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GoDesign
A modular generative design framework for mass-customization and
optimization in architectural design
Shervin Azadi1, Pirouz Nourian2
1,2Delft University of Technology
1,2{s.azadi-1|p.nourian}@tudelft.nl
We present a modular generative design framework for design processes in the
built environment that provides for the unification of participatory design and
optimization to achieve mass-customization and evidence-based design. The
paper articulates this framework mathematically as three meta procedures
framing the typical design problems as multi-dimensional, multi-criteria,
multi-actor, and multi-value decision-making problems: 1) space-planning, 2)
configuring, and 3) shaping; structured as to the abstraction hierarchy of the
chain of decisions in design processes. These formulations allow for applying
various problem-solving approaches ranging from mathematical derivation &
artificial intelligence to gamified play & score mechanisms and grammatical
exploration. The paper presents a general schema of the framework; elaborates
on the mathematical formulation of its meta procedures; presents a spectrum of
approaches for navigating solution spaces; discusses the specifics of spatial
simulations for ex-ante evaluation of design alternatives. The ultimate
contribution of this paper is laying the foundation of comprehensive Spatial
Decision Support Systems (SDSS) for built environment design processes.
Keywords: Generative Design, Spatial Configuration, Serious Gaming, Mass
Customization, Decision Problems
INTRODUCTION
This paper presents a ‘participatory generative de-
sign framework’ emblematically called ‘Go Design’
after the game of Go. This framework is designed to
enable Mass-Customization and application of Multi-
Criteria Decision Analysis for supporting multi-actor
decision-making processes such as those aimed at
reaching consensus among stakeholders on goals
and design requirements, objective decision-making
processes such as finding the best configuration re-
spective to environmental factors (e.g. light, en-
ergy), and finally subjective processes such as choos-
ing styles, materials, and colors of the final struc-
ture. The focus of this paper is on the mathemati-
cal formulation of the spatial configuration problem,
given exemplary inputs for user preferences to estab-
lish the generality of the framework as to different
optimization/decision-making approaches and vari-
Computational design - Volume 1 - eCAADe 39 |285
ous participatory processes. Thus, the details of im-
plementation and the participatory processes are be-
yond the scope of this paper. Effectively, the pro-
posed framework reformulates architectural design
as a chain of systematic decision-making problems in
terms of given inputs and desired outputs rather than
ad-hoc drawing and representation challenges.
We present a mathematical categorization and
formulation of archetypical design problems, that
provides for adequate utilization of a variety of com-
putational methodologies. This categorization sets
out a spectrum of decision-making problems rang-
ing from the most abstract to the most concrete: 1)
[space] planning in the context of Graph Theory, 2)
configuring in the context of Algebraic Topology, and
3) shaping in the context of Computational Geom-
etry. This categorization distinguishes the priorities
of decision-making and specifies the widely-spoken
notion of early-stage design decisions. By revisit-
ing such typical architectural design problems from
‘drawing’ problems to ‘decision’ problems, they fall
naturally within the purview of “The Sciences of the
Artificial” (Simon, 2008), as defined by Herbert A. Si-
mon. As such, this framework is a tribute to the ini-
tiative of several pioneers of computational design,
namely the eloquent quest of Yona Fridman’s “To-
wards a Scientific Architecture” (Friedman, 1980).
BACKGROUND
It has been argued that design and planning prob-
lems are “wicked problems”(Rittel, 1973); evading
formulation, benchmarking, objective definitions of
goals, etc. Inspired by (cf. (Voordijk, 2009)) we pro-
vide four lenses for revisiting such compound com-
plexities by suggesting that the multi-dimensional
and multi-criteria complexity of decision-making in
design is attributable to the physical nature of the
design task, while the multi-actor and multi-value
complexities of decision-making are attributable to
the concerning human factors in design (see Fig-
ure 1). Multi-dimensional complexity corresponds to
the complex spatial (geometrical, topological, and
graph-theoretical) relations that need to be orches-
trated between spaces and elements. Multi-criteria
complexity is concerned with balancing static and
dynamic/operational qualities that a design is re-
quired to provide, such as light, solar energy, etc.
The multi-actor complexities stem from the differ-
ence in the goals of stakeholders. Finally, the
multi-value complexity originates from the uncer-
tainties and ambiguities inherent to human percep-
tion and communication, which can be traced in self-
contradictory preferences, bounded-rationality, mis-
communication of goals, and individual-communal
good dilemmas as discussed in Game Theory (q.v.
(Cunningham, 2018)).
Given this decision-making approach, we natu-
rally aim to structure the decisions to maximize the
customizability for the actors while maintaining the
explainability of the process. In doing so, we gener-
alize this framework to incorporate an arbitrary num-
ber of spatial quality criteria, some of which might
be related to human factors. In addition, we prof-
fer a mechanism for integrating Multi-Criteria Deci-
sion Analysis (abbr. MCDA, q.v. (Ogrodnik, 2019) &
(Huang, 2011)).
Figure 1
Variety of
complexities
involved
Explicitly discretizing the decision space facilitates
analyzing the computational space and time com-
plexity of procedures, enabling the simulation of spa-
tial quality aspects related to accessibility, visibility,
etc. Discretization of a design space not only facili-
tates the computational processes for providing play
& score ‘design games’ (q.v. (Sanoff,1978) & (Bots,
2003)) but also inherently supports ultimate mod-
ularization of buildings as products, thus reducing
the costs of production (q.v. (U|lrich,1995), (Salvador,
2002), (Salvador, 2007), and (Rocha, 2015)).
286 |eCAADe 39 - Computational design - Volume 1
However, the mathematical formulation of de-
sign and planning problems is a challenge that pre-
cedes the use of computation and explainable Artifi-
cial Intelligence. A r igorousmathematical framework
for design processes can create the methodical foun-
dation necessary for developing Artificial Intelligence
that can incorporate objective environmental factors
and multi-actor user preferences in the process of de-
sign/planning. Within such frameworks, it is neces-
sary to include a set of objectives for the design tasks
that can describe the user preferences and environ-
mental necessities, a model for spatial relations and
qualities, and an assessment module that can assess
the spatial relations and configurations based on the
user preferences and environmental factors.
FRAMEWORK
We propose to organize the order and priority of
design decision-making processes from abstract to
concrete through three significant procedures: Plan-
ning, Configuring, and Shaping as a meta-level pro-
cedures with precise inputs, outputs, and problems.
Planning is the first procedure in which stakehold-
ers will collectively specify the relations and criteria
of spaces. Planning involves multi-value, multi-actor,
and multi-criteria complexities and aims to reach
a graph theoretical description of spatial specifica-
tions, spatial relations, and collective design goals.
Configuring is a procedure focused on generating
a configuration of spaces from the specified crite-
ria and relations in the previous step. Configuring is
primarily concerned with the multi-dimensional and
multi-criteria complexities and aims to explore dif-
ferent spatial configurations and represent them as
graph mappings that describe ‘discrete dimension-
less [topological] design’ (Steadman,1983). Shaping
is the latest step that focuses on concretizing the
geometry of the last procedure’s topological design.
Shaping involves multi-dimensional and multi-value
complexities of design as it determines the aesthetic
styling of design.
The precise formulation of the data structures
passed between these procedures is crucial as they
function as interfaces between the procedures. To
ensure the modularity and generality of the frame-
work, we propose a mathematical formulation of
these data structures. The same logical transition
from abstract to concrete that is present in the order
of steps is also evident in the data structures passed
between steps as they are formalized using different
branches of mathematics from graph theory to topol-
ogy to geometry.
Table 1
Meta-procedures in
the proposed
framework
Avoiding the black box approach and explicating the
design process in utmost clarity to the actors funda-
mentally supports human participation. This verti-
cal inclusion of stakeholders will enable them to cus-
tomize the design not only to match their personal
goals but also to adhere to the societal context that
the design is situated in.
Generally, this framework utilizes feed-forward
mechanisms in the micro-level when decisions are
numerous, and they need objective adherence to
preset spatial constraints and criteria, and feedback
mechanisms at the macro-level when human insight
is required in societal and cultural connotations of
spatial constraints and criteria, or when subjective
opinions are to be addressed in customization.
Framework: Planning
Ensuring actors’ participation with customization ca-
pabilities requires strategies for targeting social, eco-
nomic, and environmental sustainability goals. For-
mulating, communicating, and justifying such strate-
gies and decisions for/together with multiple stake-
holders is challenging from a scientific point of view,
mainly due to the multi-actor and multi-value com-
plexities. Overcoming this challenge requires in-
cluding the inhabitants [and contextual stakehold-
Computational design - Volume 1 - eCAADe 39 |287
Figure 2
Main flowchart of
the framework
ers] in the decision-making process (inclusion) as
well as explaining and justifying the decisions (trans-
parency). Thus, the planning phase frames an in-
teractive approach for collaboratively setting out the
spatial specifications and relations.
Table 2
Framework of
Planning Procedure
By abstracting and discretizing the design space,
we mathematically formulate the planning phase
as a multi-actor and multi-criteria decision-making
problem. Within this formulation, the actors/stake-
holders to negotiate, reach a consensus, and graph
theoretical objects will represent the final decision.
These objects consist of the relation of spaces with
each other as a uni-partite graph and the relation of
spaces with criteria as a bipartite graph. This phase’s
gamification provides for reaching consensus on the
user-preferences (Bots, 2003) and provides transpar-
ent and inclusive decision-making processes for the
planning phase.
Framework: Configuring
Given the contextual information, the main objective
of configuring is to find a configuration as a colour-
ing of a discretized design space (building enve-
lope) that satisfies the local and global spatial validity
constraints, the desired spatial relations, the spatial
quality criteria, and their corresponding weights that
have been determined in the planning phase. The re-
sultant configuration will be represented by a graph
mapping or graph colouring that assigns a colour/la-
bel to each of the envelope’s volumetric cells. As
such, configuring is formulated as a feed-forward
process since the contextual information and spatial
criteria are provided at the beginning of the phase.
The buildable envelope can either be empty or con-
tain already existing buildings.
Figure 3
Z-Order Indexing of
Voxels, Visualization
of the density
matrix, and
Configuration
Within this procedure, contextual information layers
correspond directly to the set of criteria in the plan-
ning procedure. The weights of importance given by
288 |eCAADe 39 - Computational design - Volume 1
the actors will indicate how the MCDA will evaluate
the allocation of different voxels based on their value
in the quality criteria functions. Within this frame-
work, each information layer is a quantity that has a
value in each position of discrete space. Thus it can
be formalized as a field: fk:[0,1]o×n7→ [0,1]ok∈
{0,1,˙s, m}and thus they can be called spatial qual-
ity criteria functions. As such, we can distinguish
two categories of quality criteria based on their
computational nature: Firstly, Accessibility-Related
Quality Criteria, which must be computed based
on geodesics and geodesic distances on [approx-
imate/discrete] 2D manifolds. Secondly, Visibility-
Related Quality Criteria must be computed based on
straight-lines of sight and Euclidean distances on [ap-
proximate/discrete] 3D manifolds (e.g., direct sun-
light, sky view, noise, etcetera). It is impor tant to note
that field formulation of quality criteria allows for in-
cluding any quality criteria function as long as they
are computable.
Furthermore, as the configuring procedure is of-
ten iterative, fields can be categorized into three cat-
egories based on how they should be re-evaluated
given an existing configuration: firstly the Static
fields representing quantities that their value in
space are entirely independent of the configuration,
such as height, distance to the facade, etcetera; and
secondly, the Dynamic fields representing quantities
that theoretically can be evaluated in the absence
of configuration, yet the configuration affects their
evaluation (e.g., direct sunlight, sky view, etc.; and fi-
nally, the Dynamic & Dependant fields representing
quantities that their evaluation is only possible when
a configuration exists (e.g., closeness to the entrance,
closeness to the lobby, etc.)
As indicated in Table 1, the configuring proce-
dure does not include human complexities such as
multi-actor and multi-value aspects. This ensures the
generality of the framework and allows for both op-
timization and participatory decision-making formu-
lations of such configuring procedures. However,
given the typical challenges in formalizing societal,
cultural, and other human-related criteria, an opti-
mization formulation of this step could be exces-
sively simplistic and reductionist. Thus, we advocate
for a participatory decision-making formulation that
allows for explorative approaches and utilization of
various Multi-Criteria Decision Analysis methodolo-
gies.
Table 3
Framework of
Configuring
Procedure
Nevertheless, the proposed procedure is so general
that, if desired, it can frame the problem of config-
uring as a generalized Topology Optimization proce-
dure similar to those exploited in structural design,
mechanical engineering, and fluid dynamics. For this
reason, the decision variable matrix Xo×ncan con-
tain continuous density variables inside the configu-
rator so that the functions remain differentiable and
that the gradients required for the updating scheme
Computational design - Volume 1 - eCAADe 39 |289
of topology optimization algorithms can be com-
puted. However, once the decision is taken and fix-
ated at the front-end of the process, the continuous
densities will be mapped to the set {0,1}. Further-
more, as indicated in the main flowchart (Figure 2),
this step’s resultant configuration is subject to polling
amongst actors to ensure the ultimate consistency
with unquantifiable values and criteria.
A generic formulation of such configuring proce-
dures is proposed in Table3. Such configuring proce-
dures can be implemented as a Configurator (indus-
trially known as Configure, Price & Quote systems, q.v.
(Jordan, 2020)) as a Decision-Support System that is
capable of facilitating Play & Score processes, which
can be possibly multi-player or single-player. To as-
sess the different aspects of the resultant configura-
tion, we propose a set of MCDA aggregators capa-
ble of reporting the quality of a configuration con-
cerning the set of spaces, the set of criteria, the set
of actors, or one single score for the configuration as
a whole.
Framework: Shaping
In the shaping procedure, the previous step’s config-
uration will be polygonized to create the geometrical
representation of the configuration. Two main ap-
proaches can be distinguished in such procedures:
discrete & continuous. In the discrete approach, a
tileset is used to specify the geometry, which inher-
ently facilitates modular construction. In the contin-
uous approach, a level set is generated based on the
difference in the voxel colors. The continuous ap-
proach offers a more robust process though it lim-
its the customizability of the architecture of the re-
sultant mesh. In its utmost generality, however, the
continuous approach can significantly increase man-
ufacturing costs -only if continuous density variables
are to be permitted. It must be noted that given
a voxelated domain and discrete densities from the
set {0,1}even a continuous iso-surface will be a
mesh that can be post rationalized as a modular sur-
face. The discrete approach, on the other hand, al-
lows the actors to customize the tilesets and conse-
quently personalize the final design; while still ben-
efiting from the economy of scale in that they will
be using a set of few tiles (to be precise, between 8
to 256 tile geometries, irrespective of their other at-
tributes). This entails that the whole building is not
only customizable to a high level of detail, it is also
going to be affordable because of the possibility of
mass-production of such tiles as construction com-
ponents.
Table 4
Framework of
Shaping Procedure
METHODOLOGY
The same way a structured collection of techniques
is referred to as a technology, a structured collection
of methods is referred to as a methodology. As indi-
cated earlier, each of the three proceduresfocuses on
different aspects of the design process and has differ-
ent complexities. In this section, we elaborate on the
suitable methods for each procedure. In the follow-
ing section, we present a spectrum of methods from
domains ranging from the digital game industry and
Procedural Content Generation (a.k.a. Scene Synthe-
sis) to Engineering Optimization methods and Arti-
ficial Intelligence, all of which can be utilized within
our proposed framework.
Methodology: Planning
An exemplary mathematical definition of a multi-
actor game for reaching consensus on the user
preferences on shared/communal spaces based on
290 |eCAADe 39 - Computational design - Volume 1
abstractions of Game Theory and Graph Theory
is proposed by (Bai, 2020). This can be ex-
tended by the opinion pooling method suggested
by (Batty,2013)or consensus Building suggested by
(Sanoff,2000) to model different decision factors and
their dynamics with Network Models.
Methodology: Configuration
As indicated in Configuring Framework Section the
configuring phase provides a problem formulation
that allows for applying a spectrum of existing meth-
ods such as Engineering Optimization, MCDA, and
gamification. However, the feed-forward nature of
such procedures requires a new category of simula-
tion and approximate evaluation tools capable of tak-
ing highly abstract inputs.
Starting from the most automated (and yet ex-
plainable) approach, this formulation provides the
structure for application of Topology Optimization
(TO) (Bendsoe, 2013) as the configuration is repre-
sented by a discrete density matrix X, and a recip-
rocal analogous of the strain energy (compliance) in
a conventional TO is the spatial quality criteria func-
tions f(see Table 3). This formulation is thus suitable
for gradient-based mathematical programming. The
caveat here is that in this framework we formulatethe
quality criteria as benefits to be maximized for better
human understanding as it is common in RL frame-
work which they formulate as rewards, howeverin TO
approach it is more common to formulate objective
functions as cost to be minimized.
Furthermore, given the spatial validity con-
straints gb, a family of Combinatorial Optimization
methods is also applicable similar to the approach
of (Hua, 2019), and(Peng, 2016) which apply Inte-
ger Programming in multiple scales to layout and
routing problems in discrete spaces; or as in (Wu,
2018) which applies Mixed-Integer Quadratic Pro-
gramming(MIQP) to discrete interior design prob-
lems. Also, Reinforcement Learning (RL) methods are
compatible with this formulation since we can define
the configuring procedure as a Markov Decision Pro-
cess (MDP) given that Xrepresents the state space,
spatial constraints can be embedded in the definition
of agents’ actions, and spatial quality criteria function
fcan provide the rewards for the learning agents.
An example of such application is “Academy Spatial
Agents” (Veloso, 2020) where spatial agents utilize
DDQN to make decisions in a discrete space.
Moreover, the search process can be gamified to
establish a play & score environment as well. Within
such an approach, grammatical itemization can be
used as the generative mechanism of playing (as ap-
plied in [ref. removed for annonymity]) and MCDA
methods (as reviewed in (Huang, 2011) for scoring
the configuration alternatives. Finally, there are also
potentials for hybrid approaches such as combining
a Multi-Agent System (q.v. ( Veloso, 2018)) approach
with local MCDA evaluators that guide their decisions
about configuration in a discrete environment ([ref.
removed for anonymity]).
Methodology: Shaping
As stated in Shaping Framework Section, polygoniza-
tion of the configuration can be performed through
a continuous or discrete approach. An exciting ex-
ample of the continuous approach is the Marching
Cubes algorithm applied in (Nourian, 2014). The dis-
crete approach can be deterministic as proposed by
(Savov, 2020) where geometric tiles are placed if a
particular combination is present in the configura-
tion, or they can follow a stochastic approach such as
Wave Function Collapse Algorithm in which the tile
selection for each location is modelled as a proba-
bility function that changes based on the selection
of tiles in the neighbouring locations (Gumin, 2021).
There have also been efforts to combine these ap-
proaches and generalize from a regular grid to non-
regular grids. (Stalberg, 2015)
APPLICATION & RESULTS
The ‘Go Design’ framework has been partially imple-
mented in the form of an open-source python pack-
age named topoGenesis to maximize its accessibility
and reproducibility. We have developed a python li-
brary called topoGenesis (Azadi, 2020) The proposed
Computational design - Volume 1 - eCAADe 39 |291
workflow and this tool-set have been applied in ed-
ucational design studios at TU Delft. In the BSc Spa-
tial Computing design studio, students are asked to
develop systems that allow future inhabitants to cus-
tomize the configuration while satisfying environ-
mental constraints such as direct sunlight, sky view
factor, noise, etc. (see Figure 4). Their site is located
in Agniesebuurt near the central station of Rotter-
dam. Students were asked to design a mixed-use
complex in a specified parcel. They were instructed
to identify future inhabitants and develop a gamified
process for the planning phase to specify the inhab-
itants‘ preferences as to the aforementioned spatial
quality criteria. Next, students were instructed to uti-
lize a Multi-Agent System in the configuring process;
embed spatial constraints in the agents’ behaviors
to avoid complex mathematical formulation of the
constraints; utilize MCDA to aggregate each voxel’s
total value concerning different spatial quality crite-
ria functions; and finally, synthesize a configuration
based on the relative advantage of allocating each
space to a particular voxel [1].
In the MSc EARTHY design studio (Nourian, 2020)
the framework has been utilized for temporary ac-
commodation of displaced communities in Al Za-
atari Refugee Camp in Jordan. Students were asked
to develop systems/games that allow inhabitants to
customize the configuration of their collective habi-
tats while satisfying structural and low-tech con-
structability constraints of adobe buildings. Their
system is required to produce assembly plans of a
set of modules to construct the buildings (see Figure
5) Students have developed combinatorial games
for exploring configurations as modular permuta-
tions. In this project, students have taken a partici-
patory grammatical approach to provide maximum
control over the configuration for the future inhabi-
tants [2],[3].
In the EARTHY studio, as the structural con-
straints are the main feasibility constraints of the
design process, successful projects have adopted a
modular approach based on different structural ele-
ments (e.g. dome, vault, arch, etc) as the basis of their
Figure 4
Examples of
application of
GoDesign
framework in
student projects:
BSc [1]
Figure 5
Examples of
application of
GoDesign
framework in
student projects:
MSc [2][3]
configuration system. With this approach, they not
only managed to gamify the decision-making pro-
cess for inhabitants but also eliminated the need
for post-design structural analysis of the structures
to increase the independence of the inhabitants in
configuring and constructing the buildings [2],[3].
On the other hand, in the Spatial Computing stu-
dio, the structural constraints were not as limiting as
in the case of EARTHY. Thus successful projects fo-
cused more on spatial quality criteria such as day-
292 |eCAADe 39 - Computational design - Volume 1
light, accessibility, visibility, noise, etc., and devel-
oped a gamified decision support system that allows
the stakeholders to set their preferences and see the
effect of their preferences on the design. [1]
CONCLUSION & DISCUSSION
Generality
As the primary feature of this framework is to offer
ageneral formulation of the design problem that
does not only provide the structure required for the
application of optimization and AI methods but also
makes the design process more transparent by pro-
viding interfaces for participants to be part of the de-
sign process, inject their preferences and customize
the design. This is particularly important as it pro-
vides for argumentation on spatial decisions in an
evidence-based approach. As a result, spatial deci-
sions can be traced back to the context conditions,
quality criteria, and stakeholder preferences. Also,
the framework in general, and the planning phase in
particular, can support various forms of multi-actor
decision-making mechanisms (participatory design)
to ensure customization of the design in various
steps. Beyond the decision-making perspective, this
framework structures the design space as a count-
able set of solutions while maintaining topological
and geometrical diversity.
Furthermore, the configuring meta-procedure
offers a generalized formulation of quality criteria
functions that encompasses any criteria that could be
expressible as a function of space (field). Besides, the
modularity of these quality critera functions allows
for including an arbitray set of multiple criteria. Simil-
iarly, various types of local and global spatial validity
constraints can be included in such proecdures.
The combined implementation of configuring
and shaping meta-procedures is compatible with
both modular and integral construction techniques.
Finally, the inherentprocess-modularity of the frame -
work provides for partially adopting it or combining
it with other frameworks.
Limitations
As explained in the Framework Section, this frame-
work mathematically prioritizes abstract decisions
over concrete ones. This prioritization structures the
solution space and facilitates the formalization of
objectives and constraints in the process. Conse-
quently, specific solutions will be harder to reach.
Mainly, designs that are geometrically simpler but
topologically complicated are less likely to be gener-
ated. Furthermore, the mathematical nature of the
framework requires the quantifiability of spatial crite-
ria prior to their integration in the framework. How-
ever, there are ongoing research projects to assess its
potentials in integrating non-quantifiable quality cri-
teria such as the heritage value of attributes of exist-
ing structures in case of renovation projects.
Future Work
Primarily, this framework provides a foundation for
the mathematical formulation of spatial quality crite-
ria fand spatial constraints g. As the built environ-
ment is present in many aspects of human life, it influ-
ences and is influenced by many physical and societal
aspects of human life. Consequently, a spectrum of
different qualities needs to be modeled, formalized
and added to the system. As such, the mainline of
future work within this framework will be about de-
veloping various specialized evaluation procedures.
The configuring procedure provides the poten-
tial for applying MCDA and optimization methods, a
couple of examples of which have been mentioned
in the manuscript. However, there is yet much more
room for exploring the applicability and suitability
of a wide range of compatible methods for solving
benchmarked problems. This is particularly impor-
tant in order to situate the framework in the AEC in-
dustry, thus further investigation into the compatibil-
ity of the framework with existing conventional work-
flows is required to consolidate more test cases.
Finally, this framework offers an explicit formu-
lation of spatial design problems that is compati-
ble with many modern Machine Learning methods,
not only for automating decision making by means
Computational design - Volume 1 - eCAADe 39 |293
of Generative Adversarial Networks (GANs), Deep Q-
Networks (DQN), etc, but also, more importantly, for
growing a body of evidence-based knowledge of
‘quality’ and its complex relations to our design de-
cisions.
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