{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:55:52Z","timestamp":1761490552953,"version":"3.37.3"},"reference-count":43,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2018,5,9]],"date-time":"2018-05-09T00:00:00Z","timestamp":1525824000000},"content-version":"unspecified","delay-in-days":8,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AIEDAM"],"published-print":{"date-parts":[[2018,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 B\u00e9zier 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 B\u00e9zier 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.<\/jats:p>","DOI":"10.1017\/s0890060417000282","type":"journal-article","created":{"date-parts":[[2018,5,9]],"date-time":"2018-05-09T07:35:59Z","timestamp":1525851359000},"page":"147-161","source":"Crossref","is-referenced-by-count":3,"title":["Exploiting lattice structures in shape grammar implementations"],"prefix":"10.1017","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2140-2415","authenticated-orcid":false,"given":"Hau Hing","family":"Chau","sequence":"first","affiliation":[]},{"given":"Alison","family":"McKay","sequence":"additional","affiliation":[]},{"given":"Christopher F.","family":"Earl","sequence":"additional","affiliation":[]},{"given":"Amar Kumar","family":"Behera","sequence":"additional","affiliation":[]},{"given":"Alan","family":"de Pennington","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,5,9]]},"reference":[{"volume-title":"Graphs and Hypergraphs","year":"1973","author":"Berge","key":"S0890060417000282_ref2"},{"unstructured":"Ben Yahia S and Konecny J (eds) (2015) The Twelfth International Conference on Concept Lattices and Their Applications (CLA 2015), Clermont-Ferrand, France, 13\u201316 October 2015.","key":"S0890060417000282_ref1"},{"doi-asserted-by":"publisher","key":"S0890060417000282_ref25","DOI":"10.1068\/b230133"},{"volume-title":"Remarks on the Foundations of Mathematics","year":"1956","author":"Wittgenstein","key":"S0890060417000282_ref40"},{"doi-asserted-by":"crossref","unstructured":"2. 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