What is a parametric family of solids?
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Boundary representation deformation in parametric solid modeling
ACM Transactions on Graphics (TOG)
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
FRONTIER: fully enabling geometric constraints for feature-based modeling and assembly
Proceedings of the sixth ACM symposium on Solid modeling and applications
Constructive topological representations
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Solving topological constraints for declarative families of objects
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Efficiency of boundary evaluation for a cellular model
Computer-Aided Design
Detecting basic topological changes in sensor networks by local aggregation
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
A framework for preservable geometry-centric artifacts
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Tracking topological changes in parametric models
Computer Aided Geometric Design
On the long-term retention of geometry-centric digital engineering artifacts
Computer-Aided Design
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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.