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The design space exploration formalism has developed data structures and algorithms of sufficient complexity and scope to support conceptual layout, massing, and enclosure configurations. However, design remains a human enterprise. To support the user in designing with the formalism, we have developed an interaction model that addresses the interleaving of user actions with the formal operations of design space exploration. The central feature of our interaction model is the modeling of control based on mixed-initiative. Initiative is sometimes taken by the designer and sometimes by the formalism in working on a shared design task. The model comprises three layers, domain, task, and dialogue. In this paper we describe the formulation of the domain layer of our mixed-initiative interaction model for design space exploration. We present the view of the domain as understood in the formalism in terms of the three abstract concepts of state, move, and structure. In order to support mixed initiative, it is necessary to develop a shared view of the domain. The domain layer addresses this problem by mapping the designer's view onto the symbol substrate. First, we present the designer's view of the domain in terms of problems, solutions, choices, and history. Second, we show how this view is interleaved with the symbol-substrate through four domain layer constructs, problem state, solution state, choice, and exploration history. The domain layer presents a suitable foundation for integrating the role of the designer with a description formalism. It enables the designer to maintain exploration freedom in terms of formulating and reformulating problems, generating solutions, making choices, and navigating the history of exploration.

Few computer implementations of shape grammars have been written that are applicable to curved shapes. The reason for this is that underlying representations of curves do not lend themselves to providing a unique description of curved shapes. Such a representation is essential for shape algorithms. This paper explains the problems posed in representing curves for shape grammar implementation. The paper demonstrates how the fundamental structures for implementing shape grammars for straight lines can be extended to shapes with curved elements.

Few computer implementations of shape grammars have been written that are applicable to curved shapes. The reason for this is that underlying representations of curves do not lend themselves to providing a unique description of curved shapes. Such a representation is essential for shape algorithms. This paper explains the problems posed in representing curves for shape grammar implementation. The paper demonstrates how the fundamental structures for implementing shape grammars for straight lines can be extended to shapes with curved elements.