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Generative specifications have been used to systematically codify established styles in several design fields including architecture and product design. We examine how designers explore new designs in the early stages of product development as they manipulate and interpret shape representations. A model of exploration is proposed with four types of shape descriptions~contour, decomposition, structure, and design! and the results of the exploration are presented. Generative rules are used to provide consistent stylistic changes first within a given decomposition and second through changing the structure. Style expresses both the analytical order of explanation and the synthetic complexity of exploration. The model of exploration is consistent with observations of design practice. The application of generative design methods demonstrates a logical pattern for early stage design exploration. The model provides the basis for tools to assist designers in exploring families of designs in a style and for following new interpretations that move the exploration from one family to another.

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The process of sketching can support the sort of transformational thinking that is seen as essential for the interpretation and reinterpretation of ideas in innovative design. Such transformational thinking, however, is not yet well supported by computer-aided design systems. In this paper, outcomes of experimental investigations into the mechanics of sketching are described, in particular those employed by practicing architects and industrial designers as they responded to a series of conceptual design tasks. Analyses of the experimental data suggest that the interactions of designers with their sketches can be formalised according to a finite number of generalised shape rules. A set of shape rules, formalising the reinterpretation and transformations of shapes, e.g. through deformation or restructuring, is presented. These rules are suggestive of the manipulations that need to be afforded in computational tools intended to support designers in design exploration. Accordingly, the results of the experimental investigations informed the development of a prototype shape synthesis system, and a discussion is presented in which the future requirements of such systems are explored.

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.

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.

Shape grammars are a generative formalism in which dynamic changes to shape structure plays a vital role. Such changes support ambiguity and emergence, and as a result shape grammars are often used as the basis for proposed developments in supporting shape exploration in computeraided design. However, the general implementation of shape grammars remains an unsolved problem, and a common solution is to adopt a fixed structure. This paper explores the consequences of assuming a fixed shape structure, via analysis of a simple shape grammar, often used as a benchmark problem to illustrate advances in shape grammar implementation. With reference to the combinatorics of words, it is proved that adopting a finite fixed structure limits the capability of a shape grammar. The paper concludes with a discussion exploring the implications of this result for shape grammar implementation and for design descriptions in CAD.

Throughout the history of CAD, a variety of interfaces have been employed with the aim of supporting designers' construction and manipulation of digital models. This paper explores the potential of eye tracking as a CAD interface, and presents a prototype that uses collected gaze data to support shape exploration in a two-dimensional vectorbased sketch editor. The eye tracking interface uses the visual interactions of users to identify interpretations of constructed shapes, according to recognised parts identified using methods from shape grammar research. It can therefore be argued that it supports construction and manipulation of shapes according to user intent. The prototype has been evaluated in a user study where design students carried out controlled shape exploration exercises which involved interpretation and manipulation of shapes. In the paper, key concepts of eye tracking methodology are introduced; the methods used to implement the eye tracking interface are described; and the user study and its outcomes are reported. The results are positive and indicate the potential for eye tracking as an interface for supporting shape exploration in CAD. Research Highlights• Explores the potential of eye tracking as an interface for computer aided-design• Describes methods for inferring user intent with respect to digital shape manipulation, based on gaze data • Presents a prototype eye tracking interface that supports dynamic shape interpretation in a vector-based sketch editor • Reports the outcomes of a user study that evaluates how successful the eye tracking interface is at inferring users' intent with respect to shape manipulation