Variation of geometrics based on a geometric-reasoning method
Computer-Aided Design
An interval step control for continuation methods
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
A systematic framework for solving geometric constraints analytically
Journal of Symbolic Computation
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
Combining symbolic and numerical solvers to simplify indecomposable systems solving
Proceedings of the 2008 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
Decomposition of geometrical constraint systems with reparameterization
Proceedings of the 27th Annual ACM Symposium on Applied Computing
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Geometric constraint problems arise in domains such as CAD, Robotics, Molecular Chemistry, whenever one expects 2D or 3D configurations of some geometric primitives fulfilling some geometric constraints. Most well-constrained 3D problems are resistant to geometric knowledge based systems. They are often solved by purely numerical methods that are efficient but provide only one solution. Finding all the solutions can be achieved by using, among others, generic homotopy methods, that become costly when the number of constraints grows. This paper focuses on using geometric knowledges to specialize a so-called coefficient parameter continuation to 3D geometric constraint systems. Even if the proposed method does not ensure obtaining all the solutions, it provides several real ones. Geometric knowledges are used to justify it and lead the search of new solutions.