The molecule problem: determining conformation from pairwise distances
The molecule problem: determining conformation from pairwise distances
Some examples of the use of distances as coordinates for Euclidean geometry
Journal of Symbolic Computation
Conditions for unique graph realizations
SIAM Journal on Computing
An accurate algorithm for rasterizing algebraic curves
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Monomial bases and polynomial system solving (extended abstract)
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Signature functions for algebraic numbers
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
A complete and practical algorithm for geometric theorem proving (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Determining the Equivalence of Algebraic Expressions by Hash Coding
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
Revisiting decomposition analysis of geometric constraint graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
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
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Numerical decomposition of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
The Interactive Geometry Software Cinderella.2
The Interactive Geometry Software Cinderella.2
Using Cayley-Menger determinants for geometric constraint solving
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Proving by example and gap theorems
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Proceedings of the 2007 ACM symposium on Applied computing
Combining symbolic and numerical solvers to simplify indecomposable systems solving
Proceedings of the 2008 ACM symposium on Applied computing
Dealing with redundancy and inconsistency in constructive geometric constraint solving
Advances in Engineering Software
Interrogating witnesses for geometric constraint solving
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Constraint-based simulation of carton folding operations
Computer-Aided Design
Detecting all dependences in systems of geometric constraints using the witness method
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Interrogating witnesses for geometric constraint solving
Information and Computation
Defining tools to address over-constrained geometric problems in Computer Aided Design
Computer-Aided Design
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Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.