What is a parametric family of solids?
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
The generic geometric complex (GGC): a modeling scheme for families of decomposed pointsets
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Boundary representation deformation in parametric solid modeling
ACM Transactions on Graphics (TOG)
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
A survey of the persistent naming problem
Proceedings of the seventh ACM symposium on Solid modeling and applications
Specification of freeform features
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Constructive topological representations
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Tracking topological changes in feature models
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Solving topological constraints for declarative families of objects
Computer-Aided Design
Efficiency of boundary evaluation for a cellular model
Computer-Aided Design
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints
Computer-Aided Design
On the long-term retention of geometry-centric digital engineering artifacts
Computer-Aided Design
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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.