Creating shapes in a three dimensional environment is a complex operation which often requires the adoption of very constrained techniques. The shape modelling phase plays a fundamental role within the design process because it allows the improvement of the visual appeal of artefacts. It also enhances ergonomics and the product’s commercial competitiveness through product differentiation. Natural and intuitive, yet mathematically correct, creation and modification of surfaces is a fundamental requirement when flexibility and intuition have to be privileged to unleash the designer’s creativity during the concept design phase. Efficient and intuitive shape manipulation techniques are therefore vital to the success of geometric modelling, computer animation, physical simulation and other computing areas.

This project proposes to investigate the possibility of defining different forms of constraint-based design. Within this context we refer to designed features as “constraints”, preliminary defined by an operator, which should be properly integrated with the final CAD product. The integration involves studying the type of representation of constraints and CAD models, analysis of their geometry and topology, identifying the points at which a constraint can fit the designed object as well as how the object should be evolved to satisfy the constraints, areas of possible interpolation of the constraints and the model.

This project is related to the first research area, namely “Change of representation”, since applying constraints to a 3D model requires adaptation of its original representation. Before the integration itself takes place, the constraints and the model should be converted to the same representation form. In this regard the need of approximate implicitization arises here to achieve robust and efficient integration.

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