use ofvisibility measures such as distance to obstacles andamount of visible space to calculate shape descriptorssuch as convexity and skeleton of the open space.Theaim of the paper is to indicate a simple, objective andquantifiable approach to understand the structure ofopen spaces otherwise impossible due to the complexconstruction of built structures.124IJAC 2-1_2 proof  14-4-04  2:46 pm  Page 1241. IntroductionVisualisation and interpretation of architectural spaces are intellectuallychallenging and multi-faceted exercises with fairly wide ranging applicationsand implications. In the context of urban planning, they are most commonlyundertaken to evaluate the usage of the architectural space to ensureefficient navigation and accessibility [1].These exercises clearly assume acertain influence of the built structures on the human cognition. However,what aspect of architectural space affects the human behaviour still remainsan open debate. In this respect, it is closely similar to an exercise to identifythe unknown visual variables in information visualization. Since a quantitativeanalysis of the architectural geometric structure on a large scale will be adaunting computational task, the open space bounded by the builtstructures is studied instead [2].The study of architectural open spacesessentially involves the computation of the visibility polygon or isovist(space visible all around a viewpoint, see Figure 1a) from a viewpoint andcalculating various shape measures of the visibility polygon.The isovistcomputation involves drawing rays from the viewpoint at very fine (<<0.1degrees) equal angular intervals and collecting the distance to the obstacles.A summary of the entire open space can be obtained by performing theisovist computation at a number of densely located set of viewpoints(Figure 1b). For example, Figure 1c shows the variation in the amount ofspace visible from different parts the simple T-shape.A number of othershape measures such as convexity, clustering coefficient and radial measuresare also computed to visualise the open space structure. See Batty and Rana[3] for more details on other isovist measures.Another type of open space shape description is based upon thedominant lines of visibility, which are considered to act as subtle cuessubconsciously followed by walkers. Hillier and Hanson [4] proposed thefirst such type of dominant lines of visibility called axial lines.The generationof axial lines involves the decomposition of the entire open space into nonoverlapping convex subspaces and drawing the minimum number of lineswhich could connect the subspaces (Figure 2)1.While, the calculation of  Figure 1.An open space with a T-shape object. (a) The isovist from aviewpoint and the radial {r} anddiametric {d} lengths, (b) discretisationof the open space with a dense grid ofviewpoints and, (c) area visible fromviewpoints plotted as a field.125 Visualising the Structure of Architectural Open Spaces Based on Shape AnalysisHighLow(a) (b) (c)dr1The discipline which deals with isovist analysis and axial lines in urban planning is called space syntax.IJAC 2-1_2 proof  14-4-04  2:46 pm  Page 125axial lines for relatively simple architectural open space systems is easilydone, it is non-trivial to compute an exact set of axial lines for largerspaces.The main shortcoming of this approach is that the space can besubdivided into more than one arrangement of convex subspaces as shownin Figure 2 in the simple case of the T-shape.Although we are able toproduce a consistent set of three axial lines in this simple case, in practicalexamples, axial lines are very likely to vary with the designer.In this paper, we will demonstrate three methods for the derivation ofthe lines of dominant visibility, quite similar in properties to axial lines i.e.allow partition of open space into discrete connected sub-spaces, basedentirely on shape measures.Therefore, our approach is novel and objective.The isovists and the other related measures were computed using IsovistAnalyst developed by the first author, which is an extension to the popularGeographic Information System (GIS) software ArcView. Isovist Analyst isavailable free of charge for non-commercial and non-profit purposes bywriting to the authors.The primary inputs of the analysis are 2Darchitectural plans e.g. of cities or building indoors either in GIS or CAD(e.g. DXF) formats and the layout of the viewpoints within the open spacebetween the plans. Isovist Analyst can compute upto twenty measures relatedto the shape of the open space as seen from the viewpoints.2. Dominant lines of visibilityOur approaches are based on two types of isovist measures namely theminimum radial length (MRL) and maximum diametric length (MDL) (seeFigure 1a). In short, the minimum radial length of an isovist is the shortestdistance to the boundary from a view point and the maximum diametriclength is the longest straight line in an isovist.We propose the followingthree types of transformation of the open space to extract the dominantlines of visibility.2.1. Network of lines of longest depthAs mentioned earlier,it is important to visualise the structural significance ofthe different parts of the open space for various reasons e.g.accessibility etc.Existing space syntax experiments rely entirely on the partition of open spacebased on axial lines which still remain subjective.We demonstrate here a rankand overlap elimination (ROPE) methodology which allows the extraction of a  Figure 2. Partitioning of a singleopen space into many valid convexsubspaces and the axial lines. Dottedlines indicate sub-space boundary andsolid lines are axial lines126 Sanjay Rana and Mike BattyIJAC 2-1_2 proof  14-4-04  2:46 pm  Page 126different set of lines,found to be similar to the axial lines in both orientationand properties.The methodology is explained in Figure 3.Figure 4 shows animplementation of the ROPE method for the T-shape.The resultant networkof lines of longest depth not only contains information about the dominantaxes of the space but it is in fact also a trivial solution to the famous artgallery problem [5]2.However,as can be seen from the figure,the axes conveylittle information about the structure of the T-shape.The main limitation ofthe network is that it only guarantees optimal visual coverage but noinformation about the variation in the shape of the open space.  Figure 3. Rank and Overlapelimination method for the generationof network of longest depth lines  Figure 4. Network of lines oflongest depth in the T-shape space.Note how the ROPE methodologyalso reveals the minimum number ofviewpoints (small dots) required toprovide complete visual coverage ofthe open space127 Visualising the Structure of Architectural Open Spaces Based on Shape Analysis2Our solution to the art gallery problem is one of the simplest treatments known to us to theproblem.Rank all viewpoints based on an isovist measuree.g. amount of visible area.Take the isovist of the highest ranking viewpointand remove all viewpoints from space whichoverlap this isovist.Take the isovist of the next ranking viewpointremaining in space and remove all viewpointswhich overlap this isovist.Viewpoints remain in the space ?NoYesKeep the viewpoint and longest line through theviewpointStopStartIJAC 2-1_2 proof  14-4-04  2:46 pm  Page 1272.2. Ridges of the MDL fieldAs shown in the last section, at each location/viewpoint the orientation ofthe MDL indicates the direction with the most depth visible from thelocation.Viewpoints with high MDL will therefore tend to dominate thevisibility of surrounding viewpoints. Figure 5a shows a 2.5D plot of the MDLmeasure for T-shape. It is evident from the figure that the visualisation of theridges of MDL reveals the otherwise unnoticed lines of dominant visibility,which could subconsciously influence our movement in the gallery (e.g. theexperience of “hey! What’s over there?”) as we move around in the space.There are many ways for extracting ridge-like morphological features fromsurfaces. Figure 5b shows an example of a ridge extraction from the MDLfield based on the analysis of the local curvature in the MDL surface at eachviewpoint.A detailed treatment on feature extraction is beyond the scopeof this article. For more information on curvature-based ridge featureextraction, please refer to Wood and Rana [6]. It must be noted that mostof the automated feature extraction methods suffer from various limitationsthat restrict their use therefore a manual extraction of the extracted ridgelines could be more efficient and accurate in some cases. In fact, acompletely manual drawing of the ridge lines is not likely to take too longsince the ridge lines are always long and straight.2.3. Medial axial linesMedial axis transform (MAT) or also called skeletonization is a popularapproach to abstract the structure of shapes and used in a variety of fieldssuch as optical character recognition and computer-aided design.A medialaxis (skeleton) is the loci of centers of bi-tangent circles that fit entirelywithin a shape being considered [7]. MAT is an image where each point onthe skeleton has an intensity which represents its distance to a boundary in  Figure 5. (a) 2.5D plot of themaximum diametric length (MDL)measure.The ridge lines highlight thesubtle and explicit clues about thestructure of the shape.Also note themerging of ridge lines indicating abruptchanges in vista. (b) Trace of the ridgeson the MDL surface after anautomated extraction.128 Sanjay Rana and Mike Batty(a) (b)IJAC 2-1_2 proof  14-4-04  2:46 pm  Page 128the original shape. It is easy to imagine that such a description is very usefulfor architectural open space however this is relatively unknown in the studyof architectural open spaces.A simple method of computing medial axes ofa shape is to calculate the distance transform of the shape i.e. calculate thedistance to the shape boundaries all over the shape.The medial axisskeleton lies along the singularities (i.e. creases or curvature discontinuities)in the distance transform [7].Van Tonder et al. [8] have proposed thatmedial axis lines pose a strong influence on our appreciation of a scene andhence some of the ancient designers could have taken this into account.In isovist analysis, the calculation of the MRL is in fact same as thedistance transform. Figure 6a shows a 2.5D plot of the MRL measure of theT-shape. Figure 6b shows an extraction of the medial axes (ridges of theMRL surface) using the method given in the last section.4. Case studyWith these descriptions, it is now possible to describe the structure of realopen spaces in cities. In this work, an example of the open space in thecentral Manchester, UK is presented. Figure 7 shows the footprints of fewnon-residential buildings in central Manchester and the amount of the openspace between them.The layout of the building footprints has a clearlydistinguishable structure and the use of our measures will highlight thisaspect of the given open space. Figure 8a, 8b, and 8C show the MDL field,the ridges and network of the longest lines of depth derived from the MDLsurface respectively, essentially highlighting the long street corridors.Visualisation was obtained almost effortlessly unlike the rigorous analysis ofconvex subspaces required in the conventional space syntax methods.However, it must be noted that the network of lines of longest depth is not  Figure 6. (a) 2.5D plot of theminimum radial length (MRL) measure.The ridge lines demarcate the medialaxes and connect together to describethe topological structure. (b) Trace ofthe medial axes after an automatedextraction129 Visualising the Structure of Architectural Open Spaces Based on Shape Analysis(a) (b)IJAC 2-1_2 proof  14-4-04  2:46 pm  Page 129at all same as axial lines but the network provides equivalent informationabout the structure of open space. One of the most obvious differencesbetween the network of lines of depth and axial lines is the strong influenceof minor irregularities of object boundaries on the result. In conventionalaxial line analysis, these minor irregularities will have to bediscarded/aggregated into the bigger subspace. However, the network oflines of longest depth will preserve these features and as a result oftenmultiple lines of longest depth may occupy a single sub-space, as also seen infigure 8c.The benefit of this sensitivity is that apart from visualisation, thenetwork of lines of longest depth can now also be used by police forsurveillance e.g. placement of CCTV camera in the town centre, by citycouncil for traffic analysis, accessibility and so on. Figure 9a and 9b show theplot of the MRL field and the corresponding ridges in the surface.Again, theridges highlight the convex and concave edges in the open space whichreveal information about the symmetry of the space for aesthetic purposesand the street layout for more practical applications.130 Sanjay Rana and Mike Batty(a) (b) (c)  Figure 7. Non-residential buildings incentral Manchester, UK and thedistribution of the open space. Lightercolours indicate more visibility andthus more open space  Figure 8. (a) Long corridorsbetween the central Manchester builtstructure highlighted by the pattern ofMDL measure at different locations inthe open space. (b) Trace of the ridgeson the MDL surface approximatelyfollowing the long visual corridors. (c)Network of lines of longest depthindicating the key visibly importantlocations (black dots) and theirrespective dominant viewing directionsshown by orientation of lines oflongest depthIJAC 2-1_2 proof  14-4-04  2:46 pm  Page 1305. ConclusionIn this paper, we have demonstrated three ways of visualising and abstractingthe structure of open spaces based on shape descriptors. However, thedescriptors are universal to any type of shapes and hence are equallyapplicable to most kinds of shape analysis.Although we have formalised an approach to detect the dominant linesof visibility, it remains to be tested whether the human navigation can bemodelled under these constraints. One of the obvious limitations of ourmethods is that they are based on a 2D open space. However, ourappreciation of space is clearly based on three-dimensional cognition andinvolves other influences such as sound.We intend to follow this in ourfuture work.The nature and implications of this analysis requires a broadplatform to evaluate these methodologies.Two real examples of thisapproach were presented in an earlier paper by us [3].The choice of theexample of central Manchester was deliberate because Manchester is one ofthe most vibrant cities in England and hence by taking this as an example,we hope that the researchers will be encouraged to experiment with theseideas.We believe that we have mentioned only a few of the many potentialapplications of our approach.Finally, it must be stressed that visualisation of an open space inquantifiable terms has to involve some notion of qualitative aspects ofhuman behaviour such as our different appreciation of colour, sound,organisation of objects in space and so on.This remains the topic of ourfuture work especially to derive analogies between the methods andmeasures of these two forms of visualisation exercise.  Figure 9. Skeleton of the open spacebetween the central Manchestershown by MRL pattern. (a) MRLpattern showing the shape of openspace. (b) Trace of the ridges of theMRL surface131 Visualising the Structure of Architectural Open Spaces Based on Shape Analysis(a) (b)IJAC 2-1_2 proof  14-4-04  2:46 pm  Page 131AcknowledgementsManchester building footprints were obtained from the Non-DomesticBuilding Project at University College London. Lakshman Prasad at LasAlamos National Laboratory kindly provided intellectual and materials helpduring the research of this paper.References1. Batty, M., Jiang, B., and Thurstain-Goodwin, M., Local movement:Agent based modelsof pedestrian flow, Centre for Advanced Spatial Analysis Working Paper No. 4,1998.2. Rana, S.,Visibility Analysis, Environment and Planning-B 2003, 30(5), 641-642.3. Batty, M., and Rana, S., Reformulating Space Syntax:The Automatic Definition andGeneration of Axial Lines and Axial Maps, Centre for Advanced Spatial AnalysisWorking Paper No. 58, 2002.4. Hillier, B. and Hanson, J., The Social Logic of Space, Cambridge University Press,Cambridge, 1984.5. O’Rourke, J, Art Gallery Theorem and Algorithms, Oxford University Press, NewYork , 19876. Wood, J., and Rana, S., Constructing weighted surface networks for therepresentation and analysis of surface topology, in: Proceedings of the 5thInternational Conference on GeoComputation 2000, GeoComputation CD-ROM,Manchester, UK.7. Fisher, R., Perkins, S.,Walker,A., and Wolfart, E., Skeletonization/Medial AxisTransform, http://www.dai.ed.ac.uk/HIPR2/skeleton.htm, 2000 (Accessed on 31July 2003).8. Van Tonder, G.J., Lyons, M.J. and Ejima,Y.,Visual structure of a Japanese Zengarden. Nature, 2002, 419(6), 359-360.132 Sanjay Rana and Mike BattySanjay Rana* and Mike Batty†,*Department of Geography, University of Leicester, Leicester LE1 7RH, UK †Centre for Advanced Spatial Analysis, 1-19 Torrington Place, London WC1E 6BT, UK*sr115@leicester.ac.uk IJAC 2-1_2 proof  14-4-04  2:46 pm  Page 132

Analysis, Environment and Planning-B

and Ejima,Y.,Visual structure of a Japanese Zen garden. Nature,

Art Gallery Theorem and Algorithms,

Constructing weighted surface networks for the representation and analysis of surface topology, in:

Local movement:Agent based models of pedestrian flow, Centre for Advanced Spatial Analysis Working Paper

Reformulating Space Syntax:The Automatic Definition and Generation of Axial Lines and Axial Maps, Centre for Advanced Spatial Analysis Working Paper No.

The Social Logic of Space,

Visualising the structure of architectural open spaces based on shape analysis

This paper proposes the application of some well known two-dimensional geometrical shape descriptors for the visualisation of the structure of architectural open spaces. The paper demonstrates the use of visibility measures such as distance to obstacles and amount of visible space to calculate shape descriptors such as convexity and skeleton of the open space. The aim of the paper is to indicate a simple, objective and quantifiable approach to understand the structure of open spaces otherwise impossible due to the complex construction of built structures

S. Rana

M. Batty

CumInCAD Digital Archive

Visualising the Structure of Architectural Open Spaces Based on Shape Analysis

Visualising the structure of architectural open spaces based on shape analysis

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