2022
DOI: 10.1017/s0890060421000263
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What shape grammars do that CAD should: the 14 cases of shape embedding

Abstract: 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 com… Show more

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Cited by 6 publications
(2 citation statements)
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“…Among them, the Shape Machine has managed to successfully resolve the challenges underlying shape embedding in the algebra Uitalic12 for straight lines and arcs and labeled straight lines and arcs in the algebra Vitalic12, effectively reworking the geometrical representations underlying the CAD representations of lines and arcs and introducing a reworking of the dual representation of the maximal elements and their underlying hyperplanes. 40 The application already boasts a rising number of successful computer implementation of shape grammar applications. 41 And yet, much more work is needed to see whether indeed the shape grammar implementations can find their way into the toolkit of most practicing architects.…”
Section: Literature Reviewmentioning
confidence: 99%
“…Among them, the Shape Machine has managed to successfully resolve the challenges underlying shape embedding in the algebra Uitalic12 for straight lines and arcs and labeled straight lines and arcs in the algebra Vitalic12, effectively reworking the geometrical representations underlying the CAD representations of lines and arcs and introducing a reworking of the dual representation of the maximal elements and their underlying hyperplanes. 40 The application already boasts a rising number of successful computer implementation of shape grammar applications. 41 And yet, much more work is needed to see whether indeed the shape grammar implementations can find their way into the toolkit of most practicing architects.…”
Section: Literature Reviewmentioning
confidence: 99%
“…In the design process, CAD is extensively employed by designers to inspire and innovate their designs (Camba et al , 2014). The use of CAD appears to provide significant benefits during the idea-generation process (Veisz et al , 2012; Hong and Economou, 2022), while it is also widely used to refine creative concepts at a later stage of the design process (Wang et al , 2021). CAD is mainly based on 2D screens, such as desktops or mobile devices, which allow designers to manipulate virtual objects in real-time.…”
Section: Introductionmentioning
confidence: 99%