Solving topological constraints for declarative families of objects

Parametric and feature-based CAD models can be thought of to represent families of similar objects. In current modelling systems, however, model semantics is unclear and ambiguous in the context of families of objects.We present the Declarative Family of Objects Model (DFOM), which enables to adequately specify and maintain family semantics. In this model, not only geometry, but also topology is specified declaratively, by means of constraints. A family of objects is modelled by a DFOM with multiple realisations. A member of the family is modelled by adding constraints, e.g. to set dimension variables, until a single realisation remains. The declarative approach guarantees that the realisation of a family member is also a realisation of the family.The realisation of a family member is found by solving first the geometric constraints, then the topological constraints. From the geometric solution, a cellular model is constructed. Topological constraints indirectly specify which combinations of cellular model entities are allowed in the realisation. The system of topological constraints is translated into a boolean constraint satisfaction problem. The realisation is found by solving this problem. The feasibility of solving topological constraints has been investigated using an existing boolean satisfiability solver.

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