Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
A systematic framework for solving geometric constraints analytically
Journal of Symbolic Computation
Sketch-based pruning of a solution space within a formal geometric constraint solver
Artificial Intelligence
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Specification of freeform features
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Using invariance under the similarity group to solve geometric constraint systems
Computer-Aided Design
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Geometric constraints within feature hierarchies
Computer-Aided Design
A correct rule-based geometric constraint solver
Computers and Graphics
Tracking topological changes in parametric models
Computer Aided Geometric 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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We present a new constructive solving approach for systems of 3D geometric constraints. The solver is based on the cluster rewriting approach, which can efficiently solve large systems of constraints on points, and incrementally handle changes to a system, but can so far solve only a limited class of problems. The new solving approach extends the class of problems that can be solved, while retaining the advantages of the cluster rewriting approach. Whereas previous cluster rewriting solvers only determined rigid clusters, we also determine two types of non-rigid clusters, i.e. clusters with particular degrees of freedom. This allows us to solve many additional problems that cannot be decomposed into rigid clusters, without resorting to expensive algebraic solving methods. In addition to the basic ideas of the approach, an incremental solving algorithm, two methods for solution selection, and a method for mapping constraints on 3D primitives to constraints on points are presented.