Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Conditions for unique graph realizations
SIAM Journal on Computing
Graph-based approach for solving geometric constraint problems
Graph-based approach for solving geometric constraint problems
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
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
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
On Spatial Constraint Solving Approaches
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
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
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Using Cayley-Menger determinants for geometric constraint solving
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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
Geometric constraints within feature hierarchies
Computer-Aided Design
Defining tools to address over-constrained geometric problems in Computer Aided Design
Computer-Aided Design
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Classically, geometric constraint solvers use graph-based methods to decompose systems of geometric constraints. These methods have intrinsic limitations, which the witness method overcomes; a witness is a solution of a variant of the system. This paper details the computation of a basis of the vector space of free infinitesimal motions of a typical witness, and explains how to use this basis to interrogate the witness for dependence detection. The paper shows that the witness method detects all kinds of dependences: structural dependences already detectable by graph-based methods, but also non-structural dependences, due to known or unknown geometric theorems, which are undetectable by graph-based methods. It also discusses how to decide about the rigidity of a witness and how to decompose it.