A Paradigm for Interpreting Tractable Shape Grammars

Abstract

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.

Developing a tractable shape grammar

“…The sub-frameworks (Yue and Krishnamurti, 2014) offer a way of ensuring tractability of the grammar. As with any traditional shape grammar the focus here is on generating all possible designs without necessarily fully specifying all conditions under which shape rules apply.…”

“…The encoded new tractable shape grammar is based on the rectangular framework (Yue and Krishnamurti, 2014) and comprises five phases: block generation: rules (1∼4); space generation: rules (5∼10); stair generation: rules (11∼16); space modification: rules (17∼20); and interior door generation: rules (21∼26). We describe the rule encodings for each phase.…”

“…Grammars exhibit a variety of characteristics thereby rendering impossible a single uniform shape grammar interpreter. Instead, a strategy for implementing tractable shape grammars has been advocated, in which the grammar is specified within a specific representational framework (Yue and Krishnamurti, 2014).…”

“…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.…”

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AbstractPreviously, 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.

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