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N. Gu, S. Watanabe, H. Erhan, M. Hank Haeusler, W. Huang, R. Sosa (eds.), Rethinking Comprehensive
Design: Speculative Counterculture, Proceedings of the 19th International Conference on Computer-
Aided Architectural Design Research in Asia CAADRIA 2014, 533–542. © 2014, The Association for
Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong
PLOT PACKING
A procedure for generating well-formed street networks
PATRICK JANSSEN1 and VIGNESH KAUSHIK2
1,2 National University of Singapore, Singapore
1 patrick@janssen.name
2 vigneshkaushik@gmail.com
Abstract. Generative design tools can accelerate the optioneering
process by allowing designers to quickly generate large numbers of
design variants, thereby enabling a wider and more thorough explora-
tion to be conducted. This paper focuses on procedures for generating
inner city street networks and city block massing studies for sites
within existing urban areas. A novel procedure is proposed that is ca-
pable of subdividing complex non-orthogonal sites into similarly sized
well-formed plots and subsequently further subdividing these plots in-
to sizes appropriate for selected city block typologies. The application
of the procedure is demonstrated on a site in Singapore.
Keywords. Urban optioneering; street networks; parametric urbanism;
quadrilateral mesh generation.
1. Introduction
Urban optioneering involves the systematic exploration of options for urban
design proposals (Holzer and Downing 2010). Generative design tools can
accelerate the optioneering process by allowing designers to quickly gener-
ate large numbers of design variants, thereby enabling a wider and more
thorough exploration to be conducted. Furthermore, the use of such genera-
tive tools will often lead to better quality designs that could not have been
developed using conventional design methods.
At the urban level, optioneering processes typically require procedures
for generating city street networks and city block massings. We refer to these
types of procedures as ‘plot packing’ procedures. This research focuses on
inner city type of hierarchical street network, consisting of plots surrounded
534 P. JANSSEN AND V. KAUSHIK
on all sides by streets, with no dead ends and with streets that tend to be fair-
ly straight (rather than curvilinear, as is the case in some suburban street
networks).
This research considers only the geometric issues, with the aim being to
develop procedures for generating well-formed street networks. However,
urban planning and design must clearly take into consideration a much wider
set of issues, including social, economic, and environmental issues. It is as-
sumed that if used in practice, the proposed procedures would only consti-
tute one tool within a broader set of tools of generating and evaluating urban
design proposals.
Previous researchers have developed a number of procedures for generat-
ing street networks using a variety of computational techniques, including
particle systems, L-Systems, and grammars. Parish and Muller (2001) devel-
oped the CityEngine software for generating city models using a number of
different L-System models. The software generates highways, streets, and
buildings. Highways connect predefined areas of high population, while the
land between the highways is divided into smaller areas surrounded by grid-
ded streets. Beirao and Duarte (2005) have developed an approach using ur-
ban grammars in which a wide variety of street networks and plot layouts
can be generated by recursively applying user-defined shape grammar rules.
These rules can either be developed from scratch or can be based on an anal-
ysis of the existing urban fabric. Braach and Fritz developed the Kaisersrot
parcelling software that was used on a series of projects for generating lay-
outs for low-rise residential developments (Kaisersrot 2000, Lehnerer 2009,
Hovestadt 2010). The generative procedure combined a particle system with
Voronoi partitioning in order to generate roads and plots.
Subdividing complex non-orthogonal sites into similarly sized orthogonal
plots is a complex task. The procedures developed by previous researchers
have been found to give insufficient control over the plot shapes and sizes
that are generated. This research has therefore set out to develop an alterna-
tive procedure for street network generation.
Section two gives a detailed description of the proposed procedure. Sec-
tion three gives an example of how this procedure can be applied to a site in
Singapore. Finally section four discusses the limitations of the current pro-
cedure and identifies future areas of research.
2. Proposed Procedure
A plot packing procedure is required that is capable of generating street net-
works and plots with the following key features:
PLOT PACKING 535
generate street networks within sites with irregular shapes, possibly including
sites with concave shapes,
generate street networks that connect to existing surrounding streets at prede-
fined points along the perimeter of the sites,
generate street networks that include different categories of streets, such as
primary and secondary streets,
generate street networks where streets tend to be fairly straight and where in-
tersections tend to have either three or four streets,
generate street networks that result in evenly sized plots that tend to be close
to orthogonal in shape.
The proposed procedure starts with a planar polygon representing the site
and then generates street and building massings as follows:
Stage 1: A regular triangulated mesh with evenly shaped triangles is generat-
ed over the entire site area.
Stage 2: A quadrilateral mesh is generated from the triangulated mesh
through a process of merging triangles.
Stage 3: Street networks of differing categories are generated by subdividing
quadrilaterals to form smaller quadrilaterals.
Stage 4: Building massings based on selected typologies are generated within
the plots defined by the street networks.
Each of the stages is described in more detail below.
2.1. GENERATION OF TRIANGULATED MESH
The quality of the street networks generated in the later stages depends to a
large degree on the regularity of the underlying triangulation. Regular mesh-
es consist of triangles that are close to equilateral and that have similar edge
lengths.
Many CAD systems incorporate tools and algorithms for working with
triangulated meshes and in some cases these may include tools for generat-
ing regular triangulations. For this research, a modelling system called
Sidefx Houdini is used, which includes such a tool. The density of the trian-
gulation is controlled by the target length of triangle edges, which is speci-
fied by the user as a parameter.
An alternative approach would be to create a customized procedure for
generating such meshes. One option for such a procedure would be to use a
particle system (Shimada 1993). The site boundary is defined as barrier to
the particles, and the desired radius of the particles is defined. The particles
are then randomly inserted and then allowed to distribute themselves evenly
536 P. JANSSEN AND V. KAUSHIK
through a process of mutual repulsion. Once a stable arrangement is
achieved, the centre points of the particles can then be triangulated.
Whatever procedure is used for generating the triangulated mesh, one
important constraint is that it should be possible to define certain points
along the perimeter of the site polygon where mesh lines will be generated.
The reason for this is that, in Stage 3, these lines will become streets. Being
able to specify points where mesh lines will be generated will ensure that the
streets that get generated within the site also connect to the surrounding
street network.
2.2. GENERATION OF QUADRILATERAL MESH
As with triangulated mesh, quadrilateral mesh are required that have a high
degree of regularity. Regular quadrilateral meshes consist of quadrilaterals
with interior angles that are close to right angles.
The procedure is proposed that converts triangulated meshes into quadri-
lateral meshes using three basic algorithms.
Merge triangle pairs: pairs of adjacent triangles are merged to form quadri-
laterals. (See Figure 1 (a)).
Merge isolated triangles: isolated triangles are merged with neighbouring
quadrilaterals and then split into two quadrilaterals. (See Figure 1 (b)).
Fix irregular quads: irregular quadrilaterals are merged with a neighbouring
quadrilateral and then split into three quadrilaterals. (See Figure 1 (c)).
Figure 1: Three algorithms used to generate regular quadrilateral meshes:
(a) merge triangle pairs (b) merge isolated triangles, and (c) fix irregular quads.
The main merge triangle pairs algorithm selects adjacent pairs of trian-
gles and merges them. However, depending on order in which triangles are
merged, certain isolated triangles will remain that cannot be merged. The
merge isolated triangles algorithm merges each of these isolated triangles
with one of the neighbouring quadrilaterals to form a five sided shape, and
then splits this shape into two quadrilaterals. For each isolated triangle, there
PLOT PACKING 537
are a maximum of 15 possible ways of merging and splitting. In order to se-
lect the one that results in the most regular quadrilaterals, all 15 merge-split
operations are performed, and the resulting quadrilaterals are then analysed.
For this, a scalar function is defined that measures the regularity of a quadri-
lateral by calculating the sum of the absolute values of the cosines of the
four interior angles (see Itoh at al. (1995) for more details), giving a score
between 0 and 4. Of the 15 possible merge-split operations, the one resulting
in the quadrilaterals with the highest scores is chosen.
Finally, the processes of merging triangles may result in some quadrilat-
erals that are very irregular. The fix irregular quads algorithm merges each
of these irregular quadrilaterals with one of the neighbouring quadrilaterals
to form a six sided shape, and then splits this into three quadrilaterals. In this
case, in order to ensure that regular quadrilaterals are generated, the six sided
shape should form an L-shape, which is then easily split into three quadrilat-
erals, with one in the corner of the L and two at the ends of the L.
With regards to the regularity of the final quadrilateral mesh, the key to
this procedure is the order in which triangle pairs are merged. Some order-
ings will result in very regular meshes while other orderings will result in
very irregular meshes. Finding the best ordering is a non-trivial problem, and
a optimization algorithm is therefore used. A hill climbing algorithm is de-
fined as a solver that iteratively explores different orderings by creating new
orderings based on the best ordering it has found at that stage. For each or-
dering, the solver executes all three algorithms described above and if the
new ordering results in a higher quality mesh, it will replace the previous
best ordering. Figure 2 shows meshes generated at different stages of the
solver optimisation process.
Figure 2: Quadrilateral meshes generated at two stages of the solver optimization process:
(a) at iteration 1 and (b) at iteration 100.
In order to be able to compare two orderings, the solver needs a way of
measuring the quality of the quadrilateral mesh. The quality of the mesh is
538 P. JANSSEN AND V. KAUSHIK
calculated as the average of the worst 50% of quadrilaterals. The aim of the
solver is therefore to try and find orderings that improve the worst quadrilat-
erals.
The final remaining issue for the quadrilateral mesh procedure is how to
generate the initial ordering. Using a random ordering is likely to result in a
very poor initial mesh. An initial ordering algorithm is therefore proposed,
based on method by Itoh et al. (1995). With this algorithm, a list is first cre-
ated of all possible pairs of adjacent triangles. The list is then sorted from
best to worst, according to the quality of the quadrilaterals that would result
from merging each triangle pair. An ordering is then generated by selecting
triangle pairs from the top of the list down. The mesh resulting from the ini-
tial ordering is shown in Figure 2(a).
2.3. GENERATION OF STREET NETWORKS
The quadrilateral mesh is then subdivided to form a well-formed street net-
work using a subdivision algorithm. This algorithm splits quadrilaterals ac-
cording to a minimum edge length, which is specified by the user as a pa-
rameter. For this minimum edge length, the maximum number of smaller
quadrilaterals is calculated, and the original quadrilateral is then split by di-
viding the edges equally.
Depending on the type of street network that is required, the quadrilateral
can be split either in one direction only, or in two directions at the same time.
If the quadrilateral is split in two directions at the same time, then the quadri-
lateral is being cut into a grid. (In Figure 3, see (f) to (g)).
If the quadrilateral is split in one direction, then the quadrilateral is being cut
into strips. An additional parameter is used to define whether the strips are
cut in the long direction or the short direction. (In Figure 3, see (f) to (i) ).
Once the smaller quadrilaterals have been generated, then it may still be
possible to subdivide some of these smaller quadrilaterals again. The subdi-
vision algorithm is therefore applied recursively, with the maximum depth
being specified by the user as a parameter.
The streets are generated by insetting the quadrilaterals adjacent to those
streets by a distance equal to half the street width. The insetting is performed
as soon as one category of streets has been fully generated, thereby allowing
each street category to have a different width.
PLOT PACKING 539
Figure 3: Generation of street networks and building massings:
(a) and (b) perimeter block typology, (c) and (d) row house typology.
2.4. APPLICATION OF CITY BLOCK TYPOLOGIES
The generation of the street network results in a set of quadrilateral building
plots. Due to the procedure used for generating the network, the city block
plot will in general be well-formed without acute angles.
For the next stage, city blocks are generated for each plot based on a se-
lected typology. It is envisaged that a library of parametric models could be
developed, so that different options could be explored with a wide range of
varying typologies. For each typology, a parametric model would be devel-
oped that would adjust itself to the boundary of the plots into which it was
inserted and create massing volumes according to certain rules.
Currently, two typologies have been implemented:
A perimeter block typology consisting of four 12 meter deep linear blocks
parallel to the edges of the plot, with an open courtyard space in the centre.
540 P. JANSSEN AND V. KAUSHIK
The blocks consist of commercial spaces at the ground floor and residential
apartments above. The height of each block is variable, ranging from 4 floors
to 8 floors (see Figure 3, (g) to (h)).
A row house typology consisting of linear rows of units arranged along pe-
destrianized roads. The height of the units are fixed at 4 floors, with a ground
floor flat on levels 1 and 2, and an upper flat on levels 3 and 4 accessible via
a shared staircase (see Figure 3, (i) to (j)).
3. Case Study
In order to demonstrate how such generative design tools can be used to
support urban optioneering, a site in Singapore has been selected as a case
study. Located in the central region of Singapore, the site has an area of 93
Ha and the proposed plan is to build 11,000 public housing flats. The current
design has a standard Singapore typology consisting of point block residen-
tial towers distributed throughout the site with a park in the centre. The gross
plot ratio of the site is calculated to be approximately 1.5.
3.1. APPLICATION OF TYPOLOGIES
For the demonstration, a density exercise was conducted for the Bidadari site.
A plot ratio of 1.5 was used as a target density and a series of alternative op-
tions were rapidly generated based on the two typologies presented above:
one set of options for the perimeter block typology and another set of options
for the row house typology. Figure 4 shows two selected options.
Given a more extensive library of typologies, urban designers would
quickly be able to explore a wide variety of urban options with real-time
feedback on key metrics such as overall density, amount of open space,
number of car parking spaces, and so forth.
4. Conclusion
A novel procedure has been proposed that is capable of subdividing complex
non-orthogonal sites into inner city street networks with similarly sized or-
thogonal plots and subsequently further subdividing these plots into sizes
appropriate for selected city block typologies. The application of the proce-
dure is explored on a site in Singapore, showing how such procedures might
be applied in optioneeering studies.
PLOT PACKING 541
Figure 4: The perimeter block and row house typologies applied to the Bidadari site.
Future research will expand on this research in three main ways. First, the
current approach does not easily accommodate additional constraints on
street networks mainly due to the simplicity of the solver. The quadrilateral
generation procedure will be updated, replacing the hill-climbing algorithm
with a multi-objective evolutionary algorithm that can potentially take into
account additional constraints. Second, in the current approach, the site is
assumed to be blank (without any existing elements, such as roads, building,
and water elements). The street network procedure will be expanded to allow
for the inclusion of obstacles in the site where neither roads nor buildings
can be added. Third, the application of typologies currently assumes that the
same typology will be applied in all areas. The city block procedure will be
542 P. JANSSEN AND V. KAUSHIK
updated to allow the user to define how typologies could be mixed in order
to generate more varied urban environments.
As mentioned in the introduction, when developing the urban form of a
neighbourhood, it is assumed that planners and designers would apply such
procedures in conjunction with a wide range of other tools and techniques
for generating and evaluating designs. Once the proposed procedures have
been further developed, their use with more realistic scenarios in conjunction
with a broader toolset can be explored.
References
Beirão, J.N. and Duarte, J.P., 2005, Urban Grammars: Towards Flexible Urban Design, Pro-
ceedings of the 23rd Conference on Education in Computer Aided Architectural Design in
Europe, eCAADe, Lisbon, Portugal.
Holzer, D. and Downing, S., 2010, Optioneering: A New Basis for Engagement Between Ar-
chitects and Their Collaborators, Architectural Design, 80(4), 60-63.
Hovestadt, L., 2010, Beyond the Grid: Architecture and Information Technology, Birkhäuser
Architecture.
Itoh, T., Shimada, K. and Doi, A., 1995, Discontinuity Meshing for Radiosity, Journal of the
Information Processing, Society of Japan, 36(11), 2632-2641.
Janssen, P., Chen, K.W. and Basol, C: 2011, Iterative Virtual Prototyping: Performance Based
Design Exploration, Proceedings of the eCAADe Conference, Ljubljana, Slovenia, 253–
260.
Janssen, P. and Chen, K.W.: 2011, Visual Dataflow Modelling: A Comparison of Three Sys-
tems, Proceedings of the CAAD Futures Conference, Liege, Belgium, 801–816.
Kaisersrot, 2000. http://www.kaisersrot.ch/kaisersrot-02/PROJECTS.html
Lehnerer, A.: 2009, The City of Kaisersrot: Not a Design, but the Result of a Mediated Pro-
cess of Negotiation, Model Town: Using Urban Simulation in New Town Planning, SUN.
Amsterdam, 135–147.
Parish, Y. and Müller, P., 2001, Procedural Modeling of Cities, Proceedings of ACM SIG-
GRAPH 2001, ACM Press, 301–308.
Shimada, K., 1993, Physically-Based Mesh Generation: Automated Triangulation of Surfaces
and Volumes via Bubble Packing, Ph.D. thesis, Massachusetts Institute of Technology.
