{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T21:58:27Z","timestamp":1747173507764,"version":"3.40.5"},"reference-count":56,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T00:00:00Z","timestamp":1644364800000},"content-version":"unspecified","delay-in-days":39,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["AIEDAM"],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:title>Abstract<\/jats:title>\n\t  <jats:p>Shape queries based on shape embedding under a given Euclidean, affine, or linear transformation are absent from current CAD systems. The only systems that have attempted to implement shape embedding are the shape grammar interpreters albeit with promising but inconclusive results. The work here identifies all possible 14 cases of shape embedding with respect to the number of available registration points, four for determinate cases and ten for indeterminate ones, and an approach is sketched to take on the complexities underlying the indeterminate cases. All visual calculations are done with shapes consisting of straight lines in the Euclidean plane within the algebra <jats:italic>U<\/jats:italic><jats:sub>\n\t      <jats:italic>ij<\/jats:italic>\n\t    <\/jats:sub> for <jats:italic>i<\/jats:italic> = 1 the dimension of lines and <jats:italic>j<\/jats:italic> = 2 the dimension of space in which the lines are defined, transformed and combined. Aspects of interface design and integration to current work design workflows are deliberately left aside.<\/jats:p>","DOI":"10.1017\/s0890060421000263","type":"journal-article","created":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T07:06:38Z","timestamp":1644390398000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["What shape grammars do that CAD should: the 14 cases of shape embedding"],"prefix":"10.1017","volume":"36","author":[{"given":"Tzu-Chieh Kurt","family":"Hong","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8406-0427","authenticated-orcid":false,"given":"Athanassios","family":"Economou","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,2,9]]},"reference":[{"key":"S0890060421000263_ref24","doi-asserted-by":"publisher","DOI":"10.1068\/b080005"},{"key":"S0890060421000263_ref54","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3702-3_4"},{"key":"S0890060421000263_ref5","doi-asserted-by":"publisher","DOI":"10.1115\/1.1577356"},{"key":"S0890060421000263_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511811685"},{"key":"S0890060421000263_ref29","doi-asserted-by":"publisher","DOI":"10.1068\/b240359"},{"volume-title":"Design Computing and Cognition \u201812","year":"2014","author":"Krstic","key":"S0890060421000263_ref30"},{"volume-title":"Interdisciplinary Systems Research","year":"1975","author":"Stiny","key":"S0890060421000263_ref38"},{"key":"S0890060421000263_ref49","first-page":"153","article-title":"Learning from users and their interaction with a dual-interface shape-grammar implementation","volume":"2","author":"Stouffs","year":"2020","journal-title":"Proceedings of the 25th International Conference on Computer-Aided Architectural Design Research in Asia, CAADRIA 2020"},{"key":"S0890060421000263_ref42","doi-asserted-by":"publisher","DOI":"10.1007\/BF01578998"},{"key":"S0890060421000263_ref35","first-page":"1","volume-title":"Formal Engineering Design Synthesis","author":"Mitchell","year":"2001"},{"key":"S0890060421000263_ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2018.12.004"},{"key":"S0890060421000263_ref4","doi-asserted-by":"publisher","DOI":"10.1006\/cviu.2000.0889"},{"key":"S0890060421000263_ref20","doi-asserted-by":"publisher","DOI":"10.1068\/b36162"},{"key":"S0890060421000263_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/S1359135502001410"},{"volume-title":"Projective Geometry","year":"2007","author":"Veblen","key":"S0890060421000263_ref53"},{"volume-title":"Introduction to Algorithms","year":"2009","author":"Cormen","key":"S0890060421000263_ref7"},{"key":"S0890060421000263_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2014.06.012"},{"key":"S0890060421000263_ref28","doi-asserted-by":"publisher","DOI":"10.1068\/b130391"},{"key":"S0890060421000263_ref27","doi-asserted-by":"publisher","DOI":"10.1068\/b190585"},{"key":"S0890060421000263_ref44","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/6201.001.0001"},{"volume-title":"SGI: a shape grammar interpreter","year":"1982","author":"Krishnamurti","key":"S0890060421000263_ref25"},{"key":"S0890060421000263_ref56","doi-asserted-by":"publisher","DOI":"10.1016\/j.destud.2017.05.001"},{"key":"S0890060421000263_ref1","doi-asserted-by":"publisher","DOI":"10.1080\/0025570X.1978.11976715"},{"key":"S0890060421000263_ref45","unstructured":"Stouffs, R (1994) The Algebra of Shapes (Ph.D. thesis). 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