The Construction of Curved Shapes

Abstract

Application of a shape grammar involves the repetitive task of matching and replacing subshapes of a design under transformation, and as such is well suited for computer implementation. As a result, ever since the conception of the shape grammar formalism, efforts have been made to develop computer programs that automate shape grammar applications. Much of this effort has been directed towards the problem of subshape detection, which involves recognising subshapes embedded in a design. Solutions to this problem have been presented for shapes composed of rectilinear geometric elements, such as straight lines, and algorithms based on these solutions have been implemented in a variety of shape grammar interpreters. However, there has been less research concerning the solution of the subshape detection problem for shapes composed of nonrectilinear geometric elements, such as curve segments. In this paper a method of intrinsic matching is presented, which enables comparison of the embedding properties of parametric curves. This method has been employed in order to develop shape algorithms which can be implemented in shape grammar interpreters for shapes composed of parametric curve segments, arranged in two-dimensional or three-dimensional space.