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Applied Spatial Accessibility Analysis for Urban Design: An integrated graph-gravity model implemented in Grasshopper


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This paper introduces a prototype for a user-friendly, responsive toolbox for spatial accessibility analysis in data-poor environments to support urban design processes. It allows for real-time computation of several evaluation indicators, mostly focused on accessibility related measures. The proposed framework is exemplified with three real-world case studies. Each of them demonstrates one part of the workflow; data gathering and preparation, sketching and developing scenarios, and impact analysis and scenario comparison.
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Applied Spatial Accessibility Analysis for Urban Design
An integrated graph-gravity model implemented in Grasshopper
Serjoscha Düring1, Andrej Sluka2, Ondrej Vesely3,
Reinhard König4
1,2,3,4AIT Austrian Institute of Technology 4Reinhard.
This paper introduces a prototype for a user-friendly, responsive toolbox for
spatial accessibility analysis in data-poor environments to support urban design
processes. It allows for real-time computation of several evaluation indicators,
mostly focused on accessibility related measures. The proposed framework is
exemplified with three real-world case studies. Each of them demonstrates one
part of the workflow; data gathering and preparation, sketching and developing
scenarios, and impact analysis and scenario comparison.
Keywords: accessibility, urban design, evidence-based design, graph model,
gravity model
Under the assumption that cities are large complex
systems, the question arises of how much planning
and regulations are desirable. On the extremes, there
are two distinct approaches to the urban planning
process; 1) readily designing cities and quarters down
to the shape of the roof or 2) supporting the self-
organization process and consciously plan with it
while protecting public interests and the commons.
As of now, most urban master plans are heavily
driven by design and normative visions that lack the
definition of measurable indicators and often ignore
the principles of self-organizational forces that shape
cities (Bertaud 2018). Thus, they are more likely to
make wrong assumptions on people’s behavior (e.g.,
in terms of location choices of developers or resi-
dents). Chances of costly infrastructure being built
at places that do not meet the demand appropri-
ately are increased. This mismatch comes with high
costs - once built, changes to the infrastructure are
difficult to carry out (Oliveira 2016). Therefore, some
planners and practitioners advocate for the second
approach mentioned above. Planning interventions
are thus preferably launched in an on-demand fash-
ion, responding to recent trends. This requires defin-
ing indicators that measure city status and their con-
stant monitoring. For new developments, models
with predictive abilities are required in order to help
with the estimation of the impact of adding or chang-
ing elements within the city systems (Achary et al.
2017, Bertaud 2018).
A vast body of literature exists on models and
methodologies for correlating and predicting the be-
havior of urban systems and societies in relation to
the built environment and socio-economic factors
(Hillier 1984, Batty 2017, Stanilov 2010). Adoption of
Data - CITY INFORMATION MODELLING AND GIS - Volume 3 - eCAADe 37 / SIGraDi 23 |333
these models into an accessible and integrated anal-
ysis framework might be a promising approach in
coping with the issues described above. Especially
in rapidly developing regions with high urbanization
rates, where authorities are pressured to act fast, and
a lack of institutional incentives to conduct an in-
depth evaluation of plans is often present, this kind
of toolbox might help to improve the allocation of re-
sources and increase the overall efficiency of urban
projects and their impact in practice. However, also
for smaller cities, projects, or design offices where re-
sources lack for the employment of detailed impact
studies, these tools have the potential to contribute
to the planning outcomes positively. More so if suffi-
cient user-friendliness allows them to be integrated
into an iterative planning and design process from
the early phases.
The general use-case of the toolbox is for projects
where larger, more sophisticated models and sim-
ulations are not applicable due to data, budget, or
know-how constraints. It offers simplified analysis
for planning and design cases that would otherwise
be executed without quantitative reasoning. There-
fore, in terms of complexity, the toolbox aims for a
rather high level of aggregation of the chosen param-
eters, to ensure greater transparency for non-experts,
better transferability to other cases and lower re-
quirements on input data and user experience. The
presented scope mainly allows for network and ac-
cessibility related analysis in interaction with basic
land use categories (eg. residential, commercial) and
point of interests (eg. Parks, shopping centers, transit
stations and so on).
In an attempt to follow the call for more data-driven,
evidence-based (Karimi 2014) approach to urban de-
sign for the use-cases depicted above, this paper in-
tends to present a first prototype for an integrated
spatial analysis framework with the following charac-
A high level of accessibility for users.
• Integration: Complete implementation in
popular CAD/visual programming package of
Rhinoceros 3D and Grasshopper, modular and
easily expandable
Low data requirements: Few and flexible re-
quirements towards data inputs, mostly de-
pending on open source data such as Open- or satellite imagery, poten-
tially allowing for “remote-monitoring” of the
towns basic state of being
• Standardization: An UI and standardized
structure for adding manual data inputs,
sketching and creating new scenarios
Scalability: The resolution and accuracy of
calculations can be adjusted to enable faster
computation and simulation on the city or re-
gional scale.
Implementation of Design / sketch mode. Allow-
ing for sketching of design variants with near real-
time feedback on selected performance indicators
Impact analysis and scenario comparison. After
full calculation of all indicators allow for streamlined
interface to compare impacts of multiple scenarios at
The core of the framework is a weighted graph-
model of an area’s mobility network (roads, streets,
transit lines etc.). Optional weights are population,
job or POI density, while POIs can be alternatively
placed manually. Most of network related calcula-
tions are performed within Grasshopper using the
plugin SpiderWeb and its implementation of the Di-
jkstra shortest path algorithm as the starting point.
For the large scale calculation of graphs betweenness
and closeness values, DecodingSpaces plugin is em-
ployed as an alternative to SpiderWeb. User interface
was implemented using plugin Human UI. In terms
of complexity the aim is a rather high level of aggre-
gation and few parameters, to ensure higher grades
of transparency, better transferability to other cases
and lower requirements toward input data.
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Figure 1
Model structure
and workflow
Here structure of model and general workflow are il-
lustrated (fig. 1). Each part is described in more detail
below. Naturally, the first step is feeding the model
with data either from external sources or by manual
addition/drawing. Next, the data needs to be struc-
tured and prepared. In the sketch mode both, the
models parameter and spatial configurations can be
changed in order to craft different scenarios. During
this process the user gets constant feedback on se-
lected indicators in near real-time. When a scenario
draft is finished, it can be exported (with all indica-
tors being computed) as a .ghdata file and, together
with other scenarios analyzed and compared in the
evaluation mode.
The model offers several channels to model Sce-
narios: Most importantly the street and transporta-
tion network, points of interest (structured in several
categories) and land uses which’s properties can be
defined by the user (eg. Population or job density,
FAR etc.) and used as weights or for the computation
of indicators.
Data Structure and scalability
The toolbox operates on different spatial scales and
supports interpolating, aggregating and disaggre-
gating between them. Basic elements of the model
are network edges, network nodes, POIs, shapes (eg.
blocks or plots) and two grids: one high-resolution
analysis grid (20 - 100 meters), that most other data is
mapped on before exporting and one low-resolution
grid (125 - 1000 meters) that is used to compute a
distance matrix and enables the model to work with
larger cities and areas in a trade-off with accuracy.
Figure 2
Generated low
resolution grids
with increasing
division threshold.
Graph and network modeling
The basic approach for modeling the network graph
is initially constructing the pedestrian and transit net-
Data - CITY INFORMATION MODELLING AND GIS - Volume 3 - eCAADe 37 / SIGraDi 23 |335
works separately before joining them in the very
end. This allows to generate graphs from geome-
tries (lines) using the spiderweb library and simulta-
neously model avg. waiting and exit times for transit
modes. Fig. 3 illustrates the graph and data structure.
Multiple transit modes can be set-up (eg. Metro, Bus
etc.) and individual average speeds, waiting and exit
times defined.
Figure 3
network graph
Figure 4
Network geometry
We currently use a planar graph where cost of edges
corresponds with travel time (or other attributes
relatable to street segments) associated to them.
Nodes can optionally be weighted with population
size, amount of working places, and so on.
Before the graph is created the underlying ge-
ometry is simplified and cleaned up. Fig 4 provides
an overview of the steps applied. In this process the
networks complexity and resolution can optionally
be decreased in order to achieve faster calculations.
Gravity function
Gravity models are among the most frequently used
model category within geography. Originally intro-
duced by Hansen (1959), they effectively model To-
bler’s first law of geography that is “everything is re-
lated to everything else, but near things are more re-
lated than distant things. (Tobler 1970, p. 234). The
general gravity function is defined as:
eβ·dij (1)
Where Gi is the gravity induced by destination j to
origin i. Wj is the weight of destination j (eg. the
total floor area of an location) while is parameter
that scales the effect of the weights. e is the natu-
ral logarithm. dij is the distance between origin i and
destination j while is the distance decay parameter.
The parameter and are ideally estimated empirically
f While in practice is often left to 1, the parameter is
crucial. Multiply empirical studies concluded that, in
the urban context, a value of 0.002 (when distances
are measured in meters) generally delivers good re-
sults for pedestrian movements (see Sevtsuk et al.
eβ2·dij (2)
The basic gravity model can be extended to
model competition between places (such as retail
centers or parks) and people’s choices on which place
to visit. This variation is also known as the Huff-model
(see Huff 1963). Its basic assumption is that the prob-
ability of a potential visit of a person to a point of in-
terest is a function of the point’s attractiveness and
its distance to the person (basically equals Gi) rela-
tive to the gravity received by all other points of in-
terests. Thus, the function can be defined as:Where
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Figure 5
Tracking of selected
indicators during
sketching scenarios
Visitors i are the total visitors to point of interest i. The
first term represents the relative gravity (gravity be-
tween point of interest i and origin j divided by the
sum of the gravitation between origin i and all points
of interest). The second term, pop j, is an additional
weight attributed to origin j, resembling the popula-
tion or potential customers.As, one could argue that
if a origin is very far away from any point of interest no
visitor at all will originate from that location. This can
simply be modeled by adding another distance de-
cay parameter (2) to the model affecting the weight-
ing parameter pop j.This approach can be, and is of-
ten applied in modeling origin / destination matrices
that form the basic for traffic and foot-fall modeling
(for instance see Hensher 2004).
This mode serves to sketch scenarios and tweak de-
signs proposals. The sketch mode is thought of to
help with preparing multiple scenarios that can then
optionally be fully computed and reviewed in detail
using the Evaluation mode (see below). The user can
deactivate the computation of indicators and mea-
sures that have long calculation times in order to get
near instant feedback when trying out different con-
figurations. Thus, facilitating an indicator-guided de-
sign process (see Fig. 5).
Additionally, creating a GUI to handle all user in-
teractions was considered an essential step for mak-
ing the toolbox accessible to parties not familiar with
Rhinoceros 3D and Grasshopper or CAD software in
general: It can be used without having to interact
with the Grasshopper canvas nor using any Rhino
text commands. The higher level of user-friendliness
raises the potential of the tool for employment in
workshops and public participation sessions for cre-
ating, discussing, and communicating multiple real
and hypothetical scenario variations.
The evaluation mode relies on previously calculated
scenarios. Up to fourof these scenarios can be loaded
at the same time and compared to one another.
The core functionality of this mode is filtering,
structuring and comparing indicators between sce-
narios. Fig. 6 and 7 provides an overview of the user
interface structure. On top are basic filters for the net-
work type (pedestrian/transit; car, etc.) and (sub) ar-
Data - CITY INFORMATION MODELLING AND GIS - Volume 3 - eCAADe 37 / SIGraDi 23 |337
Figure 6
Data dashboard
with the data
visualized on the
analysis grid
eas the indicators should be computed for. Below are
several tabs: most importantly for indicators or indi-
cator categories. In case a project required additional
evaluation criteria, a new tab can simply be attached
to the interface with ease.
Spatial filtering
The toolbox provides functionality to define up to
four sub areas to analysis the impact of a proposed
intervention on a local level. These areas can either
be characterize spatially (by sketching a curve around
the area of interest) or by defining filters.
Filters are rule based selections. Only spatial
units (such as nodes or cells) that meet all of the selec-
tion criteria are included. Criterias such as the popu-
lation, jobs, income, social-milieu etc. This allows to
keep track of, let’s say, how low-income groups ben-
efit or disbenefit from an intervention in particular.
Due to the readily accessible data and the city’s repu-
tation for its well connected multimodal public trans-
port system, the city of Vienna was chosen as a
testbed city during the development of the tool.
The road network acquired from the Open-
StreetMap database was connected to the graph of
public transit network built from General Transit Sys-
tem Feed (GTFS) data provided by the Vienna’s open
data portal. Instead of using connection times parsed
from the GTFS, it was decided to calculate public
transport connection times from the traveled dis-
tance and assumed average speeds of used transit
modes. This approach has a disadvantage of intro-
ducing slight inaccuracies into the model compared
to calculating travel times based on existing tran-
sit timetables. On the other hand, it simplifies the
model and allows for the streamlined introduction of
changes into the model. This approach enables ex-
ploration of hypothetical scenarios such as adding
a new metro line to the public transport system or
measuring the impact of increased speeds as, i.e.
converting shared bikes into e-bikes.
After series of tests and optimizations of the av-
erage speeds of each transit mode and average as-
sumed waiting times, the error in travel times using
public transport was minimized to average of ±15%
from the timetable reference (see fig. 8).
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Figure 7
Dashboard for
point of interest
(POI) related data
Figure 8
Comparison of the
calculated travel
times with results
from Google
Directions API for
the same origin -
destination pair
The first application of the method has shown
promise in assessing both current accessibility pat-
terns of the city and predicting the impact of future
developments of the transit network. However, it is
to be noted, that due to the simplified way the con-
nection times are calculated, the model is slightly in-
accurate. In the future, we would like to implement
an updated framework which would enable to pre-
serve the connection time information from the GTFS
data, if available, while still allowing for simple mod-
ifications of the network and measuring the perfor-
mance of hypothetical scenarios.
In case of Gela, our toolbox was used to simulate ad-
dition of new public transport proposals, formed dur-
ing workshops conducted with the local governance,
including introduction of new bus routes, tram-train
route and bicycle lane network.
The city Gela is located on southern coast of
Sicily, Italy. It has a population of 75,458 inhabi-
tants, and it is largely car-dependant, with almost
no existing public transport infrastructure, the only
exception being buses without clearly shown routes
or time-tables. The quality of sidewalks is also low,
and there almost no existing bicycle lanes. The city
is however currently in the process of changing this,
bringing a whole new public transport network and
bike lanes network. Taking the advantage of the tool-
box’s option of comparing different scenarios, it pro-
vided very clearly visible results, showing impacts
any of these proposals would have on accessibility
from certain locations within the city (see fig. 9).
Data - CITY INFORMATION MODELLING AND GIS - Volume 3 - eCAADe 37 / SIGraDi 23 |339
The toolbox was used to generate public trans-
port network proposals which were further stored in
the toolbox’s UI. Having the the option to easily con-
trol which of them are active for current simulation
allowed for comparison of their significance for cer-
tain areas. Furthermore, a bike-sharing system (sta-
tion based) was modeled with the toolbox, assisting
in decision making of where these stations will be lo-
Figure 9
Visualization of
changed mobility
after the addition of
a tram line
Figure 10
Visualization of
selected indicators.
First row: access to
jobs, difference
map; Second row:
Change in
potentials; Third
row: Box plots and
histogram for the
commuting to
shopping centers
The case study of Gela was a great example of using
the toolbox for comparison and simulation of new
additions of public transport to the city. Due to it ’s al-
most non-existent current public transport, most of
the additions resulted in quite a significant impact,
that is clearly communicated through visual means
to all the interested parties, resulting in much higher
awareness and interest. Furthermore, having access
to these immediate simulations proves a great assis-
tance in discussing and modifying the proposals or
designing new ones.
In a joint project by the World Bank, Superwien Ar-
chitektur and the Austrian Institute of Technology,
the toolbox was used in the master planning process
for two medium sized cities in Uzbekistan: K agan and
Chartak. The task was to develop between 4 to 8 in-
terventions (eg. implementation of a new eco-trail,
renovation of public spaces etc.) for each city and
then rank them in a cost-benefit analysis as not all
projects could be funded. The toolboxwas employed
to assist design decisions, to conduct impact analy-
sis of individual projects and to bundle projects by
testing which combinations of interventions syner-
gize with each other to bring maximum leverage ef-
As data inputs only the street network, a esti-
mated population and job distribution and points of
interests (such as schools, parks, retail centers) were
used. Exemplary, the application of the toolbox in
deciding upon the location of a second pedestrian
railway overpass in Kagan will be outlined below.
First of all, six potential locations for the second
bridge were located and evaluated by several indica-
tors. Table 1 provides an overview. Based on the re-
sults three options (A,C and D) were selected for fur-
ther analysis and comparison in the evaluation mode.
Next to accessibility and commuting related mea-
sures, the potential change on pedestrian frequency
and footfall was analyze as well. The latter can be
helpful for anticipating and planning of retail loca-
tions or prioritizing street renovations among others
applications (see Fig. 10). The spatial filtering func-
tional further allowed to estimate the specific impact
on the other proposed design interventions individ-
ually. After all a decision between option C and D was
340 |eCAADe 37 / SIGraDi 23 - Data - CITY INFORMATION MODELLING AND GIS - Volume 3
Table 1
Overview of
indicators and
results. In green:
short-list of
locations for further
analysis. Option C
ranks first in six out
of ten indicators
and therefore
outperforms both A
and D in the
recommended with the conclusion that the final de-
cision is a matter of normative standpoints: If spatial
equality and a more evenly distributed access to all
citizens is prioritized then option C appears optimal.
In case the most important goal is strengthening the
centre and perhaps fully integrate parts of it into old
Kagan, then location D appears to be the better op-
tion, despite its lower impact on the overall connec-
All in all, the toolbox proved useful in facilitating an
evidence-based discussion and decision process on
the ideal location for the second railway overpass
and was received positively from the project part-
ners. The combination of comparing multiple sce-
narios against one reference scenario at the same
time with spatial filtering options turned-out to be a
powerful framework to compare alternatives for one
project but also to test for a ideal combination of a
set projects in a streamlined manner.
It is important to emphasize that the toolbox at no
point claims to cover all issues related to and im-
portant for planning and monitoring urban systems.
Thus, it can only contribute in the fields it makes
dedicated Statements on. Moreover, its accuracy de-
pends on the data quality used as input and the cali-
bration of its parameters. As both can be challenging
the toolboxes can be seen as a planning and design
Data - CITY INFORMATION MODELLING AND GIS - Volume 3 - eCAADe 37 / SIGraDi 23 |341
decision support system - as one additional factor to
base choices on. But even in cases where the data
quality is highly questionable the toolbox could still
be used (carefully) to compare relative differences
between scenarios or in order to better understand
and discuss the underlying dynamics of urban sys-
tems and in the use-cases depicted in the beginning
of this paper.
In all three cases the model was overall well received
by the participating parties and in the context of a
workshop (Gela), the GUI and CAD-like input meth-
ods for sketching scenarios exhibited good usability,
the visualization in form of maps and a selected set
of key indicators proved useful to communicate and
discuss and decide upon design proposals. Similarly,
the tools application to quantify and evaluate various
urban design proposals was perceived help- and in-
sightful by the involved urban designers that previ-
ously have not been in touch with quantified meth-
For the further development, we aim to improve
the capabilities for local validation of the model’s pa-
rameters as well as add a range of new features in
terms of data gathering, processing and exchange as
well as adding more analytical modules and indica-
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342 |eCAADe 37 / SIGraDi 23 - Data - CITY INFORMATION MODELLING AND GIS - Volume 3
... By modeling public transport operation, configuration and surroundings of stations, a comprehensive public transport service accessibility index (CPTAI) is formulated to quantify accessibility and shows significant statistical association with trips by public transport. Düring et al. (2019) developed a toolbox for spatial accessibility analysis adapted for datapoor environments and through three different case studies demonstrated the positive effect of improved accessibility on mobility patterns for multimodal transport, access to jobs and pedestrian frequency potentials. Raju et al. (2020) carried out an accessibility analysis for healthcare centres using gravity model and geospatial techniques in Tiruchirappalli city. ...
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Metro is a rapid transit mode that helps in fast and efficient movement of the public. To make metro journey more convenient and attractive, from origin to destination, accessibility of metro must be good. In this study, tri-level analysis is carried out for the study area of Delhi. Traffic congestion and environmental condition of Delhi are degrading continuously, and to improve the situation, a sustainable Multi Modal Transport System (MMTS) with high accessibility must be explored. In this paper, policy to improve zone to zone metro accessibility for work purpose is discussed and the relation between multimodal transport system with accessibility is studied using GIS (ArcGIS), macrosimulation software (VISUM) and gravity model. It was observed that by the addition and extension of metro lines, transport accessibility is greatly improved. This study shows that percentage of zones in Delhi with higher accessibility level could increase from 5 to 13.88% with the implementation of phase IV of metro. In addition, the implementation of phase IV metro could reduce the average travel time between zones and metro stations. It will also reduce the travel time between metro stations substantially (for the zones covered in this study the average travel time is reduced by 23.63% and for the station covered in this study the average travel time is reduced by 17.73%). Further, it was found that ‘out vehicle travel time’ (OVTT) is having a major impact on the accessibility of metro. Lastly, it was concluded that with the higher level of metro accessibility, people will prefer the multimodal transport system with metro as the main mode. Travel time isochrones for public and private trips for the estimated MMTS model are also presented in this paper to depict the changes in accessibility for different scenarios. This will further help in improving private transport accessibility by reducing congestion on roads. Thus, planning for transport accessibility helps in developing the city in a sustainable manner in the future.
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The layout of urban spatial functions may play an important role in sustainable regional development. Given the rapid development of urbanization in China, this study attempts to analyze how functional specialization affects coordinated regional development. To quantitatively measure the degree of coordinated development within different regions, the coordinated degree index is used to calculate the degree of coordinated development of four Chinese metropolitan areas from 2008 to 2019. The panel vector autoregressive (PVAR) model is employed to empirically test the impact of urban functional specialization on coordinated regional development. The results indicate that high market activity is conducive to the formation of functional specialization synergy in space, and the level of social productivity directly affects the functional specialization and the level of synergy within a region. With the continuous strengthening of the implementation of local government policies, the functional specialization and synergy in metropolitan areas have gradually strengthened. However, the promotion effects and the expression of functional specialization, the coordinated development of government actions, and spatial functions differ across metropolitan areas in China.
... This set-up allows computing performance metrics, especially regarding mobility and accessibility-related measures. More details on this module can be found in [11]. Fig 2 provides an overview of the structure. ...
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This chapter introduces an analytical study of New Towns in England, aiming to provide a deeper, evidence-based understanding of their planning as well as their social reality. The core methodology of the study is based on 'space syntax', which uses configurational analysis of the spatial network to investigate the performance of urban systems and their socio-economic attributes. The chapter scrutinises the major flaws of the English New Towns and proposes an explanation for why they are not functioning as well as their historic, evolved counterparts. The study provides lessons that could be used for re-designing and re-shaping New Towns in the UK and elsewhere. © Matthew Carmona and the contributors 2014. All rights reserved.
City planning using integrated urban modeling
  • A Achary
  • K Karimi
  • E Parham
  • A Guven
  • G Uvar
Achary, A., Karimi, K., Parham, E., Guven, A. and Uvar, G. 2017 'City planning using integrated urban modeling. Jeddah Structure Plan', Proceedings of the 11th space syntax symposium