Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
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A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
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GMCAD '96 Proceedings of the fifth IFIP TC5/WG5.2 international workshop on geometric modeling in computer aided design on Product modeling for computer integrated design and manufacture
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SIAM Journal on Discrete Mathematics
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Revisiting decomposition analysis of geometric constraint graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
On the Domain of Constructive Geometric Constraint Solving Techniques
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
Numerical decomposition of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Constraint solving for direct manipulation of features
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Characterizing 1-dof Henneberg-I graphs with efficient configuration spaces
Proceedings of the 2009 ACM symposium on Applied Computing
Geometric constraint solving: The witness configuration method
Computer-Aided Design
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Proceedings of the 2011 ACM Symposium on Applied Computing
Example-based procedural modelling by geometric constraint solving
Multimedia Tools and Applications
Coordinate-free geometry and decomposition in geometrical constraint solving
Computer-Aided Design
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We present an approach for handling geometric constraint problems with under-constrained configurations. The approach works by completing the given set of constraints with constraints that can be defined either automatically or drawn from an independently given set of constraints placed on the geometries of the problem. In both cases, the resulting completed set of constraints is not over-constrained. If every well-constrained subproblem in the given under-constrained configuration is solvable, the completed constraint problem is also solvable.