Mechanical geometry theorem proving
Mechanical geometry theorem proving
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
A complete and practical algorithm for geometric theorem proving (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
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
Solving Geometrical Constraint Systems Using CLP Based on Linear Constraint Solver
AISMC-3 Proceedings of the International Conference AISMC-3 on Artificial Intelligence and Symbolic Mathematical Computation
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
Geometric constraint solving via C-tree decomposition
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Variational geometry in computer-aided design
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
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
Solving geometric constraints invariant modulo the similarity group
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Dealing with redundancy and inconsistency in constructive geometric constraint solving
Advances in Engineering Software
Reliable Implementation of Real Number Algorithms: Theory and Practice
Interrogating witnesses for geometric constraint solving
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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
A 2D geometric constraint solver using a graph reduction method
Advances in Engineering Software
Interrogating witnesses for geometric constraint solving
Information and Computation
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Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of incidence constraints, such as collinearities and coplanarities. Jurzak's prover is used to find a similar configuration.