Tracking topological changes in parametric models

In current parametric CAD systems, the relation between the values of the parameters of a model and the topology of the model is often not clear to the user. To give the user better control over the topology of the model, this relation should be made explicit. A method is presented here that determines the parameter values for which the topology of a model changes, i.e. the critical values of a given variant parameter. The considered model consists of a system of geometric constraints, which relates parameters and feature geometries, and a cellular model, which partitions space into volumetric cells determined by the intersections of the feature geometries and represented by topological entities. Our method creates a new system of geometric constraints to relate the parameters of the model to the topological entities. For each entity that is dependent on the variant parameter, degenerate cases are enforced by specific geometric constraints. Solving the resulting constraint systems yields the critical parameter values. Critical values can be used to compute parameter ranges corresponding to families of objects, i.e. all parameter values which correspond to models that satisfy a given set of geometric and topological constraints.