The Open University ’ s repository of research publications and other research outputs Implementation of curved shape grammars

Research into shape grammar implementation has largely been concerned with rectilinear shapes and there has been little research concerning implementation on curved shapes. This reflects developments of the shape grammar formalism which has traditionally been defined according to straight lines. In this paper, issues regarding the application of shape grammars on curved shapes are investigated. This investigation builds on algorithms for implementing shape operations on curved shapes, in which the embedding properties of parametric curves are compared according to their intrinsic properties. In the paper, the algorithms are implemented in a shape grammar interpreter that enables the application of shape grammars on shapes composed of quadratic Bézier curves. The interpreter is illustrated via application of a shape grammar that generates Celtic knotwork patterns. Implementing shape grammars on curved shapes highlights difficulties that arise when the shape grammar formalism is applied to curved shapes, and the paper concludes with a discussion that explores these difficulties.