A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
A systematic framework for solving geometric constraints analytically
Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Revisiting decomposition analysis of geometric constraint graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
A hybrid approach to geometric constraint solving with graph analysis and reduction
Advances in Engineering Software
Transforming an under-constrained geometric constraint problem into a well-constrained one
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Improved algorithms for graph four-connectivity
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Graphs, Networks and Algorithms
Graphs, Networks and Algorithms
Decomposition of geometrical constraint systems with reparameterization
Proceedings of the 27th Annual ACM Symposium on Applied Computing
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This paper presents a method based on connectivity analysis of graph to solve structurally under-constrained constraint problems frequently occurred during design process in parametric CAD. We give a partial solution to the optimal well-constrained completion problem, that is, adding automatically new constraints to the graph corresponding to an under-constrained geometric constraint problem G in such a way that G is well-constrained and the set of equations needed to be solved simultaneously in order to solve G has the smallest size. With this method, a connected, bi-connected, or tri-connected structurally under-constrained problem in 2D can be transformed into a structurally well-constrained one by adding new constraints automatically during the process of decomposing it into a decomposition tree.