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Research Article
Parametrising historical Chinese courtyard-
dwellings: An algorithmic design framework
for the digital representation of Siheyuan
iterations based on traditional design
principles
Yuyang Wang*, Asterios Agkathidis, Andrew Crompton
School of Architecture, University of Liverpool, Liverpool, United Kingdom
Received 27 March 2020; received in revised form 16 July 2020; accepted 18 July 2020
KEYWORDS
Digital heritage;
Parametric design;
Siheyuan;
Fengshui;
Gongcheng Zuofa
Zeli;
Algorithmic design;
Computational design
Abstract Many Beijing Siheyuan, a type of Chinese vernacular housing with significant cul-
tural value, have been lost in recent years. Preserving the few remaining has become a neces-
sity, but many contemporary architects lack an understanding of their design principles. Based
on a historical analysis deriving from Fengshui theory, the Gongcheng Zuofa Zeli ancient con-
struction manual, and craftsmen’s experience, this paper describes a parametric algorithm
capable of producing Siheyuan variants within a 4D CAD environment which by transforming
the original design principles into an algorithm contributes to an understanding of Siheyuan ty-
pology and their preservation. This algorithm was implemented in a virtual scripting environ-
ment to generate accurate virtual counterparts of historical or extant Siheyuan houses
revealing the tacit computational rules underlying traditional Chinese architecture.
ª2020 Higher Education Press Limited Company. Publishing Services by Elsevier B.V. on behalf
of KeAi. This is an open access article under the CC BY-NC-ND license (http://
creativecommons.org/licenses/by-nc-nd/4.0/).
* Corresponding author.
E-mail address: Y.Wang179@Liverpool.ac.uk (Y. Wang).
Peer review under responsibility of Southeast University.
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
https://doi.org/10.1016/j.foar.2020.07.003
2095-2635/ª2020 Higher Education Press Limited Company. Production and hosting by Elsevier B.V. on behalf of KeAi. This is an open access
article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Available online at www.sciencedirect.com
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journal homepage: www.keaipublishing.com/foar
Frontiers of Architectural Research xxx (xxxx) xxx
1. Introduction
Constrained by many traditional Chinese social and cultural
factors, the form of Beijing Siheyuan embodies significant
elements of Chinese culture. This paper employs an algo-
rithmic approach to propose an interactive tool for para-
metrically generating Siheyuan variants based on its
traditional design principles.
Today, the few Siheyuan houses that remain are facing
oblivion. Being timber frame structures, they are particu-
larly vulnerable to ageing and problems such as fire, hu-
midity, and pests. During the period 1949 to 2009, more
than eighty per cent of Beijing Siheyuan were destroyed
(Ni, 2009), to the extent that it has become hard to find
good examples to study.
Not only are they vanishing but an understanding of their
design is not being passed on to the new generation. Recent
studies (Zhang, 2015;Li, 2016) highlight the problem of
contemporary architects not understanding traditional
Chinese tectonic principles and spatial qualities. Although
both Chinese and international clients are willing to build
and live in Siheyuan houses, most contemporary Siheyuan
buildings can hardly be considered genuine, since features
such as the proper proportions and symmetry are incorrect.
The Beijing Cathay View Courtyard Residence project is a
typical case of a ‘fake’ Siheyuan. A single villa of this
project, as shown in Fig. 1, is supposed to be designed in
the traditional Beijing Siheyuan style, but it lacks an axial
plan and has incorrectly proportioned rooms. This project
might be said to lack the heart and soul of a real Siheyuan
(Li, 2016), even though the developers claim that tradi-
tional architectural features recorded in Gongcheng Zuofa
Zeli (Structural Regulations,Qing Department of Qing
Dynasty, 1733) had been incorporated. It is no more a
real Siheyuan than an English Tudor Ethan house of the late
nineteenth century onwards is real Tudor.
Although there has been plenty of research on Siheyuan,
the traditional design principles for generating Siheyuan
variants have been little studied. Over the past decades,
scholars such as Lu and Wang (1996,2013), Ma (1999),Deng
(2004),Chan and Xiong (2007),Zhao (2013), and Zhang
(2015) have dedicated themselves to understanding Chi-
nese courtyard housing’s cultural connotations as seen in
the literature of history, most of which focused on its
symbolism, beliefs, materials, and spaces using methods
originating in the humanities.
More interesting for us, are the few researchers who
have investigated traditional Chinese architecture using
typological approaches, such as compositional analysis,
shape grammar, and space syntax. Inspired by J.N.L
Durand’s simplified geometric scheme of classical archi-
tecture (Villari, 1987), Ni (2009) and Li (2010) respectively
investigated Beijing Siheyuan’s compositional rules by
setting a set of criteria to categorize variants of Beijing
Siheyuan examples. Their studies revealed the large variety
of Siheyuan forms and proved the flexibility of its design
principles, but perhaps failed to show the core principles to
generate variants. Shape grammars have been developed
for some Chinese traditional designs (Stiny, 1977,2006).
Stiny’s followers such as Chiou and Krishnamurti (1995,
1996), presented the grammar of vernacular Taiwanese
courtyard dwellings based on the traditional local design
principles. By successfully presenting the generation of
many house examples using shape grammar, their studies
grasped the essence of vernacular Taiwanese courtyard
housing’s design principles using computational ap-
proaches. Li (2001) revealed the grammar of standard
Chinese building types recorded in Ying Zao Fa Shi (Li,
1103). Xiong et al. (2013) investigated the grammar of
Gulou, a wooden tower building type in south China, and
implemented this grammar computationally. Huang et al.
(2019) employed space syntax techniques to study Beijing
Siheyuan’s cultural connotations, which computationally
explored spatial configuration of Chinese courtyard hous-
ing, but it focused on a representative building example
rather than varied individuals without considering how
houses respond to different contexts. Moreover, Chiou and
Krishnamurti (1997) investigated the computational
consideration underlying Fengshui, a kind of Chinese
geomancy, which constrains the design of Chinese court-
yard housing. The algorithm presented in that study
focused on building orientation and auspicious construction
dates but overlooked the rules of site selection which in
fact dominates the design of Siheyuan, as governed by
Fengshui.
Rule-based approaches to architecture are old. Even De
Architectura by Vitruvius (Murphy et al., 2013), can be seen
as a rule-based description of classical architecture. Simi-
larly, A Pattern Language by Christopher Alexander et al.
(1977), lists architectural tropes that can be composed to
shape buildings and communities. In recent years, para-
metric design techniques have been employed by architects
to design ‘computationally generated complexities’
(Agkathidis, 2015). Scholars, on the other hand, have used
the same idea to find the simple principles that underlie
complexity. Brown and Steadman (1987) used Flemming’s
“DIS” program (1987) to generate variants of three types
of British housing plans based on a set of constraints
shaping rooms composition, which revealed their history
and social meaning. Duarte (2005) developed a recursive
grammar for designing plans like those of Alvaro Siza’s
houses at Malagueria leading to a program, that could
generate 2816 variants in the “Siza style”. Liu and Wu
(2015) produced a computer program to parametrically
generate Beijing Siheyuan examples based on its
constructional rules, however, as their focus was to study
the modular system underlying ancient Chinese architec-
ture, they did not display Siheyuan’s traditional design
principles.
Studies like these have demonstrated the usefulness of
computer-aided tools in architectural design. However, the
software described here, such as Shape Grammar Inter-
preter and DepthmapX, is not widely used by architects in
design practice, but only by academic researchers. On the
other hand, although researchers such as Chiou and
Krishnamurti (1997),Liu and Wu (2015) are developing
their own software by using coding in C/Cþþ and Python
programming languages, such approaches remain inacces-
sible for architects as they lack knowledge of such skills.
Grasshopper, a visual scripting application (Tedeschi, 2011)
embedded in Rhinoceros 3D modelling software, allows
architects and students, with limited programming knowl-
edge, to explore algorithmic design. Li (2016) used
2 Y. Wang et al.
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
Grasshopper to parameterize the design rules in the
ancient manual Ying Zao Fa Shi (Li, 1103), in order to clarify
the details of Song dynasty buildings. Although her exami-
nation was limited to the examples recorded in the manual,
she demonstrated that algorithms could integrate archi-
tectural design rules in a tool that could have a wider
application.
Computational approaches offer a new way to access
the literature and drawings of traditional Chinese designs
that are otherwise difficult to understand. With this aim in
view, we translated the design rules underlying Siheyuan
design into a Grasshopper algorithm, an interface with
which many architects are familiar. We then verified our
tool by comparing the models it created to existing drawn
examples, and thus, we hope to answer the following
questions:
Could we embed the tacit Siheyuan design rules in an
algorithm?
Could such an algorithm be used as an interactive tool
for designing traditional Beijing Siheyuan houses and
generating models?
Could such a tool deal with traditional Siheyuan variants
corresponding to the different contexts of a real-life
project?
Two limitations of this work should be highlighted. First,
we only focused on common Siheyuan types as they
emerged in Beijing, thus rare cases such as parallel-grouped
Siheyuan and Siheyuan with a garden have not been
considered. Second, this paper focuses on the Siheyuan
form down to the scale of the timber frame, we have not
(yet) considered decorative details.
2. Materials and methodology
2.1. Materials
Many forces, such as feudalism, Confucianism, Taoism,
clans, cosmology, construction law, and geographic loca-
tion, have shaped Siheyuan. Although the logic of these
forces has been clarified in anthropology (Chan and Xiong,
2007), they do not necessarily account for significant
Fig. 1 The rendering picture and floor plans of a showroom of the Beijing Cathay View Courtyard Residence project.
Parametrising historical Chinese courtyard-dwellings 3
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
differences between examples. In our view, the variation in
Beijing Siheyuan is the result of Fengshui and construction
rules, both explicit and implicit.
Fengshui provides guidance to geomancers and crafts-
men. Specifically, the “Xing Shi (observing context)”
method helps householders select an auspicious site and
the “Li Qi (regulating vital energy)” method based on
the concept of “cosmic resonance” helps craftsmen and
householders predict and select auspicious orientations,
qualitative space, and appropriate dimensions of rooms.
Chinese buildings were governed by construction laws,
which imposed a modular system for the dimensions of
building components. Beijing Siheyuan reached its peak
during the Qing dynasty (1616e1912) and most remain-
ing Siheyuan houses from this period follow the Gong-
cheng Zuofa Zeli compiled by the Qing government. As
this work is linguistically difficult to understand, we used
Liang’s study Qing Shi Yingzao Zeli (Qing Style Building
Regulation,Liang, 2006c), which referred to Gongcheng
Zuofa Zeli supplemented with interviews with craftsmen
in order to describe the modular system. Although the
government required householders to follow the con-
struction law strictly, many house variants occurred,
based on the experience of the old craftsmen passed
from each generation to the next. This tradition provides
tacit and unwritten codes underlying Siheyuan form.
2.2. Methodology
Beijing Siheyuan design principles were conventionally
represented in text supplemented with drawings of proto-
typical examples on an ideal site that did not reflect the
flexibility of Siheyuan design. All Siheyuan houses are var-
iants of these ideal examples (Ni, 2009). We extracted the
design principles using the previously named sources to
clarify design procedures and parameters to make our al-
gorithm. We then implemented the algorithm by using
Grasshopper scripting components. The models we gener-
ated were then verified by comparing them with the corpus
of historical examples. Over many iterations, we revised
our algorithm to eliminate discrepancies between our
models and the historical variants.
3. Developing the Siheyuan algorithm
3.1. Phase one: selecting a site
Once a householder has decided on a site, its suitability and
potential are assessed by a section of Fengshui called
“observing context”, which considers its shape and
environment.
3.1.1. Site shape
Fengshui geomancers compare the length of edges on each
side (north, south, east, and west) of the site. Although the
Beijing grid had been mainly rectangular since the Song
dynasty, some irregular polygon sites still existed. We found
seven common site plan types, which are categorized as
auspicious or ominous according to their shape (Fig. 2).
In the algorithm, each edge of the site is measured and
lengths compared. The closest corresponding pattern in
Fig. 2 is identified. This determines the fortune of the site.
The generative process is as follows:
Identifying each edge of the site (length,
location) /identifying site shape pattern /identifying
shape fortune.
3.1.2. Site environment
Ancient geomancers looked for a relationship to local
landmarks. The surrounding area was divided into octants
(east; northeast; north; northwest; west; southwest; south;
southeast, Fig. 3). How far away landmarks could be to
count as significant is uncertain. We assume that ancient
geomancers defined this distance based on their own
preference, rather than using a unified standard, and took
this distance to be a parameter in our algorithm.
For Siheyuan in rural areas, geomancers considered five
types of landmarks to be significant: the tree, the pond, the
river, the hill or the mountain, and the junction of circu-
lation. In Beijing, some of these landmarks found their
counterparts to urban objects, hills and mountains for
instance, were analogized to surrounding buildings espe-
cially any tall and large buildings. Rivers were analogized to
streets and alleys because rivers in Fengshui, in one aspect,
are seen as symbols of circulation enabling the delivery of
the necessaries of life. However, although rivers, streets,
and alleys all exist in Beijing city, it is noted, as mentioned
by Yi et al. (1996) and Zhang (2009), that streets and alleys
are defined as one type and rivers should be a different
one, rather than categorizing all of them as one type in the
assessment of the site. We guess the reason for this is that
rivers could also be analogized to other objects, whose
meanings may differ from circulation and it leads to
significantly different results in site assessment. Therefore,
the types of elements to be assessed for the Siheyuan
design are the tree, the pond, the river, the street or the
alley, the neighbouring building (or the hill or the mountain
if present), and the street junction or the alley junction
(Fig. 3).
Geomancers also had to identify the comprehensive
pattern of the site’s environment (CPSE). In each octant,
the existence or non-existence of each of the six types of
landmarks was recorded. In Fengshui, the huge number of
possible combinations fall into just three categories:
auspicious, ominous, and non-auspicious and non-ominous.
According to historical literature (Zhao, 2011), we counted
28 auspicious and 25 ominous patterns (Fig. 3). The other
CPSEs are considered as non-auspicious and non-ominous.
In practice, if the CPSE of a site is not auspicious, geo-
mancers usually advise the householder to artificially re-
form the environment in order to make it auspicious. The
exact site reformation process remains unknown, however,
after the reformation having been completed, the site
should fit within one of the 28 auspicious patterns, which is
used for computation in our algorithm.
We encoded a site’s CPSE as a binary string 48 characters
long, representing the eight surrounding areas from east to
northeast clockwise in blocks of six digits. In each block,
each digit represents one type of the six environmental
elements, 1 indicates existing, otherwise 0. We identified
the 53 codes in representing the auspicious or ominous
4 Y. Wang et al.
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
CPSEs. Meanwhile, to simplify the computation, for the
non-rectangular sites, an outer rectangle of the site plan is
generated by our algorithm and assumed as the site for the
computation in this step.
3.1.3. Site size
Another factor that defines the quality of a site is its size.
By observing the historical Beijing map, Qianlong Jingcheng
Quantu (Qianlong Capital Map, 1748e1750), it is noted that
the range of sizes of an available site for Siheyuan con-
struction is broad, depending on the number of courtyards
it contains. When describing the word ‘courtyard’ in
Siheyuan context, it usually means the outdoor space
enclosed by walls, which includes the open courtyard space
and all the buildings surrounding that space. In many cases,
some parts of the ‘courtyard’ are not completely enclosed
by walls, instead, the rear boundary of a building is
extended to define the boundary of a courtyard. In olden
times the determination of the proper size of a Siheyuan
was affected by the household’s budget, social status,
living demands, personal preference, and so on. To
simplify, the value of the proper site size is set as an
inputting parameter Sdesired size in this algorithm, which is
decided by the householder’s circumstances. A criterion,
Dsite size, represented as a numeric value, to evaluate the
degree of the size difference between the actual site and
the one desired by the householder is set. The Dvalue is
defined by calculating the absolute size difference per cent
to the desired one, whose equation is shown below.
Dsite size Z
jSdesired size Sactual sizej
Sðdesired sizeÞ
Although this factor doesn’t influence the fortune of
Siheyuan, it is an important factor taken into account in
real projects.
In the algorithm, the three factors were given numeric
values. For the site shape and the site environment, the
criterion is its fortune, entered as 1 if auspicious or as 1if
ominous. For the site size, it is important to identify the
size of the difference between the desired site and the
actual site, the smaller the difference the more likely the
householder is to proceed. Therefore, the larger the value
of the Dsite size is, the less the possibility for the site to be
selected. We assume the householder would tend to select
a site when the value of the Dsite size is smaller than 0.2. The
site size parameter value is given as 1 when Dsite size <0:2,
1 otherwise. The relative importance of the three criteria
depended on geomancers’ preferences, thus we added
weighting to these values, so it could be set by users. The
comprehensive assessment is defined by the summation of
the three weighted values: the higher the result value,
Aassessment, the fitter the site.
AassessmentZfCsite shape ;Csite environment;Csite size ;Wsite shape;
Wsite environment;Wsite size ZCsite shapeWsite shape
þCsite environment Wsite environment þCsite sizeWsite size
In many practical situations, where householders had
more than one site to choose from, geomancers could
compare them by using this assessment method. We have
integrated this formula into our algorithm to find the most
suitable site. The algorithm compares the results of the
iterative solutions of different sites using the same values
of the parameters, such as Sdesired size,Wsite shape ,
Wsite environment,Wsite size , and the distance from the site
edge to the surrounding area’s outside boundary, which can
be initially inputted by the users. It then indicates the site
with the highest Aassessment value. Each of the parameters in
this phase affects the assessment result, but the weighting
ratio between the three above aspects is the most signifi-
cant one, which is freely decided by users. The value of the
parameter corresponding to the range of influence of local
landmarks, the distance from the site edge to the sur-
rounding area’s outside boundary, is usually around the
width of the site. The value of another parameter, the
householder desired site size, should be within a reasonable
range (up to 2800 m
2
), which was the size range of Siheyuan
according to Duan’s survey (2016).
3.2. Phase two: designing the floor plan pattern
Once the site had been selected, craftsmen would design
the floor plan pattern taking into account the householder’s
preferences, his budget, and status, incorporating the
correctly sized rooms, walls, verandas, front gates, back
gate, and festooned gate. According to traditional princi-
ples, we divided this process into four stages: defining the
central axis, defining location pattern of the front gate and
back gate, dividing the site into courtyards, and deter-
mining the floor plan pattern of each courtyard. Previous
studies on the traditional design principles by Lu and Wang
(1996,2013),Ma (1999),Zhao (2013) were used to derive
the rules. However, in practice, the plan pattern of each
courtyard seems to have been flexible and there is no direct
historical material to explain its principles, or anything to
be found in these studies. Additionally, we examined plans
Fig. 2 Seven types of auspicious/ominous site shape patterns.
Parametrising historical Chinese courtyard-dwellings 5
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
of extant Siheyuan by Duan (2016), survey data by Ni
(2009), and referred to Li’s (2010) studies on the Qianlong
Capital Map to inform our constraints.
3.2.1. Defining the site’s central axis
The site’s central axis is a key parameter, not only are many
components aligned to it, but it also determines the
orientation of the primary room (Zheng Fang, in the form of
an individual building, is the core space of a courtyard, and
for Siheyuan with multiple courtyards, there is a most
important primary room (MIPR), which is thought as the
core space of the Siheyuan). To define the site’s central
axis, the geomancer had to determine a key point (which is
the central point of the MIPR’s floor plan) on the site by
observing the underground soil texture to find the proper
area to construct the MIPR which then created the central
axis crossing the key point. We simplified the orientation of
the central axis into two principles. The first, and more
significant principle fixes the MIPR’s front elevation ac-
cording to the site orientation and its access to the outer
Fig. 3 Assessment process of the site environment to determine its fortune.
6 Y. Wang et al.
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
urban fabric. Since the orientation of the central axis is the
same as the orientation of the MIPR’s front elevation, this
principle forces the site central axis to be south-north or
east-west. In fact, it was traditional in a north-south ori-
ented site, to make the central axis, as well as the MIPR’s
front elevation, seven degrees anti-clockwise off the south.
A site longer in the east-west oriented direction will have
an east-west central axis. If its main access to the urban
fabric is on the east edge, the MIPR’s front elevation will
also be to the east, and if it is on the west edge, the
orientation of the MIPR’s front elevation is west. The sec-
ond principle requires the MIPR’s front elevation to face
natural water elements such as a river or a lake but have its
back to any hill or mountain.
To transfer these rules into our algorithm, we employed
the force vector algorithm. We created the algorithm to
identify the actual site orientation and the main access to
the urban fabric that detects the accessible urban space
adjacent to the site, thus determining the MIPR’s front
elevation. To simulate the three patterns shaped by site
orientation and urban fabric in the first principle, we set
three vectors on the key point correspondingly: one vector
to seven degrees contra-clockwise off the south-oriented,
one east oriented, and one west oriented, and created the
corresponding algorithm to decide the selection of the
application of the vector determined by identifying site
orientation and urban fabric. To simulate the natural ele-
ments’ effect in the second principle, we set two types of
vectors. One derives from the key point to the geometrical
centre of a river or a lake on plan, while the other from the
geometrical centre of a hill or a mountain to the key point.
For each natural element, the force vector can be calcu-
lated that is inverse proportional to the distance of the
natural element from the key point, which is based on
detecting the location of these elements surrounding the
site. The MIPR’s orientation is the vectorial calculation of
the forces on the key point from the three vector types. As
the first principle is much more influential than the second,
we have assigned a weight ratio between the vector
derived from the first principle and from the second prin-
ciple as a parameter (A:B:C) to enable the site orientation
and urban fabric vector larger than the other two. The
vectorial calculation follows the below formula:
!
FðorientationÞ
ZA!
Fðsite orienation and urban fabricÞþB!
Fðwater0s attractive line forceÞ
þC!
Fðhill or mountain0s repulsive point forceÞ
The location of the key point, set by the user, is repre-
sented by a coordinate point (x,y) on a two-dimensional
plane where the site plan is positioned, whose value is
constrained by the requirement that the key point is
located within the site plan. The surrounding area defined
for considerable natural elements is determined by a
square plan with two hundred metres long sides, whose
centre point is positioned on the geometrical centre of the
site. The surrounding natural elements and the location of
the key point affect the orientation of the MIPR, but their
effects are slighter than the site orientation and the site
outer urban fabric, which is pre-decided by site context.
Therefore, the orientation of the site’s central axis is
always parallel to, or few degrees off the site orientation.
The orientation of the MIPR’s front elevation and the cen-
tral axis can be generated using our algorithm (See the
example in Fig. 4).
3.2.2. Defining the location pattern of the front and back
gates
The location of the gates is defined by two factors: the
site’s orientation and the neighbourhood’s context. First,
the site’s orientation is categorized into two types: east-
west oriented, or north-south oriented. Second, for the
neighbourhood’s context, we identify the adjacent area on
the four sides of the site’s rectangle by observing if it is
occupied by neighbouring buildings or accessible urban
spaces, such as streets or alleys. The two parameters
comprehensively determine the front gate’s location as
shown in Fig. 5:
For a south-north oriented site, there are three
patterns:
First pattern: when a street or an alley is on the south of
the site, the gate is located at, or close to the east end
of the south side of a Siheyuan.
Second pattern: when there is a street or alley on the
east or west of the site but not on the south, the gate is
located at, or close by, the southern end of the boundary
between the street/alley and the site.
Third pattern: if a street or an alley can only be found
on the north, the gate is to be located at, or close to
the end of the north edge. Remarkably, in Siheyuan
with multiple courtyards it is common for a north-
south corridor to allow for a gate at the south end
of the site, so the circulation starts with the courtyard
on the south. See the two-courtyard example in
Fig. 6.
For an east-west oriented site, there are two patterns:
First pattern: when there is a street or an alley next to
the east or west of the site, the front gate is located at,
or close to the south end or north end of the boundary to
the street/alley.
Second pattern: when there is no street or alley to the
east or west but only to the north or the south, the front
gate is located at the east end (when primary rooms face
east) or the west end (when primary rooms face west) of
the boundary to the street/alley.
Siheyuan houses with a back gate are rare. The back
gate is usually located at, or close to, the end of an edge of
the last courtyard, where it enables the circulation con-
necting from the Siheyuan interior to the exterior space.
Usually, the front gate and the back gate cannot be located
on the same edge of a Siheyuan.
Accordingly, in our algorithm, the identification of
available pattern(s) is fixed by the two factors: the site’s
orientation and the neighbourhood’s context, of which both
are predetermined upon site selection. This process is as
follows:
Identifying site context (site orientation, neighbourhood
context) /identifying available gate location pattern (s).
Parametrising historical Chinese courtyard-dwellings 7
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
Fig. 4 An example of generating the central axis using force vectors.
Fig. 5 Patterns of front gate location.
8 Y. Wang et al.
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Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
We produced the algorithm to identify the site context
by defining four areas (east, south, west, north) adjacent to
the site and then detecting whether any street or alley was
existing in each area. Based on this identification and the
determination of site orientation, the algorithm then gives
the pattern of the front gate and back gate. Since the back
gate is infrequent, a parameter for users to decide if it
exists is defined. Since the locations of a gate given in Fig. 5
are rough, and it is noted that gates were moved and
rotated slightly on the edges of Siheyuan in many cases, one
parameter is defined to enable users to slightly move and
rotate gates on the plan.
3.2.3. Dividing the site into courtyards
For most Siheyuan housings, the courtyards lie on the site in
a row, and consequently, the sum of edges of all courtyards
of a Siheyuan are the edges of the actual site and the
boundaries of each two adjacent courtyards. In most cases,
a boundary of two adjacent courtyards is a segment, whose
orientation is perpendicular to the site orientation.
Two constraints shape the division of a site: the site size,
and the ratio between width and depth of each courtyard.
The site size was constrained by the urban grid system of
Beijing, which consequently fixed the number of courtyards
in Siheyuan, most commonly between one and five. Ac-
cording to Ni’s (2009) statistic measuring survey data on
historical Siheyuan examples, we inferred the relationship
between the site area of a Siheyuan and its number of
courtyards (Table 1).
Another division constraint is the ratio between the
depth and width of each courtyard. Normally Beijing
Siheyuan sites are rectangular, or nearly rectangular, and
courtyards are in the row along the site orientation,
consequently, the courtyards it contains are, or close to,
rectangular as well. For a non-rectangular site, we use the
outer rectangle of the site plan for computation. The size
of a courtyard contains two parameters: the dimension
parallel to the short edges of the site, called courtyard
width, and the dimension parallel to the long side, called
courtyard depth. The width of each courtyard is easy to be
identified by measuring the actual site, as it is the same
with its short edges. However, the dimension of each
courtyard depth varies. It is noted that once the site width
and the ratio between the depth and width of each court-
yard are identified, the courtyard depth can be deter-
mined. Since both a site and its courtyards are rectangles,
and the site area is pre-determined once a site is selected,
and the site width and courtyard width are pre-determined
as the same, each courtyard’s size and location could be
identified once the number of courtyards and each cour-
tyard’s depth has been decided.
Based on the above analysis, we defined two types of
parameters: the number of courtyards ðXcourtyard numberÞand
the ratio between the depth and width of each courtyard
ðXratioÞ. The first parameter is constrained by the area of
the site, as illustrated in Table 1. The second one is a set of
numbers ðXratio 1;Xratio 2;.Xratio NÞ. Since the site and its
courtyards are rectangles, the sum of all ðXratio Þs is a pre-
determined value linked to the site selection. This rela-
tionship constrains both values of the two parameters. The
value range of each ratio between the depth and width of
Fig. 6 A two-courtyards Siheyuan with a south-north oriented corridor connecting the front gate to the south courtyard (after
Ma, 1999).
Table 1 The number of courtyards in relation to Siheyuan
sizes.
The number of
courtyard
123 4 5
Area (m
2
) 100
e400
300
e800
500
e1200
1000
e1900
1700
e2800
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each courtyard is constrained by the type of the courtyard
(standard, non-standard). As shown in Fig. 7, courtyards in
the middle are standard courtyards, while courtyards at the
front or back can be either standard courtyard or non-
standard courtyard. The ratio ðXratioÞbetween the width
and depth of a standard courtyard is Xratio 0:5, and the
one of a non-standard courtyard is Xratio <0:5. The two
types of parameters interactively affect the plan form of
each courtyard. The formula indicating the relationship
between the two parameters is set, as shown below, in
which both the Lsite depth and Lsite width are pre-determined
value once a site is selected and the Xcourtyard number and
Xratio are variables inputted by users.
Lsite depth ZXXcourtyard number
NZ1Xratio N Lsite width
To divide a site into courtyards, the algorithm operates
in the following steps:
Defining site area, site width, and site depth /defining
the available number of courtyards /determining the
number of courtyards /determining of the depth of each
courtyard.
An examples of three variants of dividing the same site
into courtyards with different values of the number of
courtyards ðXcourtyard numberÞand ratios between the depth
and width of each courtyard ðXratioÞare shown in Fig. 8.
3.2.4. Determining the floor plan pattern of each
courtyard
As previously mentioned, there is no historical evidence for
any rules concerning the floor plans of courtyards,
Fig. 7 Floor plan patterns categorized by location of the courtyard (at the front, middle, or rear), and type of the courtyard
(standard).
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digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
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therefore, we investigated the relevant statistical and
historical studies to categorize floor plan pattern types
based on two criteria: location of the courtyard (at the
front, middle, or rear of the Siheyuan), and type of the
courtyard (standard or non-standard). The floor plan pat-
terns of standard courtyard could contain any components
of the veranda, the primary room, the east secondary room
(Dong Xiang Fang), the west secondary room (Xi Xiang
Fang), the east wing room (Dong Er Fang), the west wing
room (Xi Er Fang), the east secondary wing room (Dong
Xiang Er Fang), the west secondary wing room (Xi Xiang Er
Fang), the festoon gate (Chuihua Men, usually only in the
first mid courtyard), and the floor plan patterns of the non-
standard courtyard must contain the opposite rooms (Dao
Zuo Fang) or the backside rooms (Hou Zhao Fang) and may
have some other components the same with standard
courtyard or not. There must be a front gate in the front
courtyard and maybe a back gate in the back courtyard (or
a corridor connecting the front gate and the front court-
yard). A non-standard courtyard at the front must contain
the opposite rooms. If a non-standard courtyard is located
at the back, besides its back gate, it must contain the
backside rooms. We have categorized the common floor
plan patterns by courtyard location and courtyard type
(Fig. 7).
Meanwhile, another tacit rule derived from Confu-
cianism requires that in each courtyard, the primary room
is generally located at the middle of the backside edge on
the plan with the courtyard’s central axis crossing its floor
plan centre, and most other components such as wing
rooms, secondary rooms, secondary wing rooms, and ve-
randas, are pairwise axisymmetric about the courtyard’s
central axis. For the courtyard where the MIPR is located,
the courtyard axis is the same as the site central axis. For
the other courtyards, the way of determining the courtyard
central axis is not being described in historical materials.
According to our observation on extant Siheyuan examples,
we inferred it is defined to be parallel to the site central
axis and crossing the plan centre of the primary room of the
courtyard or the midpoint of the boundary between the
courtyard and the adjacent rear courtyard (when the
courtyard does not contain a primary room). Since the
orientation of the site central axis is parallel to, or a few
degrees off the site orientation, the location of rooms and
verandas shown in Fig. 7 could be slightly moved and
rotated when the site central axis is not parallel to the site
orientation.
In this step, our algorithm identifies the location and
type of each courtyard, which have been decided in the
previous step. Finally, users can choose from one of the
available floor plan patterns. After the location and type
are determined, the algorithm can correspondingly move
the location and rotate the orientation of individual rooms
and verandas, as they are illustrated in Fig. 7. In our al-
gorithm, we defined the location of the central point of the
floor plan of each room and verandas with a two-
dimensional coordinate on the plane where the site plan
is positioned. The movement of each room and verandas is
defined as a line vector and their rotation is measured in
degrees. The algorithm of movement and rotation enables
the primary room crossing the courtyard central axis and
other individual rooms and verandas generally pairwise
axisymmetric about the courtyard central axis. Therefore,
the values of the line vector and the rotation degree are
Fig. 8 An example of three variants of dividing the same site into courtyards with different values of the number of courtyards
and ratios between the width and depth of each courtyard.
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digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
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determined by the location of the courtyard central axis.
The generation process is the following:
Defining courtyard location /deciding courtyard
type /identifying available floor plan
patterns /deciding the floor plan pattern /moving and
rotating each room and verandas.
3.3. Phase three: designing the individual
architectural components
The main types of architectural components that may exist
in a Siheyuan are the veranda, the primary room, the sec-
ondary room, the wing room, the secondary wing room, the
opposite room, the backside room, the festoon gate, the
front gate, the back gate, and the edge wall. Once the floor
plan pattern is determined, craftsmen design them using
rules from Gongcheng Zuofa Zeli and Fengshui, adjusted
according to their experience. Specifically, Liang’s findings
(Liang, 2006c) from his Gongheng Zuofa Zeli study were
used to derive the rules constraining these components. In
parallel to this, a section of Fengshui called “regulating
vital energy (Li Qi)” method and other ancient social
forces, such as Confucianism and ancient clans, fixed their
dimensional relationship.
3.3.1. Individual buildings
Aside from the festoon gate, veranda, and edge wall, the
rooms in a Siheyuan, and the gates were constructed as
individual buildings without any structural connection be-
tween them. The most important components of these
buildings are the carpentry structural frame and podium,
the design of which was based on a modular method
recorded in Gongcheng Zuofa Zeli, which results in similar
forms that differ only in terms of scale, orientation, and
exquisiteness of craftsmanship.
Normally an individual building has a rectangular plan
composed of rows of columns. The space between two
neighbouring columns is called a bay (Jian), with many
rafters in each bay on the roof top (See three examples in
Fig. 9). The four corners of each bay could be occupied by a
column. For convenience, it is assumed that there is a
column on every corner point when calculating the height
of an individual building, although it never happens in
practice. In fact, as shown in Fig. 9, there are three vari-
ations of the vertical side section of individual buildings
corresponding to three types of the layout of columns: a)
when the number of bays in the vertical side section view is
6, columns exist on the first and second outmost rows of the
bay corner points on the long side of the building plan and
the middlemost row’s outmost points; b) when the number
of bays in the vertical side section view is 5, the columns
exist on the first and second outmost rows on the front side,
the outmost rows on the rear side, and the fourth row’s
outmost points on the front side; c) when the number of
bays in the vertical side section view is 4, columns exist on
the outmost rows on the long side and the middlemost
row’s outmost points. The outmost columns on the front in
the vertical side section view are called eave columns (Yan
Zhu). It is noted that, on the plan of an individual building,
the length of the carpentry structural frame in the front
view, called ‘building width’, is the sum of all lengths of
bays in the front view. Similarly, its length in the side view,
called ‘building depth’, is the sum of all lengths of hori-
zontal projections of rafters (See Fig. 9). The ratio between
lengths of bays in the front view varies, but the lengths of
horizontal projections of the rafters are the same. Ac-
cording to Gongcheng Zuofa Zeli, the important parameters
Fig. 9 Three examples of individual rooms corresponding to three types of vertical side sections (after Liang, 2006b).
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digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
are the number of bays in the front view, the number of
rafters in the side view, and the diameter of an eave col-
umn. The value of the three parameters varies, depending
on the type of the room. The available values of the first
two parameters are constrained by the type of the room, as
shown in Table 2. The value of the diameter of an eave
column is the basic unit to calculate dimensions of other
components. This value should not exceed the size of the
available timber. It is noted that the height of an eave
column equals the length of the middlemost bay(s) in the
front view multiplied by 0.8, and the length of the rest of
the bays, from the middlemost to the outmost, are pairwise
symmetrical around the middlemost bay(s). In practice,
craftsmen would decide the building width first, and then
calculate the diameter of the eave columns based on the
ratio between lengths of bays in the front view, the number
of bays in the front view, and the ratio of an eave column’s
diameter to its height. Once the diameter of the eave
column is obtained, the length of the horizontal projection
of a rafter and the building depth could also be calculated
based on the number of rafters in the side view, and the
ratio of an eave column’s diameter to the length of hori-
zontal projections of a rafter in the vertical side section
view. The building width and building depth are constrained
by the rule that the individual building has to be smaller
than the courtyard it is located in. By using a calculation
Table 2 The available values of the number of bays in front view and the number of rafters in side view of different room
types.
Primary
room
Secondary
room
Primary wing
room
Secondary wing
room
Opposite
room
Backside
room
The number of bays The number of
rafters
343414141434
3535242444
363454
564464
5474
6484
94
Fig. 10 The algorithmic process to generate an individual building example (Units: in metres).
Parametrising historical Chinese courtyard-dwellings 13
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Table 3 Mathematical calculation of dimensions of components of structural carpentry and podium (Units: in cuns).
Name
Code Translation Width Height Depth Diameter
column eave column 1 yanzhu檐柱11-12D D
gold column 2 jinzhu金柱raising truss method Dþ1
mountain column 3 shanzhu山柱raising truss method Dþ2
beam embracing head beam 4 baotouliang抱头梁4~5Dþ1/10D 1.4D or 1.5D 1.1D or Dþ1
or 1.2D
five-frame beam 5 wujialiang五架梁length of middlemost
two bays in flanked
viewþ2D
1.5D 1.2D or Dþ2
three-frame beam 6 sanjialiang三架梁length of middlemost
two bays in flanked
viewþ2D
1.25D 0.95D
fang (tie beam) crossing fang 7 chuanchafang穿插枋4~5Dþ2D D 0.8D
eave fang 8 yanfang檐枋width of room D 0.8D
down gold fang 9 jinfang金枋width of room D or 0.8D or D-2 0.8D or 0.65D
or 4/5D-2
up gold fang 10 shangjinfang上金枋
ridge fang 11 jifang脊枋width of room 0.8D 0.65D
purlin eave purlin 12 yanlin檐檩 width of room D or 0.9D
down gold purlin 13 shangjinlin上金檩width of room D or 0.9D
up gold purlin 14 xiajinlin下金檩width of room D or 0.9D
ridge purlin 15 jilin脊檩width of room D or 0.9D
underboarding panel
and short column
eave underboarding panel 16 yandianban檐垫板width of room 0.8D 0.25D
down gold underboarding
panel
17 shangjindianban上金垫板width of room 0.65D 0.25D
up gold underboarding
panel
18 xiajindianban下金垫板width of room 0.65D 0.25D
ridge underboard panel 19 jidianban脊垫板width of room 0.65D 0.25D
gold short column 20 jinguazhu金瓜柱D distance between
five-frame beam
and three-frame
beam
D
ridge short column 21 jiguazhu脊瓜柱D~0.8D distance between
three-frame beam
and ridge purlin
D
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method, called “raising truss method (Ju Jia)”, the heights
of the other columns are determined. There are three types
of compositions of columns of individual buildings in the
vertical side section view. The “raising truss method” gives
ratios from the length of horizontal projections of rafters to
the height difference of two adjacent columns in the ver-
tical side section view, as shown in Fig. 9.
In later checks, we found out that the dimensions of the
individual buildings generated by our algorithm based on
Liang’s work are inconsistent with the historical ones. By
re-studying Gongcheng Zuofa Zeli, we noted that the dif-
ferences are caused by the fact that the values of some
constants in calculation formulas in Liang’s Qing Shi Ying-
zao Zeli are different from the original ones underlying
Gongcheng Zuofa Zeli. We note that these values were
flexibly decided by craftsmen in practice rather than by
strictly following rules from Gongcheng Zuofa Zeli. These
values also shape the dimensions of individual buildings.
The most influential one is the ratio between lengths of
bays in front view.
Based on the above analysis, the algorithmic logics to
define the geometrical dimensions of an individual building
and the height and location of each column are clarified.
They depend on five parameters: the building width, the
number of bays in the front view, the number of bays in the
side view, the ratio between the length of bays in the front
view, and the ratio of an eave column’s height to the length
of the horizontal projection of a rafter in the vertical side
section view, all of which are set as parameters in our al-
gorithm. The algorithmic process to generate an individual
building example is shown in Fig. 10. The dimensions and
positions of the remaining components of a building’s
structural frame are mathematically determined by the five
parameters. The calculation of the sizes of the structural
carpentry components and the podium is illustrated in
Table 3, and the compositional relationships of these
components are demonstrated in Fig. 11 by an example of
individual building, from which their positions are expli-
cated. The numbers in Fig. 11 correspond to the numbers in
Table 3, which are the different structural components.
Eighteen variations with different values of the five pa-
rameters are shown in Fig. 12.
What is the order of sizes of rooms? Supplementary to
the seven parameters two rules were used. The first,
influenced by Confucianism and ancient clans, requires a
hierarchy of rooms. One way to embody this is to make
rooms follow a sequence from large to small such as pri-
mary room >secondary rooms >wing rooms >secondary
wing rooms. Second, in the “regulating vital energy”
method of Fengshui, there is a rule predicting the house-
holder’s fortune by defining auspicious areas and ominous
areas of a courtyard, called ba gua qi zheng da you nian
(eight trigrams seven politics big tour calendar). This rule
divides a courtyard into nine areas by a 33 grid with
different degrees of fortune for each area. We transformed
this rule into an algorithm, whose parameter is the house-
holder’s birth year. We noted there are eight patterns of
the results indicating the fortune of each area, which
constrain scale relationships between the individual build-
ings in a courtyard. The constraint is that the most auspi-
cious part of the site is used for the largest individual
building and so in ranking order, and vice-versa for the
rafter, connecting
eave, roof
boarding panel,
tile edging
circle rafter 22 yuanchuan圆椽distance between eave
purlin and down gold purlin
(in oblique direction)
1/3D
square rafter 23 fangchuan方椽1/3D 1/3D or 3/10D distance between eave
purlin and down gold purlin
(in oblique direction)
flying rafter 24 feichuan飞椽1/3D 1/3D or 3/10D up extension method
flower frame rafter 25 huajiachuan花架椽1/3D 1/3D distance between the top point
of down gold purlin and the
top point of up gold purlin
(in oblique direction)
brain rafter 26 naochuan脑椽1/3D 1/3D distance between the top point
of up gold purlin and the top
point of ridge purlin
(in oblique direction)
big connecting eave 27 dalianchuan大连椽width of room 0.4D or 3/10D 1/3D or 3/10D
small connecting eave 28 xiaolianchuan小连椽width of room 1/3D or 3/10D 3/10D
podium base floor 29 taiji台基2.2D
hard mountain
base extension
30 yingshanchushan硬山出山1.8 Dþ3.6
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ominous spaces. Therefore, the eight patterns of fortune
are eight patterns of sequences of the scale of individual
buildings in a courtyard (Fig. 13). The constraint derived
from Confucianism and ancient clans is much more influ-
ential than the other one from Fengshui. Therefore, when
the two rules conflict, the Confucian rule takes
precedence.
The design principles of individual buildings were trans-
formed into an algorithm directly. The complete algorithm
uses five input-parameters from the Gongcheng Zuofa Zeli,
plus two constraints governing the size hierarchy of the
parts. Additionally, for Fengshui related version, the house-
holder’s birth year is set as a parameter to obtain the
constraint of the individual buildings’ scale relationship.
Fig. 12 Eighteen variations of the individual building with different values of the five parameters.
Fig. 11 Relationship of an individual building’s components’ positions.
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Fig. 13 Eight patterns determining the fortune of parts of a courtyard.
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3.3.2. Veranda
One obvious feature distinguishing a veranda from other
parts of the buildings is its curved rooftop. For the most part,
however, an algorithm for verandas, based on the modular
system to determine the size and location of components is
similar to that for individual buildings. However, rather than
an individual building shaped by the seven parameters, a
veranda is fixed by two factors. The first is the location of the
primary room and secondary rooms of the courtyard where
the veranda is placed. These are fixed by determination of
courtyard size in the second phase and of users’ preferences
in the fourth phase. The second is the side length of a
veranda column in plan view, whose value is chosen by
craftsmen between 4.8 and 6 cuns. In our algorithm, the
locations of these rooms are measured once these parame-
ters are inputted, and, for simplification, the side length is
defined as a constant in the value of 6 cuns.
3.3.3. Gates
There are two gate types: the front/back gate and festoon
gates. Constructed as individual buildings, the form of front
gatesandbackgatesissimilartorooms.Thedifferenceisthat
a gate doesn’t have an enclosed partition for defining the
interior, but a single partition defining the outside and inside
of a Siheyuan. This partition is usually a wall containing a door.
The design principles of the structural carpentry frame of the
gates and of individual buildings are the same, whose differ-
ences are the available value of parameters. For the gates, the
valueofthenumberofbaysinthefrontviewandofthe
number of rafters in the vertical side section view is set as 1
and 5 respectively. The principles of festoon gates are
different and will be the subject of further research.
3.3.4. Edge wall
The form of the wall is not parametrically constrained but is
defined by the division of the courtyard edge. Wall usually
exists on the edge of each courtyard, but in many cases,
some parts of the courtyard edge are occupied by buildings
so no wall is needed. The wall’s form can vary in detail, and
in our cases, for convenience, we assume it is in a cuboid.
The thickness of the wall is usually between 11 and 16 cuns
and the height between 70 and 120 cuns. For convenience,
our algorithm set them as constant values, 11 and 90 cuns
respectively.
3.4. Phase four: relocating architectural
components
Although the location of each architectural component is
fixed once each courtyard’s floor pattern is decided, we
Fig. 14 Flow chart of the design framework.
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note that in some Siheyuan examples supplied by Duan
(2016) and recorded on the Qianlong Capital Map individ-
ual rooms and verandas are additionally moved or rotated.
They are located freely within the courtyard but generally
pairwise axisymmetric about the central axis. It is noted
that in these cases the courtyard axis does not corre-
spondingly change even if the primary room moves in this
phase. Similar to the algorithm in the step of determining
the floor plan pattern of each courtyard, we define the
location of the central point of the floor plan of each in-
dividual room and verandas in a two-dimensional coordi-
nate (x,ycoordinate axis) on the plane where the site plan
is positioned. The movement of each individual room and
verandas is defined as a function of a line vector repre-
sented by variable x,y. The distance and direction of the
movement are represented by the values of xand y, which
is defined as a parameter and its values range is constrained
that the movement limits the individual rooms and ve-
randas to be within the plan of the courtyard. The rotation
of each individual room and veranda is defined as a
parameter measured in degrees, which positions the room
or veranda rotated clockwise. According to our observation
of built Siheyuan examples, the rotation is small. There-
fore, the value of the degree is defined between 20and
þ20.
3.5. The algorithm’s structure/design framework
The parametric logic attenuates Siheyuan design to just
twenty-four types of parameter. The workflow (Fig. 14)
shows the algorithm in Grasshopper, enabling users to
generate a Siheyuan by inputting these parameters.
4. Verifying the algorithm
To verify our Siheyuan algorithm, we generated models by
setting the same parameters’ values in our tool as the ones
observed in historical examples and then comparing the
results with reality. Due to the difficulty in collecting in-
formation from a complete Siheyuan, the comparison is
conducted using data of different Siheyuan fragments from
different sources. In particular, we examined the fortune of
24 representative site examples given by Yi et al. (1996),to
see if they followed the “observing context” method in
Fengshui to assess their fortune. Since our produced results
are the same as their assessment, our site selection algo-
rithm is confirmed.
To verify the floor plan pattern, we collected Siheyuan
plans from Duan’s measured survey (2016) and Ma’s work
Fig. 15 An abnormal (and inauspicious) Siheyuan example that cannot be generated by our tool (after Ma, 1999).
Parametrising historical Chinese courtyard-dwellings 19
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
(1999). We then applied our algorithm to re-produce the
same floor plan patterns. We have successfully reproduced
a typical three-courtyard Siheyuan, as presented by Ma
(1999). However, we have noted there are some floor
plan patterns that cannot be created by our tool, as evident
in the example given by Ma (1999) (Fig. 15), whose orien-
tation of each courtyard central axis varies from each
other, resulting in a pathological composition of architec-
tural components.
We note that it is impossible to verify the room-scale
relationship, since the essential data for historical Siheyuan
examples, such as the householder’s birth year, are not
recorded. However, according to our observation of plans
of extant examples, the constraint deriving from Confu-
cianism and ancient clans are inferred to be much more
influential than the one from Fengshui, which embodies on
obvious differences between room scales. Therefore, in
this study, we ignored the Fengshui constraint.
To verify whether the algorithm produced valid archi-
tectural components or not is challenging because most
Siheyuan components existing today are badly damaged or
reconstructions of original buildings built after the Qing
dynasty, and measuring materials about historical examples
are very few and limited in detail. Alternatively, we
examined architectural components from Liang’s drawings
(Liang, 2006b), which contains detailed component di-
mensions. Liang produced the drawings referring to the
Gongcheng Zuofa Zelie and interviews with the successors
of ancient craftsmen. Consequently, the buildings in his
drawings are believed to be following the rules of the Qing
dynasty. To verify this, we compared the structural
component dimensions produced by our tool with their
Fig. 16 The comparison of an individual building of Siheyuan represented by Liang, 2006b and the corresponding example.
20 Y. Wang et al.
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
counterparts on Liang’s drawings. The two versions are
consistent. (For example, a building drawn by Liang is
selected to derive values of parameters and used to
generate the counterpart by our tool. The two examples
were overlapped to observe, as shown in Fig. 16.). By
controlling the five parameters for each room, it could be
ensured that the relationship of scales of the generated
rooms in a courtyard satifies the constraint from Confu-
cianism and ancient clans.
Despite the discrepancy between Liang’s study (Liang,
2006c) and our algorithm on the one parameter, we suc-
cessfully generated many Siheyuan houses. Some of Duan’s
plan drawings (2016) from his measuring survey on extant
Siheyuan and corresponding models generated by our tool
in top view have been overlapped, thus we can test po-
tential discrepancies (See two examples in Fig. 17).
Evidently, our tool can reproduce Siheyuan housings with
high accuracy, if compared to drawings, photos, and text in
Fig. 17 Two comparisons of algorithmically generated Siheyuan overlapped with Duan’s survey on extant examples (2016).
Parametrising historical Chinese courtyard-dwellings 21
+MODEL
Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
Duan’s measuring survey. However, it has to be noted, that
these drawings lack detailed dimensional data, and conse-
quently, we cannot verify our tool in terms of its ability to
reproduce the architectural components in every detail.
5. Conclusions
With this research, the tacit design rules have been
revealed and transformed into an algorithm in coherence
with the Fengshui, Gongcheng Zuofa Zeli, and the crafts-
men’s experience. The proposed algorithmic tool proved
capable of producing Siheyuan types with high accuracy,
which replicate key features of traditional Siheyuan since
we successfully verified it by producing examples consistent
with examples given by other scholars.
Siheyuan, the most common dwelling type of Beijing
during the Qing dynasty, is much sought after today. Pre-
viously, to design a Siheyuan, architects needed to follow
the design principles to determine locations and dimensions
of each component by complicated computing and calcu-
lating manually, however, using this tool, they just need to
input the required parameters and the three-dimensional
representations will be created automatically. Compared
with the conventional method of design and modelling, our
tool takes only a few seconds to generate models by
inputting parameters. The formulated algorithm is easy to
use and saves time to design models and modify Siheyuan,
thus it will be useful for today’s architects who wish to work
in the Siheyuan idiom.
The discrepancy between Liang’s study (Liang, 2006c)
and our algorithm on the one constant resulted in the in-
consistencies of the size of individual buildings and its
carpentry structural frame and podium. We noted, using
the values of the constant given by Liang, that the algo-
rithm can neither generate the buildings recorded in Liang’s
drawings (Liang, 2006b) nor the extant Siheyuan examples
with the same sizes. This discrepancy may be caused by two
factors. First, it is possible that Liang mistakenly recorded
some constants, since we found self-contradiction in his
studies. Liang has published two books (Liang, 2006b,
Liang, 2006c) introducing design principles of architecture
of the Qing dynasty. One explains the design principles
using text and photos, including the calculation of di-
mensions of construction components in the form of a pithy
formula, and the other illustrates these principles by
developing architectural drawings of building and con-
struction component examples complete with dimensions.
We have noted that these dimensions of components on the
drawings of Qing Gongbu Gongcheng Zuofa Zeli Tujie
(Liang, 2006b) are not consistent with the calculation of
them in Qing Shi Yingzao Zeli (Liang, 2006c). Therefore, as
Liang, 2006a stated, “over the past decade I have found
many mistakes”, his data are not entirely reliable, despite
the fact that both books are widely accepted by scholars.
Second, by studying built Siheyuan examples, we found that
these values varied case by case. Consequently, even if we
apply the original values of these constants in Gongcheng
Zuofa Zeli to our algorithm, it is impossible to correctly
generate counterparts of every built Siheyuan. It is noted
by many scholars (Ma, 1999;Zhao, 2013;Lu and Wang,
2013) that Siheyuan, as the most common dwellings in
Beijing constructed by residents rather than official build-
ings constructed by the government, did not strictly follow
the rules from Gongcheng Zuofa Zeli. We speculate that
craftsmen, who used formulas to pass the design principles
from each generation to the next based on their individual
experience rather than the rulebook, changed the values of
some constants. Nevertheless, by parameterising the
influencial constant, we still can use this tool to generate
Siheyuan designs the same with extant examples that
emerged in Duan’s (2016),Ma’s (1999), and Ni’s (2009)
studies once we obtain the necessary inputting parame-
ters. While we are alert to the possibility that there might
be more tacit rules than we are aware of, we view these
pathological cases as illuminating the normal: since the
shapes of these sites are usually irregular and many other
uncertain factors are shaping the results, craftsmen often
improvised but always tried to be as close as possible to
what would occur with no constraint, so that even in
irregular circumstances something approximating an ideal
form was produced. This explains the common view that
Siheyuan is based on some ideal models.
We noted that the rules for Siheyuan are a way of con-
trolling the standard of buildings, and those rules were
applied more rigorously in Beijing than further afield in
China. The fact that an algorithmic model of a house is even
possible is a reflection of an attempt to control houses by
means of rules, which is then reflected in their typology.
Funding
This research was supported by the funding from The China
Scholarship Council (No. 201708510109).
Declaration of conflicting interests
There is no potential conflicts of interest with respect to
the research, authorship, and/or publication of this article.
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Parametrising historical Chinese courtyard-dwellings 23
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Please cite this article as: Wang, Y et al., Parametrising historical Chinese courtyard-dwellings: An algorithmic design framework for the
digital representation of Siheyuan iterations based on traditional design principles, Frontiers of Architectural Research, https://doi.org/
10.1016/j.foar.2020.07.003
