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Abstract Shapes are considered as finite arrangements of spatial elements from among points, line and plane segments, circles and ellipses, (circular) arcs, quadratic Bezier curves, of limited but non-zero measure, in 2D and 3D. Augmented shapes are defined as shapes augmented with attributes, e.g., labels, weights, colors, enumerative values, and (parametric) descriptions. Different attribute types specify different behaviors under operations of sum, product and difference and a part relationship. We review different shape–attribute propositions from the shape grammar literature and characterize them uniformly. This uniform characterization of augmented shapes is intended to assist in formalizing new shape–attribute propositions that may have been visually conceived. Highlights • A uniform characterization of different shape-attribute propositions is presented. • A uniform description of the behavior of shapes with attributes is proposed. • Characterizations of attribute types and spatial element types are almost uniform. [ABSTRACT FROM AUTHOR]

Previously, we examined tractable parametric shape grammars and developed a general paradigm for implementing classes of such grammars. 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. The development is for a specific application context— 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]