Chau, HH orcid.org/0000-0003-2140-2415, McKay, A orcid.org/0000-0002-8187-4759, Earl, CF et al. (2 more authors) (2018) Exploiting lattice structures in shape grammar implementations. AI EDAM, 32 (S2). pp. 147-161. ISSN 0890-0604
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) Cambridge University Press 2018. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Ambiguity; Bill of Materials (BOM) Structures; Complemented Distributive Lattice; Design Descriptions; Maximal Representation; Set Grammars; Shape Emergence |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Systems and Design (iESD) (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/N005694/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Jul 2017 10:39 |
Last Modified: | 23 Jun 2023 22:32 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/S0890060417000282 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:118705 |
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