Economou, A. (2025). Shape computation. Springer. [Forthcoming].
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Abstract:

The subject matter of the book is the presentation and an in-depth account of new trajectories in shape grammars, one of the most powerful approaches in the generation of designs. The purpose of the book is to foreground shape and shape computation as the key foundational characteristics of formal composition in design and creativity at large.

The book builds on top of the formidable discourse of shape grammars that for forty years now has been reshaping the foundations of design research and design computation but significantly extends it in three ways:
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a) it revisits the underlying computational description of shape in terms of carrier lines and maximal lines to provide the shape signature, a uniform characterization of shape that can be used to calculate and visually represent all possible shapes in parametric models;
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b) it sets the fundamental ideas of shape grammars in practice by trying them all out in the shape machine, a software environment designed from scratch to mechanically create and test the work in ways that have never been achieved in the past; and

c) it attempts to relate the computational approach to past practices, conventions and inquiries to essentially recast and rework trajectories of intellectual discourse in design inquiry.

‍Table of contents:
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1. Introduction
On design and visual representation. Brief overview of shape grammars; history and logic of their computational foundations and formal relations to other generative and parametric approaches in analysis and synthesis in design. Broader relations to visual art and mathematics.

2. Shape signatureThe theoretical framework of the shape grammar formalism and the maximal element representation of shape is connected with foundational work in group theory and combinatorics and especially the Burnside’s Lemma and Polya’s theorem to provide a new way to uniquely describe shapes and its emergent parts. The notion of carrier lines and maximal lines in introduced to facilitate the enumeration of all non-equivalent arrangements of maximal lines that make up shapes. The numbers of shapes made up of i maximal lines for j carrier lines and i ³ j is given for up to i, j = 6. The visual enumeration of shapes made up of 3maximal lines for up to 3carrier lines is given too and for specific classes of shapes consisting of 4 maximal lines.

3. From shape rules to rule schemata and backShape rules and rule schemata are introduced as the two key foundational mechanisms in analysis and synthesis in design. Both are compared in terms of their expressive and productive features in design inquiry. The first proceeds from shape rule instances and infers rule schemata that the shape rules can be defined in. The second proceeds from rule schemata and postulates shape rule instances that can be defined within the schemata. These two parallel processes mirror our intuition in design: the conceptual need to frame explicit actions within general frameworks of principles, and the productive need to supply general principles with an explicit system of actions. A rich series of visual examples show structured experiments between shape rules and rule schemata and the ways they inform one another.

4. Shape machineThe computational puzzle of subshape recognition is taken on and the current state-of-the-art in the field is briefly discussed and contrasted. The shape machine, a new computational framework to allow the seamless visual computations designers intuitively do, is introduced. A generous set of visual examples showcase the power of the shape machine to decompose shapes in terms of shapes defined ad hoc during the design process. The series starts from the query of well-defined polygons including triangles, quadrilaterals, pentagons and so on, and extend to open-ended polylines and intersecting arrangements of polylines, to spatial relations of polygons to polygons and to polylines, and so on. All rule applications are demonstrated under identity, isometry, similarity, affinity, linearity and topology transformations. Simple substitution rules exemplify the powerful computational mechanism to produce new designs following specific rule sequences or on a user-interactive manner. A parametric version of shape machine is introduced to provide definitions and applications of parametric shape rules.

5. Paperless computationsA workshop in formal composition using machine-based specifications of parametric shape rules is presented. The workshop is structured along two different trajectories: one starting from existing grammars and one starting from scratch, and both in a rising complexity in the specification of the rules and the ways they affect design. Rules, productions and designs in corresponding languages illustrate the findings. The speculation on a new design workflow whereas the designers seamlessly design and test their rules within their design processes is discussed as well.

6. A new synthesis: Vitruvius ComputatusThe computational apparatus discussed in the book is discussed and contrasted within current epistemological discourse in design. The emergent tripartite scheme of design, including algebras of design, design rules and criticism rules, is reiterated. It is suggested that this scheme provides a new light to the oldest surviving discourse in architectural design, the Ten Books on Architecture by Vitruvius and more specifically to the six principles of design, one of the most opaque and unwieldy topics in the Vitruvian lore. It is suggested here that the scheme can cast a whole new light to the esoteric nature of the six principles of design, relate them coherently to the three Vitruvian prerequisites of design, and more significantly, propose an intellectual thread of architectural theory and discourse that can remain useful throughout the ever-changing nature of architectural program, new technologies and aesthetic concerns.

Eloy S., Pauwels P. and Economou, A. “Advances in Implemented Shape Grammars: Solutions and Applications”, Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AIEDAM), 32(2), 2018.
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Abstract:

This special issue frames the topic of computer implementations of shape grammars, both with a theoretical and an applied focus. The starting point of the volume is the current state-of-the-art of the field of 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. The volume includes contributions that document existing software implementations of shape grammars (shape grammar interpreters) including their newest features and technological advances; in depth technical discussions of various software implementations with detailed accounts of the strengths and weaknesses of the available systems; and critical accounts of technological advances of shape grammar interpreters in relation with other technological advances in design and decision support tools, including parametric design tools, generative design tools, genetic algorithms, optimization algorithms, procedural modelling and semantics based applications.

‍Table of contents:

‍Sara Eloy, Pieter Pauwels, Athanassios Economou. Advances in Implemented Shape Grammars: Solutions and Applications. pp. 131-137

Thomas Wortmann, Rudi Stouffs. Algorithmic Complexity of Shape Grammar Implementation. pp. 138-146

Hau Hing Chau, Alison McKay, Christopher F. Earl, Amar Kumar Behera, Alan de Pennington. Exploiting Lattice Structures in Shape Grammar Implementations, pp. 147-161

Rudi Stouffs. Implementation Issues of Parallel Shape Grammars. pp. 162-176

Mark E. Whiting, Jonathan Cagan, Philip LeDuc. Efficient Probabilistic Grammar Induction for Design. pp. 177-188

Luca Zimmermann, Tian Chen, Kristina Shea. A 3D Performance-Driven Generative Design Framework: Automating the Link from a 3D Spatial Grammar Interpreter to Structural Finite Element Analysis and Stochastic Optimization. pp. 189-199

Andrew I-kang Li. A Whole-Grammar Implementation of Shape Grammars for Designers. pp. 200-207

Thomas Grasl, Athanassios Economou. From Shapes to Topologies and Back: An Introduction to a General Parametric Shape Grammar Interpreter. pp. 208-224

José Beirão, José P. Duarte. Generic Grammars for Design Domains. pp. 225-239

Sara Garcia, António Menezes Leitão. Shape Grammars as Design Tools: An Implementation of a Multipurpose Chair Grammar. pp. 240-255