This dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed.

Product development has both innovative and analytic sides. Starting from the requirements, a design suggestion is generated. In order to assess how well the envisioned design fulfils the requirements, it is sometimes necessary to build a computer model of it for the analysis. The overall motivation of the work presented is to reduce the time spent on creating the model by reusing knowledge gained from developing similar products by suggesting, building and evaluating IT-systems. To verify the systems real design examples, obtained from companies that have participated in the research projects have been used. The work is based on two major application examples. The first, involving the automated geometrical idealisation of die-cast parts (Paper I-III), and the second involving manufacturability of powder metallurgy pressed and sintered parts (Paper IV-VI). The work starts from the point in the product development process where it exists a design suggestion represented as an arbitrary format CAD-model. In the powder metallurgy case the object is to secure that the geometry is suitable for the production process. In the die-casting case the object is to automatically create an idealised version of the model for shell elements meshing. These two tasks have previously been treated as two separate cases, addressed by completely different software. This thesis suggests a common method for addressing the two cases. The method is based on converting the CAD-models, using the geometrical restrictions of the production processes, into a format with a specialised feature structure, parameterisation and construction history using a feature recognition approach. The features are then automatically reconstructed in a target CAD-system. The resulting, specialised CAD-model can be used for automated design and design evaluation purposes, demonstrated in the thesis. The models are therefore called DAR (Design Automation Ready)-models. The DAR-models are useful in that they separate the conversion from the subsequent treatment of the models providing modularisation, flexibility and user insight in the model structure. In that a construction history and parameterisation have be constructed in the target CAD-system, the advanced geometry manipulation and means for knowledge management often provided in modern CAD-systems can be accessed in a transparent and user manageable way. This extends the usefulness of the CAD-systems from involving only interactive work to managing all components sharing the same production process. / Teknologie Doktorsexamen