From Pixels to 3D Representations of Buildings:

A 3D Geo-visualization of Perspective Urban Respecting Some

Urbanization Constraints

Rani El Meouche

, Mojtaba Eslahi

, Anne Ruas

and Muhammad Ali Sammuneh

Institut de Recherche en Constructibilité (IRC), ESTP Paris, 28 Avenue du Président Wilson, 94230 Cachan, France

LISIS/ IFSTTAR, Université de Marne-la-Vallée, 5 Boulevard Descartes, 77420 Champs-sur-Marne, France

Keywords: 3D Modelling, GIS (Geographic Information System), CA (Cellular Automata) Model, Urban Sprawl, Urban

Growth, SLEUTH Urban Growth Model, Building Footprints.

Abstract: In this paper, we generate the fictive 3D buildings and provide a 3D representation of an urban growth model

using ArcGIS. SLEUTH urban growth model, like the other CA (Cellular Automata) models, creates a

prospective 2D map containing some pixels on which urbanization is supposed to occur. These pixels have to

be transformed into 3D building representations, while respecting some restrictions on urbanization. To create

a building from a pixel, we transform the pixels from raster data to building footprints. In the process of

transformation, different considerations and constraints are considered such as the direction of the footprints

and the distances to urban objects and geographic features. To generate the 3D representations of the buildings,

the appropriate heights are added to these footprints. The height of the buildings depends on the probability

of the height of adjacent buildings. Although the provided 3D model is a primary and simple model, the 3D

representation of the urban growth allows having different images of the city of tomorrow for supporting the

scientists and authorities in charge of urban planner and management.

1 INTRODUCTION

In recent years, various researches on 3D virtual city

models have been carried out. 3D city models are

used to represent the urban surfaces and the important

objects attached to them, including the buildings and

the environment for different purposes such as

communication, management of urban heritage,

urban planning projects, and simulation modeling in

terms of noise, solar, pollution, climate changes,

flooding and urban sprawl (Shiode, 2000; Kolbe and

Gröger, 2003; Zhu et al., 2009; Billen et al., 2012;

Billen et al., 2014; Biljecki et al., 2015).

There are different techniques to generate a 3D

city model, such as 3D building creation from urban

footprints (Ledoux and Meijers, 2011; Pedrinis and

Gesquière, 2017; Chaturvedi et al., 2019) and 3D

reconstruction and data integration that are used in

merging photogrammetry or laser scanning with GIS

data (Haala and Kada, 2010; Kapoor et al., 2010;

https://orcid.org/0000-0001-5063-6638

Hervy et al., 2012; Billen et al., 2012; EL Meouche et

al. 2013; Tomljenovic et al. 2015, Pepe et al., 2019).

Nowadays, there are different tools for generating

a 3D model in different fields of architectural,

industrial, mechanical and electronical engineering

such as Maya, 3ds Max, Auto CAD, Sketch Up,

Unity, City Engine and ArcGIS. In this research, the

3D buildings are created by giving the third

dimension to 2D footprints of the buildings. The third

dimension indicates the height of the buildings that is

obtained according to the buildings’ class and

population density. The buildings are illustrated in

block models with flat roof structure (similar to LoD1

of CityGML). We have used ArcGIS 10.6 for our 3D

modeling process. GIS based applications let us

creating the 3D buildings and analyzing geographic

information. The objective here is to illustrate the 3D

representation of an urban growth model while

respecting a set of constraints.

In this paper, we have used the SLEUTH urban

growth model, and visualized the obtained 2D results

on 3D. SLEUTH is an inductive pattern-based model

El Meouche, R., Eslahi, M., Ruas, A. and Sammuneh, M.

From Pixels to 3D Representations of Buildings: A 3D Geo-visualization of Perspective Urban Respecting Some Urbanization Constraints.

DOI: 10.5220/0009408901990207

In Proceedings of the 6th International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2020), pages 199-207

ISBN: 978-989-758-425-1

199

that uses cellular automata and terrain mapping. This

model employs some growth rules to address urban

growth model, and it is widely used to simulate the

urban growth (Clarke, 2008; Project Gigalopolis,

2018; Eslahi et al. 2019). SLEUTH’s acronym is

derived from its data input requirements: Slope, Land

use, Exclusion, Urban, Transportation and Hillshade.

The SLEUTH results are limited to some raster

data that are difficult to interpret for decision makers.

The results are some pixels on which urbanization is

supposed to occur, while they do not make much

sense from urbanism point of view. Therefore, we

have proposed to transform the pixels into 3D

building representation and to place them in all of the

available spaces. The objective of this paper is not to

explain the SLEUTH model, but to give an idea to

transfer the 2D pixels, obtained from SLEUTH, to 3D

representations of the buildings.

In the next section, the study area is presented.

The procedure of transforming a pixel to a 3D

representation of a building is described in section 3.

A 3D visualization of the urban growth model is

provided in section 4. The paper is concluded in

section 5.

2 STUDY AREA

The proposed model has been applied in three study

areas with different scales including metropolis, a city

and a rural area. Due to the ease of visualization, the

application of the model to the smallest study area is

presented in this paper. The study area is Rieucros, a

small community in a rural area that is located in the

department of Ariege in south of Toulouse, France

(43° 05 ′ 07 ″ North, 1° 46 ′ 04 ″ East) (see

figure 1). The extent of the study area is 400 ha with

686 inhabitants (Legal populations, INSEE - national

institute of statistics and economic studies, France,

2016).

Geospatial database and geographic information

systems are applied to create the input maps of

SLEUTH. All the maps have the size of 100×100

pixels that feature a cell size of 20m×20m (~400m2).

Slope and hillshade maps are derived from Digital

Elevation Model (DEM) of RGE ALTI with a spatial

resolution of 5m, provided by IGN (national institute

of geographic information and forestry).

Urban areas, excluded areas and transportation

maps are generated automatically from BD TOPO

and BD ORTHO from IGN database of 2017. Urban

map is classified into two classes of urban and

nonurban. To create the urban maps, the

undifferentiated buildings with more than 3m height

and more than 50m

surfaces are used.

Figure 1: Location of the study area of Rieucros.

The compound annual population growth rate is

calculated and the average population for the coming

years (2050) is estimated for the study area. Using

SLEUTH urban growth modelling, we define

different urban fabric scenarios based on socio-

demographic data, which are integrated into the

model during 2D simulations (Eslahi, 2019).

3 FROM PIXEL TO 3D BUILDING

REPRESENTATION

As discussed before, we have used a CA model to

simulate the forecasting urban growth for our study

areas. Here, we aim to create the 3D building

representation from the pixels.

The distances from the constraints and the

neighbourhoods of geographical objects are not

explicitly considered in CA models. Therefore, we

have used the topographic objects such as buildings,

rivers, excluded areas and the current buildings, and

make a set of constraints. Considering these

constraints, we have created the footprints of the

buildings and then we have given them the value of

the height according to the urban fabric scenarios.

In order to visualize the SLEUTH results in three-

dimensional space, first, the pixels need to be

transformed from raster data to building footprints.

The number of the buildings that can be located in

each pixel depends on the pixel size and the surfaces

of the buildings. An average surface for each type of

building is calculated based on the average surface of

current buildings. Afterwards, appropriate heights are

GISTAM 2020 - 6th International Conference on Geographical Information Systems Theory, Applications and Management

200

added to these footprints. The heights are based on the

adjacent buildings. In the process of transformation

of the pixel to building footprints, different

considerations and constraints are considered, such as

the direction of the footprints and the distances to

urban objects and geographic features. The distance

of the new building to the urban objects and

geographic features (e.g. current buildings, roads,

railways, rivers, vegetation, cemeteries, airfields,

activity areas) are obtained from the average

distances of the existing buildings to them.

The procedure of generating a 3D building

representation from a pixel is presented in figure 2.

Figure 2: The 3D building representation generation

procedure.

As it is illustrated in figure 2, in order to create a

3D building model, the pixels have to first, change to

polygons that indicate the buildings footprints, and

take the value of heights. To transform a pixel to a

polygon, the SLEUTH output maps (the raster data

that are derived from SLEUTH simulation) should be

georeferenced and converted to vector data. This

provides the polygons instead of each pixel, which

simplify the processing (see section 3.1). Next, each

polygon is oriented along its nearest road section. The

polygons are divided to four squares. This is because

in our algorithm the position of the building respects

certain distances from urban objects and geographic

features. If these distances are not observed, the

polygon will be removed. Therefore, by dividing a

polygon into smaller squares, we decrease the risk of

losing the whole polygon (see section 3.2).

The urban objects and the geographic features

define some constraints for a polygon. These

constraints cause the configuration of the polygons to

be adjusted. We have defined two type of constraints

including linear constraints (e.g. roads, rivers and

railways) and discrete constraints (e.g. cemeteries,

airport, and existing buildings). The difference of

these two constraints is on the calculation of the

average distances of the current buildings to them.

The pixels that were turned along their nearest road

sections make the overlaps of the polygons that are

adjacent each other. Therefore, in this step the

overlaps and the parts of the polygons that are close

to the constraints will be removed (see section 3.3).

In next step, the small squares that are identified

as a polygon are assembled taking into account the

average area of the current buildings. The surfaces are

set according to the scenarios by making an erosion

to achieve the desired footprints for each building

(see section 3.4 and 3.5).

The process of calculation the building’s height is

done, in parallel to building footprints generation. We

have calculated the surface of each building

footprints. In the cases that the surfaces are too small

to be on the upper building class, we give the height

according to their surfaces. Other footprints take the

height of the nearest neighbours, until the rate of the

building classes that are defined will be filled. The

process of giving height to the building footprints will

be explained in detail in section 4.

3.1 From Pixel to Polygon

The SLEUTH outputs include the non-geo-

referenced raster that contains three types of pixels

representing the current urban area, new urban area

and null pixels. The purpose of this step is to geo-

reference this raster data with respect to our database

vector data. This process is based on a polynomial

transformation. It renders the Root Mean Square

deviations (RMS) as a control index, which in

general, must be below the size of a pixel.

Later, the raster data is converted to vector data to

facilitate the processing. In fact, we have extracted

raster data from shape files (vector data) for creating

the input maps of SLEUTH and now, we do the

inverse function.

3.2 Positioning and Division of the

Building Footprints

After preparing the output of the SLEUTH model for

3D procedure, in this section, the generated polygons,

should be rotated along the closest road section. The

From Pixels to 3D Representations of Buildings: A 3D Geo-visualization of Perspective Urban Respecting Some Urbanization Constraints

201

orientation is done based on the size of the polygon

and the coordinates of its centre (Xc, Yc). The

orientation is made with respect to the nearest road

section (see figure 3).

Figure 3: Orientation of a polygon, R1 and R2 are the local

and overall references respectively.

The roads are divided into the small sections,

then, their directing coefficient (Cd) is calculated

with the bellow equation:

Cd=

Ye−Ys

Xe−Xs

(1)

where (Xs,Ys) and (Xe,Ye) are respectively the start

and the end coordinates of the section. Then, the angle

of orientation of the road section is calculated

according to the horizontal axis in two cases:

Case 1, if Xe-Xs = 0 (section parallel to vertical

axis):

Ɵ = π/2 (2)

Case 2, if not:

Ɵ = arctan (C

) (3)

Finally, the squares are oriented using this angle

by associating each oriented polygon to a local

coordinate system, considering the coordinates of the

corners of the polygons in the overall reference.

Therefore, the solution becomes a simple change of

reference in the plane. The rotation according to Z is

as follows:



=

cosƟ −sinƟ 0

sinƟ cosƟ 0

001



)

The change is made according to the following

equation. The angle calculated in the counter

clockwise direction.



𝑋=𝑋𝑐+𝑥cosƟ−𝑦sinƟ

𝑌=𝑌𝑐+𝑥sinƟ+𝑦cosƟ

(5)

where (x, y) are the coordinates of the corners

expressed in local coordinate system and (X, Y) their

associates in global coordinate system.



𝑋=𝑋𝑐+

𝑅

(cosƟ−sinƟ)

𝑌=𝑌𝑐+

𝑅

(sinƟ+cosƟ)

(6)

Afterwards, we change the sign of the cosine and

sine for the coordinates of four corners.

Corner 1:



𝑥=

𝑅

𝑦=

𝑅

→



𝑋1=𝑋𝑐+

𝑅

(𝑐𝑜𝑠Ɵ−𝑠𝑖𝑛Ɵ)

𝑌1=𝑌𝑐+

𝑅

(𝑠𝑖𝑛Ɵ+𝑐𝑜𝑠Ɵ)

(7)

Corner 2:



𝑥=

𝑅

𝑦=−

𝑅

→



𝑋2=𝑋𝑐+

𝑅

(cosƟ+sinƟ)

𝑌2=𝑌𝑐+

𝑅

(sinƟ−cosƟ)

(8)

Corner 3:



𝑥=−

𝑅

𝑦=−

𝑅

→



𝑋3=𝑋𝑐+

𝑅

(−cosƟ+sinƟ

𝑌3=𝑌𝑐+

𝑅

(−sinƟ−cosƟ

)

(9)

Corner 4:



𝑥=−

𝑅

𝑦=

𝑅

→



𝑋4=𝑋𝑐+

𝑅

(−cosƟ−sinƟ)

𝑌4=𝑌𝑐+

𝑅

(−sinƟ+cosƟ)

(10)

In order to both, considering the constraints and

preserving the surfaces of the polygons as much as

possible, the polygons are divided into four smaller

squares. Therefore, if constraints drive the model to

delete a polygon, the algorithm will delete a small

square, which meet the restrictions, instead of whole

polygon.

3.3 Configuration the Building

Footprints

After orienting a polygon, some overlaps occur

between them and other layers of the land occupation.

In addition, it is necessary to define a distance

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between a polygon (which will define the new

buildings representation) and the different land

occupation entities. The adjustment and positioning

of new buildings follow the layout of the old

buildings. Therefore, we apply the situation of

existing buildings on the polygons in order to create

new buildings that would respect the distance

between buildings, and the distance to the river, and

railways. As mentioned before, two types of

constraints are taken into account:

• The constraints that have a linear distribution in

space including vegetation, water, roads and

railways.

• The discrete constraints that can be modelled by

points or small areas including remarkable

buildings, cemeteries, airfields, sport grounds,

activity areas, industrial or commercial areas and

existing buildings.

The logic of these two types of constraints bases

on finding the nearest neighbour and respecting the

distances similar to it. The only difference is the

definition of the notion 'nearest' between linear and

discrete constraints.

To explain the method of defining linear

constraints, we have used the following example of

the river. This method is essentially based on a double

geo-processing buffer as follow:

• First, we measure the distance from the nearest

existing building to the river (Dr), then we make

a buffer of ten times of this distance (10 × Dr). We

assume that all the buildings close to the sections

of the river are at this distance (second buffer),

which means the buildings that are at the edge of

the river.

• The average distance of these buildings from the

river is then calculated (the average distance of the

buildings located in the second buffer). This

average is considered as a minimum distance for

new buildings of the riverbank.

For other linear constraints, the similar procedure

is done. In these cases, the distance of the nearest

building to each road section is measured and it is

considered as an average distance for new buildings.

To apply linear constraints to the polygon, the

algorithm makes a second buffer with a distance

equal to the average distance and remove the

intersection of this buffer with the polygon. As

mentioned earlier, one of the advantages of dividing

polygons into smaller squares is that when we want

to remove the intersection of polygons with a buffer,

only the small squares that are within a buffer

constraint are eliminated. When only a part of a

polygon intersects with the buffer, this subdivision

can help the model not to lose the polygon

completely. In addition, a threshold for the

intersection of a square to a buffer is defined. This

threshold is equal to 30% of a square area that

intersects with the buffer. It means, if a buffer

overlaps more than 70% with a square, that square is

deleted. Figure 4 illustrates the sample of the linear

constraints definition.

Figure 4: Definition of river proximity constraint.

The discrete constraints are defined by the

undifferentiated buildings, industrial buildings and

some special spaces (i.e. excluded area, remarkable

buildings, cemeteries, airfields, activity areas). In

order to taking into account the distance of a polygon

from the discrete constraints, it is required to measure

the distance of the current buildings from each other

and from other discrete constraints. After obtaining

the average distance for the current buildings, this

distance is applied to the nearest discrete constraints

for each polygon. Therefore, a buffer of the average

distance is generated that defines the constraint of the

existence of a building or a special place. Afterwards,

the same argument for eliminating intersections as for

linear constraints applies to discrete constraints.

As discussed, in orientation each polygon rotates

parallel to the closest road section. In the cases that

two polygons are located next together, if the road

orientation is changed, one polygon overlaps with

part of the other. Therefore, this part of the overlap

should be deleted from one of the polygons. The

amount of the overlap depends on the angle of change

of the road direction from one section to another. The

more the road turns, the greater the overlap becomes.

From Pixels to 3D Representations of Buildings: A 3D Geo-visualization of Perspective Urban Respecting Some Urbanization Constraints

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In this step, the division of pixels plays an important

role and the small square from one polygon, which

overlaps with another, is removed. Therefore, we

have created distances between the polygons while

avoiding the problem of the superposition.

3.4 Building Footprints Generation

After considering the required distance from the

constraints, in this section we have created the

building footprints. In previous section, the polygons

were divided to small squares. Here, in order to

generate the footprints these squares are assembled

according to the building types.

The idea is to build building footprints with the

surfaces remain among the small squares. We have

defined maximum of different areas (Smax) for the

new building footprints concerning the type of the

buildings and the size of the polygons. Two types are

considered for the study area including: the single

dwelling and shop top housing, with the Smax of

156m

and 256m

respectively. The squares are

assembled according to Smax of each study area.

To make the footprints of buildings we should

first, assemble small squares (with same IDs), while

checking if the total area exceeds the maximum

defined area relative to each scenario (Smax). If the

area of the assembled squares were less than Smax,

the whole polygon represents one building. Then, we

build a layer that contains only the polygons whose

surfaces exceed Smax. For these polygons, we return

to the state of the decomposition. We gather the two

small squares which belong to the same subpixel (the

square of the first division) but which are both to the

left or the right of the set of small squares of the sub-

pixel, i.e. LU (Left/Up) with LD (Left/Down) and RU

(Right/Up) with RD (Right/ Down).

This combination is chosen because in our

algorithm we assume that the width of a building

locates on the side of the road. Since the polygons are

oriented towards the road, the sub-squares which

facing the road are chosen in such a way that they

carry the 'U' (Up). In the case that we assemble the

two squares, which bring ‘U’ together and the two

others bring 'D' together, we will have a house facing

the road and one behind the other. Therefore, the both

buildings will have access to nearest road

3.5 Positioning Building

Representations

The urban fabric scenarios are based on one or the

combination of the building types considering the

density of the population. After assembling the

squares, we have defined the different possible types

of the footprints considering an erosion to each

polygon according to their surfaces and building

types (see figure 5). Therefore, we have obtained the

desired surface for the building footprints as well as

respecting the Smax and the distances between the

new buildings. Defining different footprints is used in

next step to create the 3D representation of the

prospective urban map.

Figure 5: Building footprints by making different erosion to

each polygon according to building type.

Now, we have calculated the different

probabilities for each polygon according to its

neighbourhood building types. These gives the

information of the possible height for the new

buildings. Given the scenarios where it is necessary

to have mixed height values according to predefined

percentages associated with each height, we use an

algorithm that combines the random aspect and a

statistical interpolation.

According to urban fabric, we have two types of

buildings that have two different heights. In our

algorithm, we ordered the buildings in ascending

order of their surfaces (SB1<SB2). For each building

types of B1 and B2, their percentages of combination

in the scenarios are defined by Prs1 and Prs2,

respectively. P1 and P2 indicate the average height

probabilities for each building that are calculated

from the nearest current building’s height. To do this,

it is needed to classify the new building according to

the distance to the neighbour as follow (see figure 6):

• Class1: New buildings that have at least one

neighbour that is part of the current buildings on a

circle (r1)

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• Class2: New buildings that have at least one

neighbour that is part of the current buildings on a

limited ring between the small circle (r1) and the

large circle (r2)

• Class3: New buildings that have no neighbours

that are part of the current buildings on a circle

(r2)

Figure 6: Searching for the nearest neighbour.

The values r1 and r2 are the radiuses that are

calculated from the distance of the nearest neighbour

of each existing building and apply the quintile

classification. We have calculated the distance

between the new building and the current buildings,

which is in the spaces that is defined by the class

(DIS), then the inverse distance (IDIS) and the sum

of the inverse distance (SIDIS). Then after, we have

computed the influence weight of the type of each

building on the type of the new building (building

with height equal Hi). Finally, we have deduced the

total probability of each type associated with this

building and we have obtained a new Pi that signify

the probability of a building with height Hi.

In next step, the buildings are divided in two

classes according to their types. We have calculated

the initial percentage (Pri) of each type for the

variable percentage (Pr):

• The buildings that have the surface SB1

associated with the height, H1 (Pr1 = Pri1, Prs1)

• The buildings that have the SB2 surface

associated with the height, H2 (Pr2 = Pri2, Prs2)

Therefore, three different percentages for each

type of building are calculated including:

• Initial percentage: fixed

• Variable percentage: variable

• Desired percentage: goal

Then, we have tried to adjust the current

percentage so that it is very close to the percentages

entered by the user of the model according to the

diagram that is illustrated in figure 7.

4 3D VISUALIZATION OF THE

CITY OF TOMORROW

After, generating the footprints and estimating their

related heights, in this section we have illustrated the

3D representation of the model. In order to visualize

the 3D model of the city, we have first created the

Digital Elevation Model (DEM) using BD TOPO data

altitudes (IGN). The results are displayed in

ArcScene by making an extrusion of the various

layers including new buildings using the height

calculated in the previous section. The model is first

implemented on the map of the year 2000 to obtain

the results of 2017. The accuracy of the model is

evaluated by comparing the observed map and the

simulated result for 2017. Figure 8 illustrates the 3D

representation of Rieucros for 2050.

5 CONCLUSIONS

SLEUTH urban growth model generates the

prospective 2D maps containing some pixels on

which urbanization is supposed to occur. These 2D

maps are limited to a raster data that are difficult to

interpret for decision makers and are needed to be

transformed into 3D building representations.

In this research, we have proposed an algorithm

to transform the SLEUTH results (pixels) into 3D

building representations concerning the density of

population, urban fabric and some restrictions on

urbanization such as the direction of the footprints

and the distances to the urban objects and geographic

features. The building height depends on the

probability of the height of adjacent buildings

according to the urban fabric.

The model is applied on the simulated urban

growth maps of 2050 for Rieucros. Although the

provided 3D model is a primary model, it helps to

better understanding of the simulation results and to

facilitate the interpretation of the SLEUTH

simulation.

From Pixels to 3D Representations of Buildings: A 3D Geo-visualization of Perspective Urban Respecting Some Urbanization Constraints

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Figure 7: The algorithm of calculating the probability of the height for each building according to the building types and

urban fabric scenario.

Figure 8: (a) 2D simulated urban map for 2050, (b) Ortho-photo 2017, (c) 3D representation of the current city (2017), (d)

3D representation of the city for 2050.

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