Mechanical geometry theorem proving
Mechanical geometry theorem proving
Variation of geometrics based on a geometric-reasoning method
Computer-Aided Design
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Using geometric rewrite rules for solving geometric problems symbolically
Theoretical Computer Science
Solving geometric constraints by homotopy
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Formal resolution of geometrical constraint systems by assembling
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh 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
Combining symbolic and numerical solvers to simplify indecomposable systems solving
Proceedings of the 2008 ACM symposium on Applied computing
Characterizing 1-dof Henneberg-I graphs with efficient configuration spaces
Proceedings of the 2009 ACM symposium on Applied Computing
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
A correct rule-based geometric constraint solver
Computers and Graphics
A formalization of geometric constraint systems and their decomposition
Formal Aspects of Computing
Proceedings of the 2011 ACM Symposium on Applied Computing
Tracking Method for Reparametrized Geometrical Constraint Systems
SYNASC '11 Proceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Leading a continuation method by geometry for solving geometric constraints
Computer-Aided Design
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Decomposition of constraint systems is a key component of geometric constraint solving in CAD. On the other hand, some authors have introduced the notion of reparameterization which aims at helping the solving of indecomposable systems by replacing some geometric constraints by other ones. In previous works, the minimal change of the initial system is a main criterion. We propose to marry these two ingredients, decomposition and reparameterization, in a method able to reparameterize and to decompose a constraint system according to this reparameterization. As a result, we do not aim at minimizing the number of added constraints during the reparameterization, but we want to decompose the system such that each component owns a minimal number of such added constraints.