Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
A constructive approach to calculate parameter ranges for systems of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Solution space navigation for geometric constraint systems
ACM Transactions on Graphics (TOG)
Tracking topological changes in feature models
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Geometric constraints within feature hierarchies
Computer-Aided Design
Using the witness method to detect rigid subsystems of geometric constraints in CAD
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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In the full paper [1], we discuss the functionality and implementation challenges of the Frontier geometric constraint engine, designed to address the main reasons for the underutilization of geometric constraints in today's 3D design and assembly systems. Here, we motivate the full paper by outlining the advantages of Frontier.Frontier fully enables both (a) the use of complex, cyclic, spatial constraint structures as well as (b) feature-based design. To deal with Issue (a), Frontier relies on the efficient generation of a close-to-optimal decomposition and recombination (DR) plan for completely general variational constraint systems (see Figure 1). A serious bouleneck in constraint solving is the exponential time dependence on the size of the largest system that is simultaneously solved by the algebraic-numeric solver. In most naturally occurring cases, Frontier's DR-plan is guaranteed in minimize this size (to within a small constant factor). To deal with Issue (b), Frontier's DR-plan admits the independent and local manipulation of features and sub-assemblies in one or more underlying feature hierarchies that are input (Figures 1 and 2). A DR-plan satisfying the above requirements is generated by the new Frontsier vertex Algorithm (FA): the DR problem and its significance as well as FA and its performance with respect to several relevant and newly formalized abstract measures are described in [2, 3].Frontier employs a crucial representation of the DR-plan's subsystems or clusters, their hierarchy and their interaction This representation merges network flow information, as well as other geometric and combinatorial information in a natural manner. Some of this information is obtained from an efficient flow-based algorithm for detecting small rigid sub-systems presented in [4]. The clarity of this representation is crucial in the concrete realization of FA's formal performance. More significantly, this representation allows Frontier to take advantage of its DR-plan in surprising and unsuspected ways listed below.