Modelling Shape Languages with Type Constraint Systems (original) (raw)
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Shapes, structures and shape grammar implementation
Computer-Aided Design
Shape grammars are a generative formalism in which dynamic changes to shape structure plays a vital role. Such changes support ambiguity and emergence, and as a result shape grammars are often used as the basis for proposed developments in supporting shape exploration in computeraided design. However, the general implementation of shape grammars remains an unsolved problem, and a common solution is to adopt a fixed structure. This paper explores the consequences of assuming a fixed shape structure, via analysis of a simple shape grammar, often used as a benchmark problem to illustrate advances in shape grammar implementation. With reference to the combinatorics of words, it is proved that adopting a finite fixed structure limits the capability of a shape grammar. The paper concludes with a discussion exploring the implications of this result for shape grammar implementation and for design descriptions in CAD.
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 current state of the art regarding computer implementations of shape grammars and brings a discussion 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 implementation 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.
Developing a tractable shape grammar
Environment and Planning B: Planning and Design, 2015
Previously, we examined tractable parametric shape grammars (Yue and Krishnamurti, 2013), and developed a general paradigm for implementing classes of such grammars (Yue and Krishnamurti, 2014). A tractable shape grammar has polynomial computing complexity, and is specified in a way that is readily transformable to a computer program. By contrast, traditionally, shape grammars have been typically developed without a computer implementation in mind, either requiring ambiguity to be clarified, or it is hardly possible for the grammar to be implemented by a polynomial algorithm. Each tractable shape grammar is tied to a particular framework, which is backed by a data structure and supports a metalanguage. In this paper, we illustrate the development of tractable shape grammars by transforming a shape grammar developed, essentially, in traditional fashion for the Baltimore Rowhouse (Hayward 1981; Hayward and Belfoure, 2005). The development is for a specific application context, namely, to determine the interior layout of a building given its external features; and the process serves as a general strategy for developing tractable shape grammars.
Computer Implementation of Shape Grammars
Just as there are symbolic thinkers, people who think mainly in terms of letters and numbers and other symbols, and visual thinkers, people who think primarily in terms of shapes and colors and spatial relationships, there can be symbolic computations and visual computations.
Environment and Planning B: Planning and Design, 2013
This paper explores the theoretical basis for a concept of "computation-friendly" shape grammars, through a formal examination of tractability of the grammar formalism.
A paradigm for interpreting tractable shape grammars
Environment and Planning B: Planning and Design, 2014
Shape grammars are, in general, intractable. Even amongst tractable shape grammars, their characteristics vary significantly. This paper describes a paradigm for practical general shape grammar interpreters, which aim to address computational difficulties posed by parameterization. The paradigm is expressed in terms of frameworks each comprising an underlying data structure, manipulation algorithms and a metalanguage. The approach is illustrated through three exemplar frameworks.
Computation-friendly shape grammars
2018
NP-hardness of parametric subshape recognition for an arbitrary number of open terms is proven. Guided by this understanding of the complexity of subshape recognition, a framework for computation-friendly parametric shape grammar interpreters is proposed, which is further detailed by a sub-framework over parametric two-dimensional rectangular shapes. As both the proof of NP-hardness and rectangular sub-framework invoke elements in graph theory, the relationship between shape and graph grammars is also explored.
An Algebraic Approach to Implementing a Shape Grammar Interpreter
eCAADe proceedings, 2016
Shape grammars come in a variety of forms. Algebras of shapes have been defined for spatial elements of different kinds, as well as for shapes augmented with varying attributes, allowing for grammar forms to be expressed in terms of a direct product of basic algebras. This algebraic approach is extended here to the algebraic derivation of 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 implementation of a general shape grammar interpreter for different grammar forms.