Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Variation of geometrics based on a geometric-reasoning method
Computer-Aided Design
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Solving geometric constraints by homotopy
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Symbolic constraints in constructive geometric constraint solving
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Geometric construction by assembling solved subfigures
Artificial Intelligence
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
Using Cayley-Menger determinants for geometric constraint solving
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Subdivision methods for solving polynomial equations
Journal of Symbolic Computation
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
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In CAD, a designer usually specifies mechanisms or objects by the means of sketches supporting dimension requirements like distances between points, angles between lines, and so on. This kind of geometric constraint satisfaction problems presents two aspects which solvers have to deal with: first, the sketches can contain hundreds of constraints, and, second, the problems are invariant by rigid body motions. Concerning the first issue, several decomposition methods have been designed taking invariance into account by fixing/relaxing coordinate systems. On the other hand, some researchers have proposed to use distance geometry in order to exploit invariance by rigid body motions. This paper describes a method that allows us to use distance geometry and decomposition in the same framework.