Tracking topological changes in feature models

Current feature models do not explicitly represent the relation between the parameters and the topology of the model. For theoretical and practical purposes, it is important to make this relation more explicit. A method is presented here that determines parameter values for which the topology of a feature model changes, i.e. the critical values of a given variant parameter. The considered feature model consists of a system of geometric constraints, relating parameters to feature geometry, and a cellular model. The cellular model partitions Euclidean space into quasi-disjoint cells, determined by the intersections of the feature geometry. Our method creates a new system of geometric constraints to relate the parameters of the model to topological entities in the cellular model. For each entity that is dependent on the variant parameter, degenerate cases are enforced by specific geometric constraints. Solving this system of constraints yields the critical parameter values. Critical values can be used to compute parameter ranges corresponding to families of objects, e.g. all parameter values which correspond to models that satisfy given topological constraints.