Evaluation of a 3D Shape Grammar Implementation

Abstract

The geometric design of the exterior appearance of consumer products is a principal consideration to retain brand identity. Architectural and engineering shape grammars had demonstrated shape computation as a formal and viable approach for supporting style conformance. However, most existing shape grammar implementations operated in limited experimental domains, and lacked support for complex three dimensional geometry, shape emergence and parametric shape rules. The aim of the reported research is to address these issues. Shape algebras are reduced in terms of shape operations with their basic elements which is generally applicable to shape computation. Specifically for algebra U13, exhaustive cases were enumerated for shape sum and shape difference operations. A U13 shape grammar implementation was developed to support both rectilinear and curvilinear basic elements in three dimensional space. Mathematical representations of basic elements were based on nonuniform rational b-splines and their reduced form. This allowed a simple yet exact notation which simplified support for maximal representation and its computation. Two cases studies, a Coca-Cola bottle grammar and a Head & Shoulder bottle grammar, were used to test the implementation.