Artificial Intelligence for
Engineering Design, Analysis
Guest Editorial Promises Of
Cite this article: Eloy S, Pauwels P, Economou
A (2018). AI EDAM special issue: advances in
implemented shape grammars: solutions and
applications. Artificial Intelligence for
Engineering Design, Analysis and Manufacturing
shape grammar; implementation; interpreters;
technical design; interfaces; use cases
Author for correspondence: Sara Eloy, E-mail:
© Cambridge University Press 2018
AI EDAM special issue: advances in
implemented shape grammars: solutions
Sara Eloy1, Pieter Pauwels2and Athanassios Economou3
Department of Architecture and Urbanism, Instituto Universitário de Lisboa (ISCTE-IUL), ISTAR-IUL, Lisbon,
Department of Architecture and Urban Planning, Ghent University, Ghent, Belgium and
Architecture, College of Design, Georgia Institute of Technology, Georgia, USA
This paper introduces the special issue “Advances in Implemented Shape Grammars:
Solutions and Applications”and frames the topic of computer implementations of shape
grammars, both with a theoretical and an applied focus. This special issue focuses on the cur-
rent state of the art regarding computer implementations of shape grammars and brings a dis-
cussion about how those systems can evolve in the coming years so that they can be used in
real life design scenarios. This paper presents a brief state of the art of shape grammars imple-
mentation and an overview of the papers included in the current special issue categorized
under technical design, interpreters and interface design, and uses cases. The paper ends
with a comprehensive outlook into the future of shape grammars implementations.
This special issue frames the topic of computer implementations of shape grammars, both
with a theoretical and an applied focus. Articles in this issue display the state of the art of
these computer implementations, as well as their applicability in real design scenarios. The
development of this special issue was combined with a special workshop “Advances in
Shape Grammars: Implemented Shape Grammars”, chaired by Pieter Pauwels and Sara Eloy
and held in Evanston, Chicago preceding the Design Cognition and Computation 2016
During the DCC workshop (Pauwels & Eloy, 2016), the 23 participants had the opportu-
nity to discuss the recent developments in shape grammar research. The aims of the workshop
were: (i) to enable hands-on demonstrations, (ii) to receive on-topic feedback and discussions,
(iii) to discuss recent developments, (iv) and to discuss on three topics: technical design, inter-
face design, and use cases. These last three topics were also the main topics that were planned
to be addressed in the AIEDAM special issue. Terry Knight and Thanos Economou each gave
a brief talk in the beginning followed by the hands-on demonstrations provided by Thomas
Grasl with GRAPE and Andrew Li with The Interpreter Project during which they showed
the potentials and drawbacks of both interpreters. Presentations were done by Hau Hing
Chau “Exploring lattice structures in shape grammar implementations”, and Luca
Zimmerman “A generative design framework integrating spatial grammars, simulation and
optimization”, allowed to discuss technical advancements. Sara Garcia with “A multipurpose
chair grammar implementation”, and Nikolaos Vlavianos with “Shape grammars Augmented
Reality (SGr): A novel rule-based method for designing with eyes”brought the use of shape
grammars in a practical context.
The starting point of this special issue is the current state of the art regarding computer
implementations of shape grammars and a discussion about how those systems can evolve
in the coming years so that they can be used in real-life design scenarios. Shape grammars
have been researched for more than 40 years now reaching several areas of design as architec-
ture, engineering, and product design. Besides the intellectual challenge involved in the devel-
opment and use of shape grammars, the potential they would have in addressing real-life
design problems is enormous. Several shape grammar implementations have been developed
the last years but a true impact in the design methods is still to be proven possible and illus-
trated. To be able to show shape grammars to industry partners, the grammarians need to
implement them in working software prototypes that fully demonstrate their potentials and
their generative power. Besides the focus on pure computer implementations of shape gram-
mars, this special issue also called for contributions regarding real design scenario applications.
Several recent computer implementations use parametric design tools to generate design alter-
natives. Nevertheless, most of these implementations realize only a part of the potentials that
were originally attributed to shape grammars, thereby leaving some important features as
emergence, interactivity, and ambiguity behind in favor of other features. Considering this
myriad of implementation approaches, computer-implemented
shape grammar interpreters might be usable for diverse applica-
tion scenarios, ranging from shape grammars for personalized
customization for mass-housing to flexible, on-the-spot design
grammars that are able to evolve with the design process of the
With the above two main tracks (computer implementations
and real-world use cases), this special issue aims at: (1) addressing
current shape grammar design computer tools and (2) discussing
future paths of implementations towards the real use case scenar-
ios. In the next subsections, we present a brief state-of-the-art
overview (the section “State of the art”), to be complemented
with the state-of-the-art review of the articles in this special
issue. In the section “Advances in implemented shape grammars”,
we present a short summary of the articles that are included in the
current special issue, after which we give a comprehensive outlook
into the future in the section “An outlook”.
State of the art
Shape grammars applications have been developed for over 40
years addressing several areas of design, most particularly archi-
tectural design, engineering, and product design. Significantly,
several shape grammars implementations developed over the
last 10 years have managed to successfully integrate early pioneer-
ing work on shape representation and computation and begin to
explore emerging applied technologies, including parametric
design tools, generative design tools, procedural modeling tools,
information modeling applications, and rule-based design sys-
tems. These recent applications offer extensive support for
Euclidean and parametric rules, visual definition of rules, interac-
tive rule application including manual, semi-automatic, and auto-
matic modes, and address issues of interoperability between shape
grammar interpreters and state-of-the-art modeling tools.
Parallel to these advances, several classifications have been pro-
posed over the last 15 years to classify shape grammar applica-
tions: some concentrate on the tasks for programs that
implement shape grammars, for example, generation, parsing,
and inference tasks and their interactions with CAD modelers
(Gips, 1999). Others focus on technical and/or expressive charac-
teristics of interpreters, including underlying computing lan-
guage, subshape recognition, the dimensionality of shapes, etc.
(Chau, 2002). Others focus on usage in design, including general
interpreters versus specific domain applications; schematic design
versus design development; industrial strength interpreters versus
proof-of-concept applications, etc. (Chase, 2010; McKay et al.,
2012); and others focus on the systematization of concepts
Our approach builds upon all these trajectories and generously
recasts them in two distinct approaches to reflect upon the
current-state-of-the-art as well as speculate on the design of
new shape grammar applications: the first one privileges the
design of software that allows the visual querying of a design in
any conceivable way. The second privileges the design of software
that allows the specification of visual rules in any conceivable way.
Both approaches complement each other and both address the
core of the shape grammar formalism: the dynamic play between
seeing and doing and the need to accommodate both in a seam-
less manner in design. Note that these two approaches are related
to the classic distinction in the shape grammar discourse between
general interpreters and specific design domain applications, but
not entirely. For example, existing general interpreters may not
support emergence at all, or they may support some types of
emergence, say, for example, identification of polygons, stars,
and so on, but not all possible shapes and spatial relations; and
existing specific design domain applications may support visual
specification of rules or not while they may not support any
emergence none so ever. Still the initial distinction between gen-
eral interpreters and specific domain interpreters is useful, and is
used below in Table 1 to rework the evolving shape grammar soft-
ware list in the bibliography currently given in a variety of sources
(see, e.g., Gips, 1999; Chau et al., 2004; Kunkhet, 2011; McKay
et al., 2012).
Advances in implemented shape grammars
In this section, we give a brief summary of the diverse papers that
are included in this special issue. The papers chosen for this vol-
ume reflect current research and concerns within the shape gram-
mar research community on two main topics: (i) technical
advancements and (ii) practical implementations both concerning
interface and/or real-life design scenarios. Hence, we have divided
the accepted papers into a number of categories, namely: (i) tech-
nical design, (ii) interpreters and interface design, and (iii) use
On the first topic, technical design, five articles have been
included. The selected papers in this category are highly technical
in nature and delve into very specific advances that can be made
on the purely technical level. They include existing software
implementations, yet advance beyond the current state of the
art by giving a detailed impression of the strengths and weak-
nesses of the available systems, and making suggestions for future
development opportunities at the heart of technology.
The paper by Wortmann and Stouffs discusses the algorithmic
complexity of shape grammar implementations and categorizes
existing implementations by their algorithmic complexity.
Instead of just discussing subshape detection and emergence as
the way to discuss algorithm complexity, the authors consider
complexity in terms of the number of potential target shapes
(or possibilities for rule application). More specifically, the
authors describe how different sets of transformations (isometries,
similarities, affinities, and so on) admit a number of potential
possibilities for rule application in both shape grammars
and parametric shape grammars and how important this is to
secure design freedom. In the end, the authors propose new
matching algorithms for non-parametric and parametric shape
grammar implementations along with an analysis of their
Chau, Mckay, Earl, Behera, and Pennington provide a robust
framework for a general shape grammar interpreter that brings
together various theoretical inquiries that have remained so far
somewhat independent. The key idea of the work to use lattices
to transform rapidly and on-the-fly a given shape grammar to a
set grammar that can be computed by a machine before it reverts
back to a shape grammar representation. The results are very con-
vincing: the structure of the design depends on the rules that are
used to structure it; the emergent parts of the design (temporal
atoms) are all represented as nodes in a lattice and are all com-
puted efficiently; all rule matchings and resulting applications
are readily visualized; and as if all these are not enough, the com-
putations are all using curves in two-dimensional (2D) and 3D
132 Sara Eloy et al.
space (along with straight lines too) and both under a similar rep-
resentation so that a straight line can be represented as a degen-
erate Bezier curve. The work is nicely presented within a useful
overview of current shape grammar interpreters and its contribu-
tion is discussed within a more critical overview of visual ambigu-
ity in creative design.
The paper by Stouffs aims at the implementation of a generic
shape grammar implementation, similar to the aim pronounced
by Chau et al. Stouffs indicates how algebras of shapes have
been defined for elements of different kinds, as well as for shapes
augmented with varying attributes. Grammar forms could hence
potentially be expressed in terms of a direct product of basic
algebras. Stouffs extends this algebraic approach in this paper:
he derives combinations of basic shape algebras with attribute
algebras. This algebraic abstraction at the same time serves as a
procedural abstraction, giving insights into the modular imple-
mentation of a general shape grammar interpreter for different
grammar forms. In addition, Stouffs considers practical limita-
tions on algebraic compositions of basic shape algebras with
The paper by Whiting, Cagan and Leduc discusses the possi-
bility of efficiently generating grammars in design and analysis
from arbitrary sets of data. Indeed, the authors point to the lack
of automated ways to induce grammars from arbitrary structured
datasets. They argue that machine translation methods can allow
inducing grammars from coded data. Their proposed process for
Efficient Probabilistic Grammar Induction for Design includes
Table 1. List of existing general shape grammar interpreters and purpose-built
design shape grammar applications
General interpreters References
shape grammar interpreter (SGI) Krishnamurti (1982)
Shape generation system Krishnamurti and Giraud (1986)
SG interpreter Chase (1989)
GRAIL Krishnamurti (1992)
Shape grammar system Stouffs (1994)
GEdit Tapia (1999)
Shape grammar editor Work by Shelden in 1996, cited
by Gips (1999)
GraphSynth Anon (n.d.)
U13 shape grammar
Chau et al. (2004)
SGI for rectilinear forms Trescak et al. (2009)
Parametric SG interpreter Yue et al. (2009)
SG development system Li et al. (2009)
Subshape Detector and SD2 Jowers et al. (2010)
Grape: U12 and U13 SG interpreters Grasl and Economou (2013)
Shape grammar implementation Strobbe et al. (2013)
Grape: agent-based rule decision Grasl and Economou (2014)
Specific design domain interpreters References
Shepard–Metzler analysis Gips (1974)
Simple interpreter Gips (1975)
Palladio grammar Stiny and Mitchell (1978)
Queen Anne houses Flemming (1987)
Genesis Heisserman (1991)
Grammatica Carlson (1993)
Genesis (Boeing) Heisserman (1994)
Basic grammar Duarte and Simondetti (1997)
EifForm Shea (2000)
3D shape grammar Piazzalunga and Fitzhorn (1998)
SG-Clips Chien et al. (1998)
3D Shaper Wang (1998)
Coffee maker grammar Agarwal and Cagan (1996)
MEMS grammar Agarwal et al. (2000)
Shaper 2D McGill (2002)
Yingzao fashi grammar Li (2002)
Harley Davidson Pugliese and Cagan (2002)
Grammar use and interaction Chase (2002)
Buick McCormack and Cagan (2004)
Coca-Cola grammar Chau et al. (2004)
Cross-over vehicle grammar Orsborn et al. (2006)
Digital camera design parametric
Lee et al. (2012)
Malagueira Duarte (2005), Duarte and
Table 1. (Continued.)
General interpreters References
Shape designer Wong et al. (2005)
Marrakech Medina grammar Duarte et al. (2007)
Tibet Tangka grammar Zhang and Lin (2008)
Baltimore Row-house Aksamija et al. (2010)
QI curves Jowers (2006), Jowers and Earl
Design synthesis and shape
McKay et al. (2011)
Urban grammar for Praia Beirão et al. (2009)
Shape grammar and Tangible
Chen et al. (2009)
Humanoid grammar Fiedler and Ilčík (2009)
Shape Grammar Machining Planning Ertelt and Shea (2010)
Interactive 3D Spatial Grammar
Hoisl and Shea (2011)
Grappa Grasl (2012)
Thonet chair grammar Barros et al. (2011)
SG parsing via reinforcement
Teboul et al. (2011)
Rabo-de-Bacalhau grammar Eloy and Duarte (2015), Strobbe
et al. (2016)
Entelechy grammar Ligler and Economou (2015)
Dirksen grammar Park and Economou (2015)
Multipurpose chair grammar Garcia and Romão (2015)
Artificial Intelligence for Engineering Design, Analysis and Manufacturing 133
four steps: (1) extracting objects from the data; (2) forming struc-
tures from the object; (3) expanding structures into rules based on
frequency; and (4) finding rule similarities that lead to consolida-
tion or abstraction. To evaluate this method, grammars are
induced from generated data, architectural layouts and 3D design
models of Andrea Palladio’s Villa Foscari, La Malcontenta. This
evaluation demonstrates that this method is capable of automati-
cally offering usable grammars which are functionally similar to
grammars produced by hand.
Zimmermann, Chen, and Shea discuss the adoption of spatial
grammars in engineering applications by providing a method that
enables the automated link between the designs generated by the
spatial grammar [developed in spapper (Hoisl & Shea, 2011)] and
their evaluation through finite-element analysis. The authors pro-
pose a framework that combines a 3D spatial grammar interpreter
with automated finite-element analysis and stochastic optimiza-
tion using simulated annealing and tests it in the automated
design and optimization of spokes for inline skate wheels. The
results presented verify that the framework can generate structu-
rally optimized designs within the style and additive manufactur-
ing constraints defined in the spatial grammar, and produce a set
of topologically diverse, yet valid design solutions.
Interpreters and interface design
On the topic of interpreters and interface design, two key contri-
butions have been included. They both document existing soft-
ware implementations of shape grammars, including their
newest features and technological advances. Both articles focus
on the connection with the end user, giving an idea of what
sort of features can be made available to an end user.
Li reports the implementation of a grammar editor using
Rhinoceros3D and Python, and a stand-alone general interpreter
that supports subshape detection. The grammar can be modified
directly in Rhinoceros3D and exported to the interpreter, and a
derivation file can be exported back from the interpreter to
Rhino. Users have an intuitive way of using the system being
shielded from most of the subdomain tasks. This shape grammar
implementation has been developed from the earlier work by
Chau et al. (2004) through the inclusion of a graphical interface
to shapes and rules. The current implementation also evolves
from the stand-alone interpreter report in Li et al. (2009). Li
reports as well the good feedback of participants during several
classes and workshops where he tested the implementation
under design scenarios.
Grasl and Economou describe the structure of a generic para-
metric shape grammar interpreter named GRAPE. The inter-
preter is based on graph grammars and supports emergence,
parametric rules, and several types of geometric objects. The
shape grammar engine is an agent-based rule selection system
designed to be independent of other packages and platforms.
Several plugins for commercial CAD packages, such as Rhino,
AutoCAD and Revit, and one web application have been created.
Users may create rules by directly using the GrGen.NET graph
grammar rule modeling language or via the visual editor imple-
mented in the web interface. This paper evolves from a previous
article by the authors, namely Grasl & Economou (2013), by dis-
cussing the graph model, the visual rule editor, incorporating
additional geometries (curvilinear and 3D), and introducing
rule selection agents. A number of designs developed in struc-
tured workshops starting from existing grammars or from scratch
show telling results and the potential of the interpreter too.
Finally, we included two use case contributions which document
applications of shape grammars in product design and urban
design. These articles indicate how computer implementations
of shape grammar system can be used in practice and where
some of the key difficulties lie in building a wide end-user base.
Both papers present practical implementations close to real-life
design scenarios. They discuss the technological advances of the
documented systems in close relation with advances in design
and decision support tools, including parametric design tools,
generative design tools, optimization algorithms and approaches,
and semantics-based applications.
The problem addressed by Beirão and Duarte in their paper is
the development of generic grammars that, instead of generating
designs specific from one design language may encode design prin-
ciples that are general and common to a large group of designs. A
generic urban grammar is then presented which was inferred from
specific urban grammars that resulted from the analysis of different
corpi in the same design domain. To implement the grammar
authors converted the shape grammar into a parametric design
model and implemented it using Rhinoceros and Grasshopper to
facilitate computer implementation. According to the authors,
parametric design interfaces are more suitable for designers than
state-of-the-art shape grammar’s interpreters and represent better
visual stimuli. Nevertheless, with the adoption of such process
emergence is not supported. Such a design system can be used
by designers that starting from existing elements in the urban
area, references, may create an urban design solution step by step.
The second case contribution is by Garcia and Leitão that pre-
sent a multipurpose chair grammar and its implementation in the
design tool ChairDNA. The aim of this research is the development
of a parametric set grammar design tool that allows the generation
and exploration of chair design alternatives. Such a system could be
used during the conceptual stages of chair design to help designers
explore design alternatives that simultaneously are unexpected solu-
tions and comply with the chair design’s restrictions. In order to
help designers non-familiar to shape grammars to use the interface
authors opted to translate the set grammar into graphical user
interface elements that are presented to users and control rule appli-
cation and the derivation process. In this sense, the grammar is cast
primarily as a schema whereas the designers pass numerical values
to variables and sets of variables to instantiate a model based on
these numbers. The authors provide an evaluation of ChairDNA
done by design students and design practitioners. In this evaluation,
designers assessed several criteria related to usability and others
related to the usefulness of ChairDNA as a design tool. The results
appear to be positive and useful providing insights on how to
improve the tool and integrate it into daily life design practice.
This special issue contributes to the debate on how shape gram-
mars are finding their way into the design process and will, as
such, extend beyond the current state of the art. A question raised
in the call concerns with what more can be done in shape gram-
mars’implementation to make them useful to a real-life design
scenario. Another issue raised relates to the path being followed
by current research and its focus aiming both at the design market
and at the academic challenge of innovation.
Future challenges highlighted both by authors and by current
literature cover four main topics: (i) the creation of new algorithms
134 Sara Eloy et al.
to expand the power of computer design generation, (ii) the inclu-
sion of evaluation strategies during the computer generation pro-
cess, (iii) the development of computer implementations that are
easy to use and adaptable to designers’knowledge and work pro-
cesses, (iv) and the development of specific and generic shape
grammars that can be used immediately in the design practice.
The need to create new algorithms, highlighted in this issue by
Wortmann and Stouffs, contributes to the expansion of
computer-automated design systems’generation power and there-
fore the possibilities to make a larger type of visual calculations
reachable. Further research is needed in order to extend the pre-
sented bounds and algorithms to higher dimensions and other
types of geometries.
Parallel to the generation capabilities of shape grammars,
design solutions need to be evaluated using several criteria. The
main aim is that the processes of evaluation can be conducted
during the generation process and not just at the end in such a
way that the generation process may only produce valid design
solutions. Zimmermann et al. bring an example of how this pro-
cess is helpful for structural optimization problems that require
manufacturing constraints, a variety of solutions, and the compli-
ance with a personal style.
Concerning the development of computer implementations,two
main lines of research exist. On one hand, authors aim at imple-
menting a general shape grammar interpreter that includes all
the shape grammar formalisms but does not have the concern of
generating designs with a programming purpose (as housing,
product design, etc.). On the other hand, there are authors that
sacrifice some shape grammar characteristics, as emergence, so
that a feasible computer-automated design system is developed.
The evolution of software is a common concern, also referred by
Li, and Grasl and Economou, since the now existing compatibility
between interpreters and design software may be lost in future
updates. Even though, the next steps will include the development
of interpreters inside commonly used CAD systems. This will lead
to a less formal way of using grammars and, as stated by Li, to a
more congenial one to designers. Simultaneously, the development
of shape grammar design tools that enable designers with few or no
programming or grammar knowledge to use the generative power
of such systems should also play a role in the current development.
The developments of specific and generic shape grammars that
can be immediately used in design processes will foster its use by
designers. Grammars that are applied to specific design problems
in for example, product design and architecture may have an
immediate use by designers if they respond to an existing prob-
lem. Also, the application of the concept of generic grammars
to several design domains by designers from different fields can
create specific styles, specific contexts, customizations, or any
combinations of these.
Acknowledgements. We would like to thank Yan Jin, the former Editor-
in-Chief of Artificial Intelligence for Engineering Design, Analysis and
Manufacturing (AIEDAM), for supporting the proposal and development of
this special issue, and Amaresh Chakrabarti, the journal’s current Editor-
in-Chief for his help in realizing it. We would also like to praise the authors
for their contributions and views and also the reviewers for making this
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136 Sara Eloy et al.
Sara Eloy is an Assistant Professor at Instituto Universitário de Lisboa
(ISCTE-IUL). Her main research interest is shape grammars and the
possibilities of using them in real design scenarios. Other areas of research
are CAAD, the use of immersive virtual and augmented Reality for the design
process, and the analysis of the building space namely considering space per-
ception and space syntax. She graduated in Architecture (FAUTL 1998) and
has a PhD in Architecture (IST UL 2012) where she investigated on a transfor-
mation grammar-based methodology for housing rehabilitation. She is the
Director of the Information Sciences and Technologies and Architecture
Research Center (ISTAR-IUL), and was the Director of the Department of
Architecture and Urbanism (DAU), and of the Integrated Master in
Architecture at ISCTE-IUL in Lisbon between 2013 and 2016.
Pieter Pauwels is an Assistant Professor at Ghent University, Department of
Architecture and Urban Planning. He holds Master (2008) and PhD degrees
(2012) in Engineering: Architecture from Ghent University. He teaches
Computer-Aided Design (CAD) and Building Information Modelling (BIM)
to architectural engineering students and industry professionals. His research
focuses on Building Information Modelling; Linked Building Data; ontologies
(ifcOWL); regulatory compliance checking; (semantic) web technologies;
information integration, exchange, and management. He actively chairs two
technical international community groups, namely the W3C Community
Group on Linked Building Data and the BuildingSMART Int’l Linked Data
Working Group (LDWG). In that context, he is actively involved in the defi-
nition and management of an ifcOWL ontology that can be used as a recom-
mended standard for capturing and publishing building data using the latest
Athanassios Economou is a Professor in the College of Design at Georgia
Institute of Technology. Dr Economou’s teaching and research are in the
areas of shape grammars, computational design, computer-aided design,
and design theory. He is the Director of the Shape Computation
Laboratory, a research group that explores how the visual nature of shape
can be formally implemented with new software technologies to assist see-
ing and doing in design in new ways. Dr Economou holds a Diploma in
Architecture from NTUA, Athens, Greece, an MArch from USC, and a
PhD in Architecture from the University of California, Los Angeles
Artificial Intelligence for Engineering Design, Analysis and Manufacturing 137