Exploiting lattice structures in shape grammar implementations

Hau Hing Chau, Alison McKay, Christopher F Earl, Amar Kumar Behera, Alan de Pennington

Research output: Contribution to journalArticle

3 Citations (Scopus)
292 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)147-161
JournalArtificial Intelligence for Engineering Design, Analysis and Manufacturing
Volume32
Issue numberSpecial Issue 2
DOIs
Publication statusPublished - 09 May 2018

Keywords

  • Ambiguity; bill of materials (BOM) structures; complemented distributive lattice; design descriptions; maximal representations; set grammars; shape emergence

Fingerprint Dive into the research topics of 'Exploiting lattice structures in shape grammar implementations'. Together they form a unique fingerprint.

  • Cite this