Abstract
AbstractThe 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.
Highlights
Shape grammars have been used successfully to explore design spaces in various design contexts (Strobbe et al, 2015)
This paper provides a mechanism where lattices are used to reduce this complexity by decoupling computational geometry and shape computation
The approach proposed in this paper explores the potential of lattice structures to decouple steps in a shape computation from the geometrical operations associated with specific grammars
Summary
Shape grammars have been used successfully to explore design spaces in various design contexts (Strobbe et al, 2015) They are used to both analyze existing styles and generate new designs. This paper provides a mechanism where lattices are used to reduce this complexity by decoupling computational geometry (needed for the geometrical operations associated with specific grammars used in the generation of new shapes) and shape computation (needed for sub-shape detection and the application of rules). Five shape grammar implementations that support shape emergence are considered here (Table 1). They were selected because technical details on their use of basic elements and how they support shape emergence are readily available in the literature. The other two (Li et al, 2009; Jowers & Earl, 2010) use circular arcs and curves, respectively, with the latter using parametric Bézier curves or their variations to describe curves.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
