Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Solving geometric constraints by homotopy
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
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
Geometric Constraint Solving and Applications
Geometric Constraint Solving and Applications
Geometric constraint solving via C-tree decomposition
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Numerical decomposition of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Nonlinear systems solver in floating-point arithmetic using LP reduction
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Algorithms for identifying rigid subsystems in geometric constraint systems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Geometric constraint solving: The witness configuration method
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
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Hi-index | 0.00 |
Classically, geometric constraint solvers use graph-based methods to analyze systems of geometric constraints. These methods have intrinsic limitations, which the witness method overcomes. This paper details the computation of a basis of the vector space of the free infinitesimal motions of a typical witness, and explains how to use this basis to interrogate the witness for detecting all dependencies between constraints: structural dependencies already detectable by graph-based methods, and also non-structural dependencies, due to known or unknown geometric theorems, which are undetectable with graph-based methods. The paper also discusses how to decide about the rigidity of a witness.