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Exploiting lattice structures in shape grammar implementations

Chau, Hau Hing; McKay, Alison; Earl, Christopher F.; Behera, Amar Kumar and de Pennington, Alan (2018). Exploiting lattice structures in shape grammar implementations. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 32(2) pp. 147–161.

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The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible.

Item Type: Journal Item
Copyright Holders: 2018 Cambridge University Press
ISSN: 1469-1760
Project Funding Details:
Funded Project NameProject IDFunding Body
Embedding design structures in engineering informationEP/N005694/1EPSRC
Keywords: Ambiguity; bill of materials (BOM) structures; complemented distributive lattice; design descriptions; maximal representation; set grammars; shape emergence
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Engineering and Innovation
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Research Group: Design and Innovation
Item ID: 55543
Depositing User: Christopher Earl
Date Deposited: 20 Jun 2018 15:15
Last Modified: 10 May 2019 09:47
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