Modeling South African Informal Settlements Using

Procedural Techniques

Kevin Glass∗ Chantelle Morkel†

Computer Science Department, Rhodes University

Figure 1: Real world road patterns versus procedurally generated patterns.

Abstract

The formation of informal settlements in and around ur-ban complexes has largely been ignored in the contextof procedural city modeling. However, many cities inSouth Africa and globally can attest to the presence ofsuch settlements. This paper analyses the phenomenonof informal settlements from a procedural modeling per-spective. Aerial photography from two South Africanurban complexes, namely Johannesburg and Cape Townis used as a basis for the extraction of various featuresthat distinguish different types of settlements. In partic-ular, the road patterns which have formed within suchsettlements are analysed, and various procedural tech-niques proposed (including Voronoi diagrams, subdivi-sion and L-systems) to replicate the identified features.A qualitative assessment of the procedural techniquesis provided, and the most suitable combination of tech-niques identified for unstructured and structured settle-ments. In particular it is found that a combination ofVoronoi diagrams and subdivision provides the closestmatch to unstructured informal settlements. A combi-nation of L-systems, Voronoi diagrams and subdivisionis found to produce the closest pattern to a structuredinformal settlement.

CR Categories: I.3.7 [Computer Graphics]: Three-dimensional graphics and realism I.3.5 [ComputerGraphics]: Computational Geometry and Object Mod-eling I.6.5 [Simulation and Modeling]: Model develop-ment

Keywords: Procedural modeling, city modeling, infor-mal settlement, Voronoi, subdivision, L-systems

∗email: kglass@rucus.net†email: g99m0761@campus.ru.ac.za

1 Introduction

1.1 Problem Statement

The problem addressed in this paper is the creation offeasible graphical models of informal settlements. Inparticular, the identification and use of algorithmic (pro-cedural) techniques in the production of such models isaddressed, with specific focus of identifying techniquesthat produce the closest matching features to those iden-tified in aerial photographs of informal settlements.

1.2 Background

Modeling of modern cities has become a topic of greatinterest. Three-dimensional city modeling in particularrefers to the construction and representation of terrain,streets, buildings, and vegetation of urban areas. How-ever, the complexity and size of most urban cities is suf-ficient to make the creation of a 3D model a challengingone. In addition, there are many social issues inherentin a modern city, which affects both the appearance andevolution of areas within an urban setting.

Three-dimensional city models have applications inmany areas and a broad variety of users. Four categoriesof application have been identified [Shiode 2001]: plan-ning and design; infrastructure and facility services;commercial sector and marketing; and promotion andlearning of information on cities. In addition to these ap-plications, such models provide great potential as a toolfor the understanding of urban structure, the mechanismof urban growth and spatial analysis. Hence, there area large number of users of such models including cen-tral and local governments, urban and rural planners, en-vironmental agencies, telecommunications companies,surveyors, architects and engineers.

Three-dimensional city models also have applications inentertainment and virtual reality. In such cases, the truestructure and layout of the city is not as important as thevisual believability of the city.

Procedural modeling, as opposed to manual modeling,is the process of creating models through the use of al-gorithms which encode the instructions needed for thecreation of a model. Manual modeling processes re-quire direct interaction with a user in order to physi-cally model an object (using commercial 3D modelingpackages). Procedural modeling alleviates the need fordirect human interaction. The user sets parameter val-ues for the algorithms, which in many cases is the onlyform of interaction a user has with the system. Thereare a number of benefits of procedural modeling:

• Procedural modeling provides an abstraction ofthe inner workings of the procedure [Cutler et al.2002]. The meaning of the parameters and thevalid ranges of those parameters are all that is re-quired. Procedures within procedural modelingparadigms are aware of geometric requirements(including primitives and transformations).

• Procedural modeling is parameterised, which al-lows for an almost infinite amount of variation ofa model. Parameterisation also allows for changesto a specific model without the need to change theentire scene [Marshall et al. 1980].

• Procedural modeling promotes database amplifi-cation, which is closely related to parameterisa-tion. Database amplification takes in a smallamount of data to begin with and through some op-eration generates a large amount of output [Apo-daca and Gritz 2000].

• Procedures have the ability to replicate processeswhich occur in natural systems, and lead to the cre-ation of structures which reflect the real world.

Procedural city modeling refers to the autonomous con-struction of three-dimensional cities, where only a smallnumber of initial parameters need to be provided. Suchsystems make use of algorithms, rather than manualspecification, to define road patterns and placement ofstructures on a terrain. The initial parameters affectthe appearance of the final outcome, and often seededrandom values are used in order to generate a rich andnon-uniform appearance. However, finding the correctset of parameters (and corresponding values) in order toexactly model an existing city is near-impossible, andhence procedural cities are aimed at simulations, virtualreality and entertainment applications.

One particular feature of many cities in South Africaand around the globe is that ofinformal or spontaneoussettlements.This refers to

“dense settlements comprising commu-nities housed in self constructed shelters un-der conditions of informal or traditional landtenure” [Hindson and McCarthy 1994].

The physical formation of such settlements in andaround urban complexes has largely been ignored in thecontext of city modeling, as can be seen in Section 2.In addition, theories regarding the choice of location forsuch settlements have been provided, but very little issaid about the internal road structure and layout of thesesettlements. This paper analyses the phenomenon of in-

formal settlements in the context of two major SouthAfrican urban complexes, namely Johannesburg (andsurrounding municipalities) and Cape Town. In partic-ular, the road patterns and layout of shacks which haveformed within such settlements are analysed, and var-ious procedural techniques proposed and implementedwhich model the identified phenomena.

1.3 Overview

This paper is structured as follows. Section 2.1 presentsa review of work done in city modeling. Both non-procedural and procedural modeling techniques havebeen discussed as motivation for city modeling, as wellas to highlight the absence of work related to proce-dural modeling of informal settlements. In additionSection 2.2 presents observations made in literature re-garding the formation and structure of informal settle-ments. Section 3.1 analyses a number of aerial pho-tographs of informal settlements, and motivates a num-ber of schemes to be used for modeling settlement pat-terns. Implementation details, as well as a discussionregarding the success of these schemes are presented inSection 3.2 and Section 3.3 respectively. Finally a sum-mary of findings is presented in Section 3.4.

2 Related Work

2.1 City Modeling

A number of different modeling techniques are em-ployed in constructing three-dimensional city models.We make a distinction between models which are con-structed from real world data, and procedurally gener-ated models.

2.1.1 Non-procedural approaches

Much has been done in constructing accurate models ofexisting urban cities. This type of model-constructionrequires a large amount of input data, for example, dataregarding the layout of buildings and roads, as well aselevation data corresponding to the height of buildings.Many types of input data are used for this purpose, andcan be ranked in order of geometrical detail [Shiode2001].

• 2D digital maps and orthophotographs: This in-cludes conventional aerial photographs, as well asdata from Geographic Information Systems (GIS).This data is largely two dimensional and are in-capable of providing the required detail for 3Dmodel generation.

• Image-based rendering: Otherwise known asphotospatial virtual reality,this technique mod-els urban environments by converting panoramicphotographs into navigable scenes [Dodge et al.1998]. The drawback of this approach is that the

viewpoint is limited to the fixed location of thecamera.

• Prismatic building block models: This methodapplies a combination of 2D building footprints(gained from sources such the GIS) with heightinformation in order to determine the size, loca-tion and orientation of buildings. Buildings arerepresented using primitives such as cubes, prismsand cylinders. A commonly used method for col-lecting height information is using laser scannersystems [Brenner and Haala 1999], which providehigh density height information at a resolution ofapproximately one point per square meter. The 2Dground plane (provided by the GIS in the form ofa topographical map or aerial photograph) is de-composed into primitives (rectangles), which arethen extruded into the third dimension based onthe height information.

• Block Modeling with image-based texture map-ping: This method extends the prismatic buildingblock models by mapping image-based facadesonto the 3D primitives. The difficulties are numer-ous, and include acquiring facade images, as wellas automatically detecting the correct placementof textures on the correct primitives. A methodhas been developed which is able to link digitalmaps in the form of real world video (recorded bya camera) to real-world positions with the aid of aGPS system [Kawasaki et al. 1999].

• Models with architectural details and roof mor-phology: This method allows for the extractionand reconstruction of 3D surface details. Thismethod uses automated search techniques to iden-tify and match roof geometries against templates[Brenner et al. 2001]. The best fitting geometry ischosen for the 3D surfaces.

• Full volumetric CAD models: This techniquerefers to the manual modeling of individual build-ings based on physical building surveys and terres-trial photogrammetry.

The above methods all have the inherent problem thata large amount of data is required before the 3D modelcan be generated. Since this data is often in the formof aerial photographs, laser or video data, much filter-ing and interpretation must be done before the data canbe used for model construction. Since all features ofa city are encapsulated in this data, very little focus isplaced on issues such as street pattern formation. All ofthe above techniques focus primarily on the modeling ofbuildings, and there is a distinct absence of reference tothe formation of informal settlements.

2.1.2 Procedural approaches

Procedural city modeling techniques make use of algo-rithms and rules to generate street patterns, and positionbuildings. The key to this approach is a minimal set ofinput parameters. A number of tools exist which facili-tate the generation of convincing city models.

The generation of street patterns is an important featureof procedural city modeling. For example, in [Parishand Muller 2001], L-systems are used to generate streetpatterns based on a number of global and local con-straints. Initially a number of image maps are suppliedwhich represent factors such as population density andelevation. These maps provide the underlying data forthe global constraints which determine what types ofstreets form. Once the street patterns have formed, theareas between the roads are divided intolots on whichbuilding models (generated using L-systems) are placed.

Similarly Sun et al. [2002] make use templates (cre-ated from input maps representing, for example, ele-vation and population density) and rules that describeroad patterns to create road networks. Four types oftemplate are used, namely population-based templates,raster templates, radial templates and mixed templates.The population-based templates are based on Voronoidiagrams, with the edges of the Voronoi cells formingthe roads. Raster and radial templates are created in amanner similar to the growth depicted by an L-system.The template starts with the placement of a single point,and production rules that grow the road (either in a ra-diating or raster pattern) until a boundary of the map’sbounding box is reached. Road patterns are guaranteednot to have any dead-ends, as the system will either ex-tend the road segment to join another, or it will removethe road segment altogether.

Another technique for generating street patterns is usedin [Marvie et al. 2003]. An initial non-oriented graph isused to represent streets, where the vertices of the graphrepresent the crossroads. Edges (representing roads) areremoved and vertices displaced by small amounts to in-troduce variation. The remaining graph is used as a basefor the generation of roads, crossroads and footprints forthe extrusion of buildings.

A similar approach is used in [Greuter et al. 2003],where procedural techniques are used to create citieswith grid street patterns. The city terrain is subdividedinto squares that form a two-dimensional grid. Eachsquare’s location determines what type of structure isgenerated within its bounds. Structures are created ac-cording to a series of pseudo-random numbers that areseeded by the position of the square within the grid. Thebuildings are created through a series of extrusions andtexture mappings.

Buildings within a city model can also be procedurallymodeled, as in [Wonka et al. 2003; Parish and Muller2001], where modified L-systems are used to generatebuilding features such as window and door patterns.

2.2 Sociological Studies

Investigation has been done regarding the reasons whyinformal settlements form, as well as regarding thelifestyle of the residents of such areas. This sectionbriefly presents evidence from selected sources regard-ing the structure and layout of informal settlements. Inparticular features such as settlement location and struc-ture, as well as housing characteristics are discussed.

A number of assertions are made in [Dwyer 1975] re-garding the location of informal settlements in urban ar-eas. One trend identified is that informal settlementstypically develop on any empty land, governmental orotherwise, in and around urban complexes. This trendcan be easily motivated by examples in the Ekurhulenimunicipality (East of Johannesburg) where settlementshave rapidly formed on mining land which recently be-came vacant due to the removal of mine-dumps. Thistrend is motivated primarily by the fact that few dwellersin informal settlements can afford the costs of commut-ing, and hence vacant sites close to industrial areas areespecially valued. Additionally, it is often claimed thatmigrants first settle in centrally located settlements tobe close to areas of employment, but relocate to morespacious areas on the peripherals of the city when morefinancial stability is achieved [Drakakis-Smith 1987].

The structure of informal settlements in urban areas ismore difficult to define. Dwyer [1975] indicates thatoften regular grid formations occur in informal settle-ments, but equally often the building patterns are toochaotic to be rationalised. Manonaet al. [1996] distin-guishes between two types of settlement patterns basedon studies of informal settlements in the Eastern Cape.Poor quality structures, and chaotic patterns tend to oc-cur when people erect structures knowing that they willleave and build elsewhere. However, when people haveclear intentions of settling, more formal patterns andhigher quality structures are erected. In these cases,plots must even be requested from a local committee- resulting in neat arrangements with accessible streets.Drakakis-Smith [1987] highlights an important featurewhich influences many South African informal settle-ments - aided self-help programmes. These schemesaim to upgrade informal settlements by providing ba-sic essential infrastructure such as water, sewerage andelectricity which are provided on prepared lots. This re-sults in the formation of regular street patterns.

Typically housing structures in squatter settlements areperceived to be cube-shaped shacks built fromad hocmaterials ranging from wood, to corrugated iron. How-ever, according to Hindson and McCarthy [1994] andManonaet al. [1996] this is not always the case. In fact,often the condition of housing in informal settlementstends to improve over time, resulting, in some cases, inmud-brick structures with corrugated iron roofs. How-ever, temporary structures tend to be of low quality,containing only a single room, and appear to be in themajority according to Manonaet al. [1996], where athird of the households studied contain only one room.In addition, the aerial photographs of informal settle-ments around Johannesburg and Cape Town reveal thatthe general structural shape of shacks is predominantlycube-shaped (see Figures 2, 3 and 4).

3 Identi�cation and Evaluation ofModeling Techniques

This experimentation has a number of goals:

Figure 2: Unstructured informal settlement near Johan-nesburg

1. Identify a subset of visual patterns found in infor-mal settlements from South Africa

2. Suggest and motivate the use of procedural tech-niques which may be able to emulate such patterns

3. Implement the identified techniques

4. Provide a qualitative evaluation of the believabil-ity of each scheme in comparison with actual pho-tographs of informal settlements

The first two goals are discussed in Section 3.1. Issuesrelating to the implementation of the identified tech-niques are discussed in Section 3.2, with evaluationspresented in Section 3.3.

3.1 Design

A number of aerial photographs of informal settlementsfrom the Johannesburg region and Cape Town have beenanalysed. Figures 2, 3 and 4 are aerial photographs ofinformal settlements near Johannesburg and Cape Town[Google Maps Beta 2005]. Figures 2 and 3 representunstructured settlement where no external planning orimprovement efforts have been made. Figure 4 how-ever, represents a structured settlement which formedafter the provision of basic infrastructure such as sewer-age and electricity.

Features The most striking visual feature inherent inthe figures are the wide, winding pathways betweenclusters of shacks. These pathways will henceforth bereferred to asmajor-road patterns. These major-roadpatterns have been manually highlighted in white in theimages for clarity. As noted in Section 2.2 a highlyirregular pattern is present in both unstructured settle-ments (Figures 2 and 3), however where basic servicesare provided a very structured street pattern forms (Fig-ure 4). More difficult to identify is what is termedminor-road patternswhich represent auxiliary pathwaysbetween the major pathways. The density of shacks be-tween major-roads is also a feature which distinguishes

Figure 3: Unstructured informal settlement near CapeTown.

Figure 4: Structured settlement near Johannesburg,where basic services such as sewerage and electricityare provided.

Figure 5: Voronoi Polygons

Features Unstructured StructuredMajor-road pattern Irregular RegularMinor-road pattern Semi-regular Semi-regularDensity of shacks High Moderate

Crossroads Radial PerpendicularRoad orientation Star Parallel

Table 1: Perceived visual features of informal settle-ments

structured and unstructured settlements, with unstruc-tured settlements being more densely populated. Cross-roads tend to be more radial in nature in unstructuredsettlements, while the more structured settlements ex-hibit perpendicular intersections. Finally, parallel roadsare not visible in the unstructured settlements. Table1 presents a summary of the perceived visual featuresof informal settlements based on the three aerial pho-tographs.

The following procedural tools have been identifiedwhich have the potential of capturing the identified fea-tures of informal settlements:

• Voronoi Diagrams: The patterns formed by ma-jor pathways within the informal settlements inFigures 2 and 3 are highly suggestive of the re-gions formed by Voronoi diagrams. Given a setof reference seed-points on a plane, a Voronoi di-agram partitions the plane into a number of re-gions, where each region contains the locus ofpoints which are closest to each reference point[Preparata and Shamos 1985]. The result is a num-ber of irregular polygons (see Figure 5 for an ex-ample). If the edges of these polygons are inter-preted as streets, the results are similar to the ir-regular patterns in Figures 2 and 3.

• Subdivision: The seeming regularity of minor-road patterns of the informal settlements in theaerial photographs suggests the use of subdivisionas a modeling tool. Subdivision is the process ofincreasing the resolution of a mesh by adding newvertices. The locations of these new vertices arecalculated in terms of the existing mesh vertices ateach stage of subdivision. An example of subdivi-sion is presented in Figure 6, which is a plane withfour levels subdivision.

• Noise: To introduce some randomness into thelayout of the informal settlements, Perlin noise[Perlin 2002] is used to distort the regular patterncreated by the subdivision process. Figure 6 usesnoise to displace the vertices, giving an irregularappearance.

• L-Systems: As an alternative to subdivision L-systems are proposed as a scheme to model theseeming regularity of minor-road patterns. An L-system is specified by agrammar, to which pro-ductionsare applied a variable number of times,resulting in a dense tree-like structure. If regularangles are chosen at branch junctions then a veryregular pattern forms (see Figure 7).

Figure 6: Subdivision with noise

Figure 7: Regular L-system

R= 1.456ω = F(2)p1 = F(s)→ F(s)[+A(s/R)][−A(s/R)]whereF(x) represents a line segment of lengthx in thecurrent direction. The initial value ofs is 2. + and−refer to positive and negative rotation about they−axisrespectively.

Figure 8: L-system grammar

The individual use of each of the above techniquesare not sufficient to model convincing informal settle-ments. Thus combinations of the above tools are cre-ated based on observations made from the aerial pho-tographs. Voronoi diagrams are chosen as the majorstreet structure, with the initial choice of seed pointsdifferentiating between structured and unstructured pat-terns. The more random the choice of these points,the more irregular the resulting polygons. Within eachVoronoi region, either subdivision or L-systems are usedto produce grid-like patterns. Regular grids are avoidedby displacing vertices using noise. Table 2 presents asummary of the experiments conducted.

3.2 Implementation

The procedural tools used for these experiments are im-plemented in the following manner:

• Voronoi Diagrams: An initial set of points (reg-ular or random) are generated on thex− z planeas reference seed points for the Voronoi diagrams.The corresponding Voronoi diagram is generatedusing the QVORONOI application of the QHullpackage [Barber et al. 1995].

• Subdivision:√

2-subdivision, presented in [Liet al. 2004], is implemented for these experiments.The mesh to be subdivided can be of arbitrarytopology and consist of either triangles or quadri-laterals. The scheme has been altered to maintainthe area of the mesh passed to it, by not displac-ing the original vertices. Another modification tothe subdivision scheme is the addition of noise todisplace thex− andz−coordinates of each newlycreated vertex.

• L-Systems: The L-system implemented is de-scribed in [Prusinkiewicz and Lindenmayer 1990],with the grammar presented in Figure 8. This pro-duces a regular placement pattern, as shown inFigure 7. A regular pattern is produced by set-ting the angle of rotation to 90 degrees. An irreg-ular pattern is produced by randomising this anglewithin a restricted range.

The generation of procedural informal settlements isachieved as follows. The initial set of reference pointsfor the Voronoi diagram is generated (random or regu-lar), and the corresponding set of Voronoi polygons isproduced. Where subdivision is used for minor-roadpatterns, each polygon is treated as an individual meshwhich is subdivided a number of times (relative to the

Experiment Voronoi Seed-points Minor Road PatternA Random Subdivision (noise)B Random L-System (randomised angles)C Random Subdivision (noise-free)D Random L-System (consistent angles)E Regular Grid Subdivision (noise)F L-System (consistent angles) Subdivision (noise)

Table 2: Combinations of procedural tools

area of the polygon). Each resulting vertex in the meshis used as a placement location for a shack in the set-tlement. Where L-systems are used as minor-road pat-terns, the structure is grown within the polygon by ap-plying production rules a number of times. Any verticesfalling outside the polygon are discarded. The endpointsof the L-system are used as placement locations for theshacks. L-systems are also used to generate major-roadpatterns by producing a regular set of reference pointsfor the Voronoi diagram.

In order to achieve major-road patterns (in the formof gaps between shacks) in the settlement scheme, anyshack which falls too close to the edges of the Voronoipolygons are discarded.

The shape and texturing of shacks is of minor impor-tance in these experiments. Since shacks are predom-inantly cube-shaped, each shack in the model is repre-sented as a untextured cube. Images are rendered usingOpenGL.

3.3 Results

Experiment A Figure 9 presents an unstructured in-formal settlement using 80 random Voronoi seed-points,with each Voronoi region adaptively subdivided accord-ing to the area of the region. Each shack location is dis-placed according to a noise function. Additionally theorientations of the shacks are adjusted so that at leastone face of the shack is aligned with the closest Voronoiboundary.

A highly irregular major-road pattern emerges fromthis model, with unpredictable crossroads and junctions.The major-road pattern is clearly visible and is greatlyenhanced by the alignment of the shack faces with theclosest road. Minor-road patterns are more difficult toidentify. The distribution of the shacks is uniformlydense. There is no pattern to the structure of the roads,with parallel roads scarcely occurring. It is possiblehowever to identify a number of radial road patterns.

Experiment B Figure 10 presents a combination ofVoronoi regions (from 80 random Voronoi seed-points)and L-systems within these regions. In some areasthere are emerging major-road patterns, but generallythe spaces between clusters of shacks are unrealisticallylarge. This can be explained by the nature of the gram-mar used for the L-system, which tends to leave largegaps between child branches. Barring the large gaps

Figure 9: Experiment A: Random Voronoi seed,Voronoi regions subdivided with noise

between regions, the density of shacks is largely uni-form. No minor-road patterns can be identified withinthe regions, and the shack orientations are highly irreg-ular. The criticism of this model is the large number ofgaps which form between regions, which is unrealisticin terms of the aerial photographs provided in Section3.1.

Experiment C Figure 11 presents a more structuredsettlement than the previous two experiments. AVoronoi diagram is used with a smaller number of re-gions than in Experiment A and B (40 seed-points) andshack locations are not displaced during subdivision.However, the orientation of shacks is still modified toface the nearest roads. Once again major-road patternsemerge very clearly, but in this case minor-road pat-terns are more distinguishable than in previous experi-ments. The shack placement is very dense, and very uni-form, giving the impression of structure. The criticismof this model is that there are regions of shacks whichare too regularly distributed, displaying placement pat-terns which cannot be seen in the aerial photographs ofinformal settlements provided.

Experiment D Figure 12 presents another attempt at amore structured settlement. A randomised Voronoi dia-gram (with 40 random Voronoi seed-points) is used, anda non-randomised L-system (branching angles of 90 de-grees) is used within the Voronoi regions. The problemwith this model is the sparseness of shack placement.This is a result of the L-system grammar, which grows

Figure 10: Experiment B: Random Voronoi seed,Voronoi regions contain L-systems (random angles)

Figure 11: Experiment C: Random Voronoi seed,Voronoi regions subdivided without noise

Figure 12: Experiment D: Random Voronoi seed,Voronoi regions contain L-systems (regular angles)

Figure 13: Experiment E: Regular Voronoi seeds,Voronoi regions subdivided with noise

too rapidly beyond the bounds of the Voronoi regions.The sparseness of shacks is not conducive to the for-mation of clear major-road patterns. The distribution ofshacks within the regions is largely regular, often form-ing a clear grid pattern. In terms of the provided aerialphotographs this model does not appear to be realisticof unstructured settlements, but such patterns could oc-cur in more structured settlements wherelots have beenallocated.

Experiment E Figure 13 presents the results of aVoronoi scheme based on regularly distributed seed-points. This results in a major-road structure which hasa typical grid pattern. Irregularity is still maintained byemploying noise in the subdivision of the Voronoi re-gions. Minor-road patterns do not emerge clearly. Thedensity of shacks is not uniform, even though the size ofthe Voronoi regions are uniform. This is attributed to thenoise applied to the vertices during the subdivision pro-cess. The criticism of this model is the overarching uni-formity of the major-road patterns, which is uncharac-teristic of road patterns shown in the aerial photographs,which are more unpredictable.

Experiment F Finally, Figure 14 presents a hybrid ofprocedural methods. The regular L-system is used togenerate the seed points for the Voronoi diagram, andthe resulting Voronoi regions are subdivided with noisedisplacements. This figure provides a good example ofa structured informal settlement. Major-road patternssuch as parallel roads and perpendicular cross-roads areclearly visible. However, the major-road pattern is nottotally regular, and there exist a number of diagonalroads, and radial intersections. The density of the shacksis also uniform in all the regions, and their orientationsare convincingly regular. The main contributor of ir-regularity to this model is the use of noise, which hassufficiently perturbed the placement of shacks to reducethe overall impression of structure. The only criticismof the results produced by this model is the perceivedsymmetry, which is an artefact of the L-system whichwas used to create the Voronoi seed-points. In our opin-

Figure 14: Experiment F: Regular L-systems usedto generate Voronoi seeds, Voronoi regions subdividedwith noise

ion, however, this model produces the closest matchingresults to the informal settlements shown in Figure 4.

3.4 Summary and Conclusions

Voronoi diagrams, L-systems and subdivision have allbeen tested as possible procedural modeling techniquesfor informal settlements. Qualitative conclusions aredrawn regarding the best model for unstructured andstructured settlement patterns. These conclusions arebased on the features extracted from the aerial pho-tographs in Section 3.1. Table 3 presents a summary ofthe qualitative comparisons made regarding the featuresidentified in each experiment.

The conclusions according to Table 3 are as follows:

• Experiment A produces the most convincing un-structured pattern

• Experiment F produces the most convincing struc-tured pattern

• Voronoi diagrams produce convincing major-roadpatterns in all cases

• Minor-road patterns are not readily identifiablewhen subdivision (with noise) is used. This is at-tributed to the large amount of variability causedby noise.

• The formation of perpendicular and radial cross-roads is successfully achieved using various com-binations of techniques.

• Generally, subdivision works better than the cho-sen L-system for populating the Voronoi regions

It is important to note that the conclusions presentedhere regarding the closest matching settlement patternare qualitative in nature. Further work must be under-taken to identify quantitative measurements which canbe used to differentiate between structured and unstruc-tured settlements. Furthermore, a larger base of aerial

photography will be beneficial in classifying varioustypes of informal settlements.

4 Conclusion

This paper provides an overview of various types ofcity modeling techniques, both procedural and non-procedural. A novel problem, in the form of informalsettlements, has been identified within the context of ur-ban city modeling. A study of the structures of infor-mal settlements is provided, and a number of aerial pho-tographs are used to identify features of informal settle-ments including road patterns and density. These fea-tures are chosen with the aim of aiding in the choice ofprocedural techniques for the modeling of informal set-tlements. A number of procedural techniques are iden-tified and tested for appropriateness against the originalaerial photographs.

A number of novel contributions are made. Firstly, theinclusion of informal settlements into the context of citymodeling is an unexplored area. Secondly, novel com-binations of procedural techniques (including Voronoidiagrams, subdivision, and L-systems) are evaluated.

Further work includes adding a time dimension to theprocedural techniques in order to simulate the growth ofsuch settlements. Additionally, other combinations ofprocedural techniques can be tested (for example frac-tals), with the inclusion of global parameters such aswater availability and land topography. A more detailedand theoretically grounded set of features should be ex-tracted by analysing a larger set of aerial photographyand settlement literature.

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