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Intersections of Our World

Paolo Fogliaroni

Vienna University of Technology, Austria

paolo.fogliaroni@geo.tuwien.ac.at

Dominik Bucher

ETH Zurich, Switzerland

dobucher@ethz.ch

Nikola Jankovic

Vienna University of Technology, Austria

nikola.jankovic@geo.tuwien.ac.at

Ioannis Giannopoulos

Vienna University of Technology, Austria

igiannopoulos@geo.tuwien.ac.at

Abstract

There are several situations where the type of a street intersections can become very important,

especially in the case of navigation studies. The types of intersections aﬀect the route complexity

and this has to be accounted for, e.g., already during the experimental design phase of a navigation

study. In this work we introduce a formal deﬁnition for intersection types and present a framework

that allows for extracting information about the intersections of our planet. We present a case

study that demonstrates the importance and necessity of being able to extract this information.

2012 ACM Subject Classiﬁcation Information systems →Geographic information systems, In-

formation systems →Data analytics

Keywords and phrases intersection types, navigation, experimental design

Digital Object Identiﬁer 10.4230/LIPIcs.GIScience.2018.3

1 Introduction

The street network of a city is a physical artifact embedded in the natural world. Most of the

times, it consists of highways (i.e., streets meant for cars only), roads (meant for cars and

pedestrians) and pathways (only for pedestrians). Sometimes these networks are following

strict human design guidelines and sometimes they are bounded by natural constraints. Along

with historical rationales, these constraints are the primary reasons that not all parts of a

city follow a gridded design structure (e.g., curvilinear). This means that beside commonly

encountered 3- and 4-way intersections, also more complex ones can exist.

But what are the main implications of this diversity of streets and intersections, and why

is it important to know how a city, a country or even a continent are structured? What can

we learn from this information and how can this information be useful?

In the following we will exemplify our work focusing on the area of navigation studies and

experimental design. Independently of the research discipline, when planning an experiment

there is a certain process that is followed in order to come up with a correct design. At the

very beginning, information for the various relevant variables is collected that eventually will

help to make the right choices.

In the case of navigation experiments, the relevant variables concern the subjects (e.g.,

gender or age), the type of navigation aid [

13

] and the timing of instructions [

12

], if any,

©Paolo Fogliaroni, Dominik Bucher, Nikola Jankovic, and Ioannis Giannopoulos;

licensed under Creative Commons License CC-BY

10th International Conference on Geographic Information Science (GIScience 2018).

Editors: Stephan Winter, Amy Griﬃn, and Monika Sester; Article No. 3; pp. 3:1–3:15

Leibniz International Proceedings in Informatics

Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany

3:2 Intersections of Our World

and the environment (e.g., the route). When it comes to the environment, the relevant

factors that have to be considered are numerous [

15

] and decisions can be made by taking

into account possible interactions between the relevant subjects and the environment –

e.g., previous experience of the subjects with the environment. Besides factors such as

architectural diﬀerentiation and environmental landmarks [

30

], the types of intersections are

highly relevant since they contribute to the complexity of a wayﬁnding decision [

15

]. A typical

question during the design process is how the decision points along the designated route

should be selected in terms of number of choices. How many and what kind of crossroads

should the route encompass? Of course, the number of crossroads and their shape (e.g., T-

or Y-intersections) on an experimental route is strongly related to the underlying research

questions.

The aim of this work is to help answering this type of questions. We computed the

number and type of all intersections on Earth and developed a web application that can be

easily used to extract this precomputed information for any area in the world. Of course this

work is not limited to navigation and experimental design. Next to researchers of various

disciplines, industries related to the areas of transportation and urban planning can use our

work for their decision making processes. For instance, by comparing the intersections of a

street network between two areas, interesting correlations with other phenomena could be

made, allowing to draw conclusions regarding the impact of the intersection types.

As a data source for our work we resorted to OpenStreetMap (OSM), that is one of the

most commonly used source of volunteered geographical information (VGI). While approach

we present does not require any particular form of road network data, the wide and free

availability as well as the generally good quality of OSM [

16

] make it an adequate choice for

intersection analysis. OSM data was analyzed in a multitude of studies before, not only in

terms of quality and completeness [

18

], but also as a data source for answering questions

about various environments [

9

], to determine the distribution of landmarks and points of

interest [

31

,

28

,

3

], to build recommender systems [

4

] or as contextual enhancement for other

types of data, such as Twitter posts [17].

In terms of intersection analysis, most previous work focuses around the automatic

detection of roads and intersections from other sources of data, such as GPS traces [

10

,

7

]

or satellite imagery [

6

]. A variety of techniques exist, where intersection types are either

implicitly learned using machine learning techniques (such as neural networks for satellite

image analysis) [

27

,

32

], or considered directly within the model [

25

]. To the best of our

knowledge, in all of the automated detection methods the individual intersections are not

classiﬁed in any way except based on the number of roads that lead up to them.

Intersections also play a central role in many routing applications [

24

]. Not only do red

lights (commonly occurring at intersections) inﬂuence the driving time, behavior, and related

emissions [

23

,

2

], but even the diﬀerence between a right or left turn at an intersection

incurs diﬀerent penalties to route computations [

20

]. In addition, vehicular ad hoc networks

(VANETs, which are used for inter-car communications) optimally also take intersections

into consideration, as they provide data exchange points for cars driving on diﬀerent routes

and cars are likely to stop there [5, 1].

2 Types of Intersections

While the terms junction and intersection are commonly used interchangeably to refer street

joints and crossings, they have slightly diﬀerent meanings, with the term intersection referring

to a speciﬁc type of junctions. According to the Oxford Dictionary, a junction is a place

P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:3

(a) T-intersection. (b) Y-intersection. (c) Cross-intersection. (d) X-intersection.

Figure 1 The most common types of prototypical named intersections.

where two or more roads or railway lines meet, while an intersection is a point at which two

or more things intersect, especially a road junction.

The term junction unambiguously relates to the mobility infrastructure domain and

denotes roads coming together but does not specify the exact nature of their connection

(intersect, touch, meet at a square, etc.). Conversely, the term intersection has a broader

scope – as it can refer to several domains. Yet, when it comes to the mobility infrastructure

domain it clearly refers to the cases where two or more roads intersect with each other.

Intersections are mostly studied in the areas of Architecture, Civil and Traﬃc Engineering,

as well as Urban Planning. Studies in these domains are concerned with intersection design and

construction to optimize traﬃc load, road safety, and traveling time (e.g., [

29

]). Intersections

are typically split into two main categories: at-grade and grade-separated (see, e.g., [

8

]).

At-grade intersections consist of roads located at the same level (grade), while the roads

creating a grade-separated intersection are at diﬀerent levels (grades) and pass above or

below each other. Grade-separated intersections are mostly used in highways and motorways,

as they allow for a faster and smoother merging of car traﬃc but are not well suited for

pedestrian navigation.

Both categories can be more ﬁnely classiﬁed. Grade-separated intersections can be

divided into interchanges and grade-separations without ramps. Subcategories of at-grade

intersections include proper intersections,roundabouts, and staggered (or oﬀset) intersections,

among others. Proper intersections are the most prototypical type of intersection for the

layman: several road segments converge to meet at the same point. Roundabouts are circular

intersections that cars can enter and exit smoothly and in which road traﬃc ﬂows in a single

direction. In Staggered intersections several (minor) roads meet a main road at a slight

distance apart such that they do not all come together at the same point.

In the scope of this work we only take into consideration proper intersections and,

marginally, staggered intersections (that we regard as a composition of proper intersections).

The analysis of more more complex types of intersections such as, e.g., roundabouts will be

investigated in future work.

In the following we will introduce relevant terminology and discuss properties of proper

intersections. The most straightforward property to classify intersections is the number

n

of street segments stemming out of it. We call such street segments the branches of the

intersection. An intersection

I

with

n

branches is called an

n

-way intersection and we denote

it by

In

. Obviously, we need at least two street segments to meet in order to form an

intersection. In this work we focus on the intersections which call for navigational decision

making: given one street segment that is used to approach an intersection, there have to be

at least two more street segments that can be used to leave that intersection (i.e., n≥3).

A second discriminant that we use to classify an intersection is its shape. That is, the

angular arrangement of its branches. Typically, this is done by comparing the intersections

at hand to some others that are generally accepted as prototypical ones [

33

,

22

,

26

,

14

]. The

GIScience 2018

3:4 Intersections of Our World

most common ones are reported in Figure 1: they are called T- and Y-intersections for

n

= 3;

cross- and X-intersections for

n

= 4. Every intersection with more than four branches (

n >

4)

is typically referred to as a star-intersection.

There is evidence that these named intersection types are used very naturally by people

when communicating route instructions verbally [

33

,

22

] or schematically [

33

,

26

,

14

]. However,

they suﬀer from two major drawbacks. First, these namings only exist for intersections with a

small number of branches (

n≤

4). Second, they are often not precisely deﬁned: for example,

while most people would agree that a cross-intersection splits a revolution into four right

angles, there might be a large disagreement on the skewness of an X-intersection.

For these reasons, we introduce the concept of regular intersection, whose branches divide

a revolution into uniform parts. More formally:

IDeﬁnition 1

(Regular

n

-way intersection)

.

Let

b0,· · · , bn−1

be the branches of an

n

-way

intersection enumerated in circular order . We deﬁne

αi

as the angle formed by the pair

(

bi−1, bimod n

)for every

i∈N

such that 1

≤i≤n

. We say that a

n

-way intersection is

regular if and only if α1=α2=· · · =αn= 360/n and we denote it by Rn.

In general, to further characterize an

n

-way intersection we compare it to its regular

counterpart, rather than to the aforementioned named intersection types. However, it has

to be noted that regular 3- and 4-way intersections can be interpreted as exact deﬁnitions

for Y- and cross-intersections, respectively. The arbitrary skewness of X-intersections makes

them unsuitable to be taken as an objective reference for comparison. T-intersections, on

the other hand, are well deﬁned. For this reason, for 3-way intersections we also perform a

comparison to T- intersections.

Finally, we deﬁne the angular distance ∆(

In, Rn

)among a generic

n

-way intersection

In

and its regular counterpart

Rn

as the minimum sum of angles that we have to rotate the

branches of

In

to perfectly match

Rn

, while preserving the circular order of

In

’s branches.

Note that there are

n−

1possible rotations that can be performed to match

In

to

Rn

(see

Sec 3.2 for more details).

3 Intersections Framework

In the following, we present our framework that was implemented for the classiﬁcation

and analysis of intersections. As one of the goals was to make worldwide intersection data

available, the presented framework is based on OpenStreetMap data and is publicly available

1

.

The framework is able to periodically process this data and writes the resulting intersection

measures into a database, where they can be accessed through a web application.

3.1 Data Source

OpenStreetMap (OSM) is arguably one of the largest and most important volunteered

geographic information (VGI) projects. As VGI is often not only the cheapest source of

geographic information, but even the only one available in certain regions [

16

], it is an

agreeable data source for a global intersection analysis. It needs to be noted that even though

OSM data quality can be considered adequate for many purposes, its spatial distribution

is not uniform, but depends on factors such as the information of interest or social events

(e.g., an upcoming Football World Cup) in a region [

18

,

19

,

11

]. However, these quality

1See http://intersection.geo.tuwien.ac.at.

P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:5

Analysis Class

Highway Tag Values Description

Road

living_street,primary,secondary,ter-

tiary,unclassiﬁed,residential,ser-

vice,primary_link,secondary_link,ter-

tiary_link

All ways that can be traversed by both

cars and pedestrians, namely all nor-

mal roads.

Path Road highway tag values plus

path,steps,bridleway,footway,track,

pedestrian

All ways that can be used by pedestri-

ans. Including smaller tracks, hiking

routes, etc. where cars cannot drive.

Car Road highway tag values plus

motorway,motorway_link,trunk,

trunk_link

All ways that can be traversed by car.

This additionally includes highways

and motorways, where pedestrian ac-

cess is usually forbidden.

Table 1 Diﬀerent highway tag values used within the intersection analysis framework.

issues often concern single newly built roads or geographical information unrelated to the

road network, which make up for a negligible amount of data with respect to a regional

intersection analysis.

The three primary data structures of OSM are nodes,ways and relations. Nodes represent

single points in space (i.e., they have a longitude and latitude), such as points of interest or

individual objects. Ways are ordered lists of nodes, and encode linear features (like roads or

rivers) and boundaries of areas (when the ﬁrst and last node are equal). Finally, relations

describe relationships between multiple elements, e.g., a collection of ways which form a

scenic route, or turn restrictions, which state that you cannot cross from one way into another

at a certain intersection.

All the node, way and relation objects can have an arbitrary number of tags, which have

a simple key

→

value form (both key and value are arbitrary strings). The tags themselves

are not formally speciﬁed, but are chosen based on a consensus in the OSM community. For

example, the very common tag highway is assigned to way objects which can somehow be

used for travel, e.g., for walking or driving. It can take the values described in Table 1

2

.

Note that we distinguish between three analysis classes, one with ways solely accessible

to pedestrians, and another two with ways accessible to cars (including resp. excluding

motorways). To ﬁnd intersections in the OSM data, it suﬃces to look at ways that carry a

highway tag, and to determine which nodes are shared among several of these ways.

OSM data is available in diﬀerent formats. As the whole uncompressed xml planet ﬁle is

around 850 GB at the time of this writing, we opted for the protocol buﬀer binary format

(PBF) instead, which is available as a 40 GB gzipped ﬁle

3

and consists of around 4.3 billion

nodes and 470 million ways.

3.2 Data Processing

After uncompressing the PBF ﬁle, we ﬁrst search for nodes that should be considered

intersections. As stated above, this corresponds to nodes which have more than two branches

(

n≥

3). For each way in the OSM dataset that has one of the appropriate highway tag values

2

For a detailed description of the individual values, and also additional ones that are not used in this

framework, please consult the OSM documentation under wiki.openstreetmap.org/wiki/Key:highway.

3For details see wiki.openstreetmap.org/wiki/PBF_Format.

GIScience 2018

3:6 Intersections of Our World

I

b

b

b

b

(a)

Original 4-way intersection

Iwith branches b0-b3.

Rn

(b)

Overlay of perfect 4-way in-

tersection R4.

Rn

0

(c)

Angles between original and

perfect intersection.

Figure 2

Computation of ∆(

In, Rn

), the sum of all angles that each branch

bi

has to be rotated

in order to produce a regular

n

-way intersection. Note that it suﬃces to align the regular intersection

with each branch (as is done for b0in (c)), and take the minimal ∆of all possible alignments.

(cf. Table 1), we iterate through all the nodes making up this way, and build a mapping that

stores all neighboring nodes of each node. To be able to distinguish the diﬀerent analysis

classes later on, the highway tag value is additionally stored for each neighboring node.

In essence, we deﬁne intersections as a function mapping a center node

p

to a number

n

of adjacent nodes

pp,i

, where for each

pp,i

in addition the highway tag value

th,i

of the

connecting way is stored:

In:p7→ {(pp,i, th,i )|0≤i<n}(1)

As this is done for all nodes in the OSM dataset (irrespectively of

n

), in a second iteration, a

ﬁnal set of intersections

{I0, ..., Ik}

has to be built by removing all nodes that dissatisfy the

minimal number of branches condition (i.e.,

|I

(

p

)

|<

3). This set of intersections contains all

the relevant OSM nodes for the purposes of the here presented framework. To compare each

intersection to its regular counterpart (in the case of a 3-way intersection additionally to a

perfect T-intersection), it is required to compute all angles between the diﬀerent roads in a

next step.

Thus, for the remaining intersections, a second pass through the OSM data collects the

coordinates of the center node

p

itself, as well as the coordinates of all the neighboring

nodes

pp,i

that can be reached by traversing its branches

bi

. Using these coordinates, it is

possible to compute all angles between the branches and the meridian passing through the

center node. Figure 2 depicts a hypothetical 4-way intersection in black and, beneath it, the

regular 4-way intersection, where the angles between branches are always 90

◦

. In order to

compute the angular distance ∆(

In, Rn

)to the regular intersection, we rotate the regular

intersection

n

times, so that it always aligns perfectly with one of the branches

bi

. Figure 2c

shows one of the four possible alignments for a 4-way intersection. For each non-aligned

branch,

αi

denotes the required rotation to reach an alignment with the next “free” branch

of the regular intersection (in this respect, “free” simply means that no two branches of the

original intersection may be rotated to the same branch of the regular intersection). For any

alignment with a branch of the regular intersection, a ∆

0

is computed as the sum of all

αi

.

The ﬁnal ∆takes the value of the minimal ∆

0

over all

n

possible alignments. Note that this

is a globally minimal ∆, even if arbitrary rotations of the regular intersection were allowed

(and not just “snapping” to branches of the original intersection), as rotating the regular

intersection monotonically increases or decreases ∆, until another alignment is reached. As

such, all minima and maxima of ∆must occur at an alignment with the regular intersection.

P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:7

All the intersections with their coordinates, the number of branches, as well as the

computed ∆(

In, Rn

)are ﬁnally written to a PostGIS database

4

. Since it is required to know

the analysis class of each intersection, an additional database ﬁeld denotes if an intersection

is valid for road,path, and car, or only any subset thereof.

3.3 Data Service

We provide public access to the intersection data computed with our framework through a

web application that is accessible at intersection.geo.tuwien.ac.at.

The interface provides a map canvas with OSM as a basemap that can be used to freely

browse the whole globe. With the current release of the application, the user is provided

with a selection menu from where she can specify the type of intersections of interest (column

“Analysis Class” in Table 1). We plan to extend this in future releases to allow the selection

of combinations of the base intersection types.

We oﬀer three possibilities to specify the region of interest: polygon drawing, viewport,

and name search. In the ﬁrst case, the user can specify a region by drawing a polygon on the

map. With the canvas selection, the viewport currently shown on the map canvas is used to

perform the database query. Finally, it is possible to look for named entities via a search box

that provides a live interface to an OSM Nominatim

5

server. After typing in the name of

the searched feature, the user can ask the interface to draw the corresponding polygon on

the map. Given the huge amount of intersection data available, we decided to limit the area

of the search region to not overload the server. In future releases this limitation might be

removed. Also, in order to promote interoperability, we plan to include the possibility of

specifying custom geometries expressed in diﬀerent type formats (e.g., KML, geoJSON, etc.).

The intersection type and the region speciﬁed are used to submit a query that returns

a statistical summary for intersections of the given type in the provided region. This

summary contains the number of occurrences for each

n

-way intersection, the average ∆

from the corresponding regular intersection – for 3-ways, also the average ∆from the regular

T intersection. Besides the statistical summary the user is also provided with a link to

download the whole intersection data set for the speciﬁed region and type as a CSV ﬁle.

At the time of writing the CSV ﬁle only contains information about the intersection

points that were computed from OSM nodes. Beside the geometric information (reported in

WKT) each point is associated the following attributes: the number of branches and the type

of intersection, and the angular distance ∆to the corresponding regular intersection.

Note that the intersection classes deﬁned in Table 1 are not disjoint. This results in

the same intersection occurring up to three times in our database, once for each category.

Imagine the case of an intersection where both roads and paths converge. For example, we

may have 3 roads and 1 path. This intersection appears twice in our dataset: as a path and as

a road. Since roads are accessible by both pedestrians and cars but paths are only accessible

by cars, we have a 4-way path intersection and a 3-way road intersection. A similar concept

applies to the categories of road and car intersections. The relation of the number of ways

(denoted as

nclass

) between the intersections that overlap is

ncar ≥nroad

and

npath ≥nroad

.

In our database we also keep trace of the ways that form intersection branches: their

geometry (also converted to OGC standard), the original OSM highway tag, and a relation to

the intersections that they generate. This information is not accessible through the current

version of the application, but will be made available in future releases.

4PostgreSQL 9.6 with PostGIS 2.3.2, the processing application is implemented in Rust 1.23.0.

5Nominatim is a search engine for OSM data, see wiki.openstreetmap.org/wiki/Nominatim.

GIScience 2018

3:8 Intersections of Our World

3

4

5

n-way

0

10

20

30

40

50

60

70

80

Percentage

Detroit

Melbourne

Vienna

Zürich

Figure 3

Distribution of the intersections as

the number of branches nvaries.

Detroit Melbourne Vienna Zürich

3-way 46.76% 84.49% 75.16% 78.88%

4-way 52.84% 15.20% 23.74% 20.13%

5-way 0.36% 0.29% 0.93% 0.82%

6-way 0.04% 0.02% 0.13% 0.14%

7-way 0.002% 0.002% 0.02% 0.02%

8-way 0.002% - 0.01% 0.004%

10-way - - - 0.004%

Total 40929 191508 75644 26286

Table 2

Distribution of intersections over

number of ways for the four cities.

4 Use Case: Detroit, Melbourne, Vienna, and Zürich

In this section we present and discuss intersection data obtained with our framework for

four exemplary cities and showcase how this data can be used during the design process

of navigational experiments. In Section 4.1 we compare the four diﬀerent cities, while in

Section 4.2 we focus on local diﬀerences within a single city.

4.1 Comparative Study

We used our framework to extract intersection data for Detroit (USA), Melbourne (Australia),

Vienna (Austria), and Zürich (Switzerland). While the framework allows for extracting

intersection data concerning diﬀerent types of streets (cf. Section 3.1), for this case study we

focus on paths and roads (i.e., set of all walkable streets).

Table 2 reports the distribution (as percentages) of intersections as the number of branches

n

varies. From this data we can derive several interesting insights. First and foremost it has

to be noted that for all the cities in exam almost the entirety of intersections are 3-ways

and 4-ways. This becomes even more evident by looking at the graphical representation

of the data reported in Figure 3. While this fact may seem trivial, it is still surprising the

cumulative percentage that these two intersection categories reach together – ranging from

98

.

9% for Vienna to 99

.

7% for Melbourne. This pattern seems to recur everywhere in the

world. Indeed, we found it in many other cities (Athens, Rome, Kathmandu, Washington

DC, Paris, and London, among others) that we analyzed with our framework in a preliminary

analysis for this work. This pattern consistently (only with minor diﬀerences) repeats across

diﬀerent cities, independently of their very heterogeneous morphology, history, and age.

The second insight that we can derive from this data relates to the ratio between the

number of 3-way and 4-way intersections. In this respect, we notice that Melbourne, Vienna,

and Zürich present a very similar trend with the majority of intersections being 3-ways,

although with slightly diﬀerent ratios between the number of 3- and 4-ways: approx. 5.5

for Melbourne, 3.2 for Vienna, and 3.9 for Zürich. Conversely, Detroit shows the opposite

trend, with the number of 4-ways slightly bigger than that of 3-ways. This may indicate, for

example, a more blocked structure of the city.

In the following we analyze the further discriminant introduced in this work to classify

intersections: the similarity to regular intersections (see Deﬁnition 1). As discussed in

Sections 2 and 3.2, we measure this by the angular distance ∆(

In, Rn

)between a generic

n

-way intersection

In

and the corresponding regular intersection

Rn

. For the case of 3-ways,

P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:9

City Min P25 P50 P75 Max

Det ∼0% 0.58% 1.96% 15.98% 99.99%

Mel ∼0% 1.03% 4.31% 21.59% 99.65%

Vie ∼0% 1.51% 6.08% 22.16% 99.87%

Zur ∼0% 2.09% 7.54% 23.48% 99.76%

∆-range: [0°,180°]

(a) 3-way to regular T, delta percentiles.

City Min P25 P50 P75 Max

Det ∼0% 0.23% 0.59% 2.11% 50.00%

Mel ∼0% 0.63% 2.37% 8.05% 83.69%

Vie ∼0% 0.91% 3.17% 9.69% 85.81%

Zur ∼0% 1.44% 4.45% 11.41% 64.12%

∆-range: [0°,360°]

(b) 4-way to regular 4-way, delta percentiles.

Table 3

Distribution of 3-way (4a) and 4-way (4b) intersections for the four cities (normalized).

we compare against regular T intersection instead. Moreover, given that for the cities in

exam 3-ways and 4-ways combined cover almost the totality of the number of intersections,

we will only focus on those.

Tables 4a and 4b report descriptive statistics for 3-ways and 4-ways, respectively. The

numbers reported are percentages referring to the value range that the angular distances can

take on. This is called ∆-range and denotes the diﬀerence between the minimum (∆

min

) and

maximum (∆

max

) angular distances from a generic intersection to its regular counterpart.

Obviously, the minimum is always zero (∆

min

= 0

°

), which corresponds to a perfect match

with the regular intersection. Conversely, ∆

max

depends on the number of branches (

n

) of the

intersection at hand and corresponds to the angular distance of the (theoretical) worst-case

scenario where all the branches of an intersection collapse on top of each other:

∆max =

bn−1

2c

X

i=1

(2iα) + ((n−1) mod 2) π(2)

For an understanding of this formula imagine to align any branch of the regular intersection

to the ﬁrst branch of the

n

-way at hand. Subsequently, take a pair of unmatched branches

from the generic intersection and rotate them (one clockwise and the other counterclockwise)

by

α

=

360

n

to match the ﬁrst pair of unmatched branches of the regular intersection. Now

repeat for the second pair of unmatched branches. In this case, we will have to rotate 2

α

in

order to ﬁnd the ﬁrst pair of unmatched branches of the regular intersection. Generalizing

this operation we obtain the formula in Equation 2. For 3-ways and 4-ways we have ∆-ranges

equal to [0

°,

240

°

]and [0

°,

360

°

], respectively. The ∆-range for 3-ways when compared against

the regular T intersection is equal to [0°,180°].

Figures 4a and 4b plot in greater details the distribution of 3-ways and 4-ways as the

angular distance varies over the ∆-ranges for the regular T intersection and the regular

4-way, respectively. The ﬁgures show that the majority of the intersections are very similar

to their regular counterparts (which aligns nicely with Klippel’s set of wayﬁnding choremes

[

22

,

21

]), with Detroit and Zürich representing extreme cases. The intersections of Detroit

are the most regular, with approximately 70% of its 3-ways and 90% of its 4-ways showing

an angular distance below 10% to the regular T intersection (i.e., 18

°

) and the regular 4-way

(i.e., 36

°

), respectively. Conversely, Zürich is the least regular, with approximately 55% of

its 3-ways and 70% of its 4-ways showing an angular distance below 10% to the regular T

intersection (i.e., 18

°

) and the regular 4-way (i.e., 36

°

), respectively. Melbourne and Vienna

are located in between these extremes, with Melbourne being slightly more regular than

Vienna with respect to both 3-ways and 4-ways.

These ﬁndings can be used, for example, during the design of navigational experiments

to select paths that adhere to the structure of the city where the experiments are to be

GIScience 2018

3:10 Intersections of Our World

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

80 - 90

90 - 100

Delta T Percentage

0

20

40

60

80

100

Percentage

Detroit

Melbourne

Vienna

Zürich

(a) 3-way to regular T intersection.

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

80 - 90

90 - 100

Delta Percentage

0

20

40

60

80

100

Percentage

Detroit

Melbourne

Vienna

Zürich

(b) 4-way to regular 4-way intersection.

Figure 4

Dsistribution of the angular distance (∆) for 3-ways

(a)

and 4-ways

(b)

with respect

to the regular T intersection and the regular 4-way intersection, respectively. The angular distance

(on the x-axis) is reported as a percentage of the diﬀerent ∆-ranges for 3-ways (i.e., 0

°−

180

°

) and

4-ways (i.e., 0

°−

360

°

). The percentage on the y-axis refers to the number of intersections in each

bin with respect to the total number of intersections of that type (i.e., 3-way and 4-way). The

smaller the value of ∆, the higher the similarity to the corresponding regular intersection.

performed. In this way, we can avoid to select some atypical path that may lead to biased

results. Assume that for our hypothetical navigational experiment we need a path that

comprises 10 intersections. If we were to conduct the experiment with a path matching the

characteristics of Detroit, we should select a path in the real world or in a virtual environment

that encompasses, e.g., ﬁve 3-way and ﬁve 4-way intersections. Of the selected 3-ways (resp.

4-ways), three (resp. ﬁve) should present a maximum angular distance of 18

°

(resp. 36

°

)

from the regular T intersection (resp. the regular 4-way). Conversely, if we were to conduct

the same experiment with a path matching the characteristics of Zürich, our path should

encompass eight 3-way and two 4-way intersections. Of the selected 3-ways (resp. 4-ways),

four (resp. six) should present a maximum angular distance of 18

°

(resp. 36

°

) from the

regular T intersection (resp. the regular 4-way).

Moreover, the availability of intersection data for the entire world easily supports compar-

ative analysis that so far was diﬃcult to control. Imagine to run the same spatial experiment

in diﬀerent cities or areas of the globe. The availability of this data may allow for comparing

the diﬀerent paths and, consequently, for relating and gaining insights on the possibly diﬀerent

experimental results obtained in diﬀerent locations.

4.2 Local Diﬀerences

In this section we discuss local diﬀerences within the city of Vienna. We used our framework

to run analysis on all 23 districts (DIST) and focus on the two with the highest variation,

district 8 and 10.

Table 5 reports the distribution (as percentage) of the intersections as the number of

branches

n

varies. This allows for easily comparing the statistics of the selected districts

against the statistics extracted for whole Vienna. Both the selected districts adhere to

P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:11

3

4

5

n-way

0

10

20

30

40

50

60

70

80

Percentage

Vienna

DIST 8

DIST 10

Figure 5

Distribution of the intersections

as the number of branches nvaries.

Vienna DIST 8 DIST 10

3-way 75.16% 53.97% 76.46%

4-way 23.74% 44.63% 22.44%

5-way 0.93% 1.4% 1%

6-way 0.13% - 0.07%

7-way 0.02% - 0.03%

8-way 0.01% - -

Total 75644 428 7121

Table 5

Distribution of intersections over

number of ways for whole Vienna and the 2

districts in exam.

the overall distribution pattern that we discussed in Section 4.1, with almost the entirety

of intersections distributed between 3-ways and 4-ways. The graphical representation of

the data (see Figure 5) allows for glimpsing diﬀerent local patterns for the two districts.

Speciﬁcally, district 10 exhibits a distribution almost identical to whole Vienna. In contrast,

district 8 exposes diﬀerent distributions, with approximately 20% less 3-ways (resp. 20%

more 4-ways) than whole Vienna.

The distribution of 3-way and 4-way intersections can be seen in Figures 6a and 6b as

their normalized angular distance varies in the corresponding ∆-ranges – i.e., [0

°,

180

°

]and

[0

°,

360

°

], respectively. As for 3-ways, district 8 is the most dissimilar with respect to Vienna,

while district 10 exhibits only a small deviation from the distribution of the whole city. The

same pattern emerges also for 4-ways.

Assume that we want to replicate in Vienna the navigational experiment discussed at

the end of Section 4.1 for which we need to select a path encompassing 10 intersections. If

we were to conduct the experiment in district 10, according to the intersection distribution

reported in Figure 5, approximately 76% (resp. 22%) of these intersections should be 3-ways

(resp. 4-ways). Say, for example, that we choose a path consisting of eight 3-ways and two

4-ways. According to the distribution of ∆s in Figures 6a and 6b, of the selected 3-ways

(resp. 4-ways), ﬁve (resp. 2) should present a maximum angular distance of 18

°

(resp. 36

°

)

from the regular T intersection (resp. the regular 4-way).

If the experiment was to be conducted in district 8 we could either decide to stick to

the statistics of whole Vienna or to the statistics of the district. In the ﬁrst case we would

end up with a selection similar to that of district 10. In the second case we would have to

choose diﬀerently. If we opt for the ﬁrst alternative the ﬁndings that relate to the structure

of intersections could be considered as a step towards generalization to whole Vienna but

might apply more loosely to district 8. More generally, the statistical data provided by

our framework can be used to ﬁnd out areas all over the world that expose an intersection

structure similar to that of a given area where, e.g., we performed an experiment. This

information can be used to replicate the experiment in any of these areas and identify

which of the insights we derive from the experiment results are invariant with respect to the

intersection structure of the path.

GIScience 2018

3:12 Intersections of Our World

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

80 - 90

90 - 100

Delta T Percentage

0

10

20

30

40

50

60

70

80

Percentage

Vienna

DIST 8

DIST 10

(a) 3-way to regular T intersection.

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

80 - 90

90 - 100

Delta Percentage

0

10

20

30

40

50

60

70

80

Percentage

Vienna

DIST 8

DIST 10

(b) 4-way to regular 4-way intersection.

Figure 6

Bar plot visualization of the distribution of the angular distance (∆) for 3-ways

(a)

and

4-ways

(b)

with respect to the regular T intersection and the regular 4-way intersection, respectively.

See Figure 4 for reading instructions.

5 Discussion and Conclusion

The framework presented in this work can be considered as an important asset during the

design of spatial experiments and to perform spatial analysis. As shown through the case

study in Section 4, the framework can be easily used to partially validate a selected route with

respect to generalization issues. Since local diﬀerences can be found in an urban environment

that do not adhere to the overall structure of a city, a country, or even a continent, the choice

of a route has to be considered very carefully. Furthermore, by identifying similarities of

the selected route at diﬀerent scales (i.e., from district up to continent scale), one can go a

step further and carefully interpret the ﬁndings of the experiment (at least those related to

features of the intersection distributions) and draw conclusions concerning the reproducibility

and comparison with experiments performed in diﬀerent areas. Of course looking only at the

intersections of a route is not suﬃcient, but necessary. This work can be considered as a

further step towards interpreting the results of an experiment concerning generalizability

aspects.

Next to the scenario used throughout this paper to exemplify how the results of this

work can be utilized, this type of quantitative data can also be useful for a multitude of

other purposes. For instance, machine learning approaches could proﬁt from this framework,

generating relevant features that can help to describe the spatial phenomena of interest.

Another example would include work in the area of transportation, trying to model the access

and demand or relevant work in the area of urban planing. Furthermore this framework

could also easily be used as part of city modeling softwares, e.g., Esri CityEngine

6

, helping

to automatically generate look-alike urban environments.

In this paper we presented the raw intersection data that we generated from OSM data

through the procedure described in Section 3.2 and show an example of how this data can

be used for the design and comparison of navigational experiments. However, according

to the speciﬁc experiment at hand it might be necessary to clean the raw data in order to

accommodate geometrical and perceptual aspects. We identiﬁed two cases where the raw

data may need to be cleaned before usage. Both cases concern scenarios where two or more

6See http://www.esri.com/software/cityengine.

P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:13

intersections are located very close to each other. If the intersections under consideration

are of the same type, this may denote a mapping issue: due to accuracy problems a single

intersection in the real world is actually reported as several in OSM. Alternatively, the

intersections might actually be correctly reported in OSM, but we may have a perception

issue: although we physically have several intersections, they are so close to each other that

a person could perceive them as a single intersection.

The other scenario concerns the case where intersections of diﬀerent types are very close

to each other. Speciﬁcally, we identiﬁed a somewhat problematic pattern where a road

intersection is surrounded by a set of path intersections representing sidewalks and zebra

stripes. In such situations, we actually have a single intersection in the real world that is

identiﬁed as several by our framework. This issue is due to the fact that in OSM, sidewalks

can either be mapped as separate ways or denoted with an apposite tag on the corresponding

road. This means that we cannot know in advance how many times this scenario appears in

our data. For this reason we performed a simple buﬀer and cluster analysis on Vienna to ﬁnd

out the amount of groups of intersections in our data that should actually be considered as a

single intersection. We used buﬀer of diﬀerent sizes (ranging from 1m to 10m) to identify

clusters corresponding to both scenarios: intersections of same type and one road surrounded

by path intersections. For the ﬁrst scenario we found that the number of clusters ranges

from 0.04% to 4.8% (resp. from 0.2% to 12.4%) of the road (reps. path) intersections, as we

increase the buﬀer radius from 1m to 10m. For the road-to-path scenario, the number of

clusters ranges 0 to 5.7% of the road and path intersections.

Finally, it has to be noted that the implementation of our framework does not compute

the data on the ﬂy from OSM data. Rather, a snapshot of the OSM database is taken and

intersection data is generated from there. This means that the data provided on the website

might not be completely actual, although we do not expect huge discrepancies.

6 Outlook

Since in our work we focused on regular intersections, we omitted analyses of roundabouts.

In the underlying OSM data, roundabouts are modeled as multiple 3-way intersections.

Although this might look correct at a ﬁrst glance, one can argue that roundabouts form a

category of its own, or even an n-way intersection, with n equals the number of ingoing and

outgoing branches. As this is an open question that needs further investigation and probably

a user study to understand how humans perceive roundabouts, we will focus on this problem

in the future. Since this framework is not only indented to be used for experimental design, a

possible solution could be to transfer the choice to the users of this framework, by providing

multiple options on how to handle roundabouts during runtime.

Also, in this work we did not perform any scale-based aggregation of the street geometries

(e.g., aggregating two lanes of a street into a single line). Therefore, the results presented in

this paper are at the ﬁnest level of details allowed by data source. Street aggregation will

also yield a reduction in the number of detected intersections as well as a simpliﬁcation of

the resulting intersection network. Future work along this direction may potentially lead to

a hierarchical organization of the data that, in turn, may allow for further types of uses and

analyses of the intersection data.

In future work we will also focus deeper on network patterns. For instance, what is the

most common sequence of intersections for a given length (number of intersections)? What is

the typical distance between intersections or intersection types (segment length)? Being able

to extract this type of information will further improve the goals set in this paper, allowing

to draw even better conclusions and automatically create even more realistic look-alike cities.

GIScience 2018

3:14 Intersections of Our World

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GIScience 2018