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Research questions   |   Research context   |   Research methods   |   References   |   Examples of shape computations
	Research Questions Currently available computer aided design systems enable the creation of digital product definitions. Digital product definitions are created after the bulk of [shape] designing has been finished because their creation requires a detailed knowledge of the shape that is to be defined. They offer benefits by providing information for downstream processes such as analysis and manufacturing. Enhancing the act of designing itself requires understanding of how designers create design shapes in the first place [Prats et al 2006] rather than how the results of their designing might be represented. To this end, this project will address the questions, 1) How do designers, across a range of disciplines, generate shapes? 2) What similarities and differences in approach can be observed? The generation of shapes that conform to particular styles, using shape computation tools based on the mathematics of shape grammars [Stiny 1980], has been demonstrated in a number of domains [Prats et al 2006]. Researchers at the University of Leeds have built the world’s first and only 3D shape grammar implementation for curvilinear shapes [Chau 2004]. The basic elements of a shape grammar are shown in Figure 1. The box at the top of the figure shows an initial shape (that seeds the computation) and the two shape rules that are applied during the computation. The shapes at the bottom of the figure show a fragment of the network of shapes that can be computed from the initial shape through the application of the shape rules. The application of a shape rule involves two key steps. Firstly, the shape on the left-hand side of a rule must be identified in the shape from which a new shape is to be computed; this is referred to as “sub-shape detection”. Secondly, the rule is applied by replacing the sub-shape from the left-hand side of the rule with the shape on the right-hand side of the rule. Once a sub-shape has been detected, the Leeds system can automatically apply a rule. However, the sub-shapes have to be identified manually because the automatic detection of sub-shapes is an open research question within the shape grammar community.
	Figure 1. A simple two rule shape grammar
	Significant efforts around the world are being directed towards creating analytic solutions to the subshape detection problem but progress is slow. At one of the “Spatiality in Design” Designing for the 21st Century cluster workshops, a presentation by Prof Hogg (CI) initiated an idea that sub-shape detection might be achieved through the application of computational approaches that have been established in the computer vision community. In contrast to analytic approaches, which search for sub-shapes in the mathematical representation of a shape, the method used in this research will look for sub-shapes in visual objects derived from a shape’s mathematical representation. Subsequent discussions have led to the conclusion that this is an avenue worth exploring and which, if successful, will be groundbreaking. To this end, the research in this project will address the question, 3) Can computer vision techniques be used to resolve the sub-shape detection problem? A key benefit of solving this problem is that it will become possible to compute large networks of shapes where more avenues of shape generation can be explored by designers. The size of the potential shape networks is vast. An example using the initial shape and rules from Figure 1 is given in Figure 2. At each step in the computation a designer would select the red shape from which new shapes would be computed. This leads to our final research question, namely 4) How might the ability to compute shapes enhance the act of designing itself?
	Figure 2. A network of pathways through a solution space
Research questions   |   Research context   |   Research methods   |   References   |   Examples of shape computations

Department of Architecture University of Strathclyde Glasgow UK	Faculty of Engineering University of Leeds Leeds UK	Department of Design and Innovation The Open University Milton Keynes UK