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This paper proposes a design for libraries of European Classical architectural elements based on shape grammars. This design is based on a workflow which develops library objects from 3D CAD primitives using architectural rules to construct parametric representations of architectural elements. In the case of Classical architecture, the design and detail for the parametric objects are based on manuscripts ranging from Vitruvius to Palladio to the architectural pattern books of the eighteenth century. The generation of 3D objects for virtual reconstruction necessitates the application of computer algorithms and rules introduced by the user to generate objects, buildings and spaces from a grammar and vocabulary of shapes. Both the use of graphicly constructed and coded parametric libraries in formal and open-source platforms will be considered here.

Shape queries based on shape embedding under a given Euclidean, affine, or linear transformation are absent from current CAD systems. The only systems that have attempted to implement shape embedding are the shape grammar interpreters albeit with promising but inconclusive results. The work here identifies all possible 14 cases of shape embedding with respect to the number of available registration points, four for determinate cases and ten for indeterminate ones, and an approach is sketched to take on the complexities underlying the indeterminate cases. All visual calculations are done with shapes consisting of straight lines in the Euclidean plane within the algebra Uij for i = 1 the dimension of lines and j = 2 the dimension of space in which the lines are defined, transformed and combined. Aspects of interface design and integration to current work design workflows are deliberately left aside.

With the development of information technology, the introduction of information technology into architectural modelling and façade design and the systematic definition of historic districts is a problem that the architectural industry continues to explore and pursue. As a shape-based and self-defining generation rule, shape grammar provides significant help in the process of the automatic generation of architectural shapes to obtain design results that meet the requirements of the original historic district. Based on the simple combination of the application of shape grammar in architectural design, combined with the field investigation method, the representative buildings in the “Three Lanes and Seven Alleys” historic district are investigated and understood in detail, and the corresponding shape grammar rules are established. The courtyard types of the historic district are divided into: “” shape, “T” shape, “=” shape, “” shape, “” shape, “” shape, “” shape, “U” shape, “” shape, and garden. In detail, the façade components include the entrance, patio, main seat, wings, cloister, pavilion, etc. The elements of its façade include saddle walls, grey sculptures, carved stones, grey tiles, wooden grilles, wooden railings, wood grain flowers, etc. On this basis, parametric design is introduced to convert the design syntax into parametric programs. Grasshopper in Rhino is mainly used to visualize and simulate the regulation, and finally, achieve the purpose of automatically generating the architectural shape and façade of the “Three Alleys and Seven Alleys” historic district by adjusting its parameters.

This study investigates patterns in the chaotic appearance of self-help incremental housing in a kampung settlement. Many previous studies have investigated suitable incremental housing for low-income residents, but the pattern of self-help incremental housing has not been carefully investigated. The shape grammar method is used to identify the delivered pattern of self-help incremental housing, and in-depth interviews are performed to clarify the reasons for the pattern found. This study finds that the organized chaotic pattern of self-help incremental housing depends on geographical location and familial relationships, which allow construction over the perimeter of a land parcel through negotiation to reach agreement between homeowners and neighbors. Further, self-help incremental housing is driven by external and internal factors, such as the lack of affordability in the housing market, the mismatch of available job opportunities with the credentials and competencies, and the practiced social relationships among kin or relatives, which demand the expansion of the size of the residence to allow sufficient meeting space and privacy for the core and extended family members.

Rapid urbanization in the Global South continues to intensify the growth of informal settlements, challenging architectural education to equip students with methods capable of addressing complex socio-spatial, environmental, and ethical conditions. While computational design and service-learning have each been explored within architectural pedagogy, their systematic integration, particularly in the context of informal settlement planning, remains underdeveloped. This article presents a pedagogical framework that combines pattern language theory, shape grammars, and parametric modeling with service-learning principles within an undergraduate architectural design studio. Implemented in ARC 4025 (Architecture Studio 5) at the O’More College of Architecture and Design, Belmont University, the framework guides students in translating empirical observations of an informal settlement in Ahmedabad, India, into rule-based and generative design systems. The methodology emphasizes process–product reciprocity, enabling students to encode settlement patterns as transformation rules that generate, test, and evaluate coherent urban forms across multiple scales. A detailed case study, Community at Scale, is presented as a proof of method, illustrating how analysis is converted into computational logic across dwelling, block, and neighborhood scales. Rather than proposing a finalized solution, the study demonstrates how computational design can operationalize morphogenetic reasoning within architectural education while remaining grounded in social responsibility. The article concludes by discussing pedagogical implications, situating the approach within urban morphology discourse, and outlining limitations and directions for future research.

Information technologies are a driving force for progress in the design field, allowing new modes of creativity. However, most of the existing computational design tools are focused on the latest stages of the design process and especially directed to drafting operations. Conceptual design tools that support the designer in the creative and inventive early stages of the design project are still in their early development. Shape grammars (SG) were introduced by George Stiny in the 1970s, allowing the generation of designs according to a set of predefined rules. SG computational implementations have the potential to answer the need for tools that can assist designers, architects, and artists in the creative process, offering design alternatives, stimulating new ideas and encouraging the search for new design generation processes. Acknowledging this potential, a user-friendly interface seems essential for the adoption of these tools. Taking Scott Chase's interaction model as background, the aim of the present investigation is to define guidelines and begin to design a graphical-user interface for SG implementations. Inspection methods of human–computer interaction (HCI) were used to analyze existing SG implementations and understand usability issues. Subsequently, HCI ergonomic criteria for interface evaluation were adapted to establish guidelines for the design of an SG implementation interface, called IM-sqi. These guidelines take into account different user groups, adjustable interaction modes for each user group, and the nature of each task performed by the user.

Computer-based shape grammar implementations aim to support creative design exploration by automating rule-application. This paper reviews existing shape grammar implementations in terms of their algorithmic complexity, extends the definition of shape grammars with sets of transformations for rule application, categorizes (parametric and non-parametric) sets of transformations, and analyses these categories in terms of the resulting algorithmic complexity. Specifically, it describes how different sets of transformations admit different numbers of targets (i.e., potential inputs) for rule application. In the non-parametric case, this number is quadratic or cubic, while in the parametric case, it can be non-polynomial, depending on the size of the target shape. The analysis thus yields lower bounds for the algorithmic complexity of shape grammar implementations that hold independently of the employed algorithm or data structure. Based on these bounds, we propose novel matching algorithms for non-parametric and parametric shape grammar implementation and analyze their complexity. The results provide guidance for future, general-purpose shape grammar implementations for design exploration.

Computational design and shape grammars hold a growing appeal in the architectural curricula. This paper aims to assess shape grammars as a visual teaching method that integrates manual exploration based on “learning by doing” in early education curricula without digital software. As a primary outcome of a visual design course at the British university in Egypt, four self-structured pavilions are fabricated by first-year architecture students. Experimentation occurs through a process of visual computing which develops a deeper understanding of material qualities. A comparison of design parameters is conducted through hands-on experiments that include design principles, unit transformations, connection types, assembly process, and functional aspects. The paper examines the skills that students acquired during the course. This study concludes that by applying shape grammars in design studios, students are adequately prepared at the foundational level for their transition towards learning computational design.

Anne Tyng’s notion of metamorphology is introduced in relation to three of the architect’s residential space structures. The interpretation of this body of work is viewed through the lens of the octetruss to examine the evolution of Tyng’s design approach where the interplay between Platonic geometries and their transformations demonstrates exponential formal and functional opportunity. This analysis provides a foundation for a constructive theory on Tyng’s space structures. The theory is constructive in two directions. First, in that it defines a lattice of spatial relations and their transformations to reconceptualize the houses, and second, in that these same conceptualizations motivate a shape grammar that produces prototypes for space structures rooted in Tyng’s examples. Sample reconfigurations generated with the grammar are offered to support discussion on the value of a metamorphological design approach and how it recalibrates understanding of Tyng’s work to inspire ongoing reinvention.

The symmetry properties of John Portman’s 1968 Midnight Sun cocktail bar are discussed in detail. A special emphasis is given to subsymmetry analysis to decompose the multiple layers of symmetry groups in the polyrhythmic design and to relate them to a foundational project in Portman’s corpus, the 1964 house Entelechy I. This analysis informs a rule-based interpretation of the cocktail bar as a transformation of the hollow column prototype developed in Entelechy I. These findings are specified formally in the Midnight Sun grammar, a shape grammar implemented in a shape rewrite technology called Shape Machine. The implementation is then used to produce a series of variations featuring a range of symmetry groups. These outcomes and their implications for design generation as well as insights into Portman’s design principles are discussed to conclude the paper.