Juno, a constraint-based graphics system
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A systematic framework for solving geometric constraints analytically
Journal of Symbolic Computation
The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory
ACM Transactions on Programming Languages and Systems (TOPLAS)
Solving Geometric Constraints By Homotopy
IEEE Transactions on Visualization and Computer Graphics
Real-Time Physically-Based Facial Expression Animation Using Mass-Spring System
CGI '01 Computer Graphics International 2001
A hybrid approach to geometric constraint solving with graph analysis and reduction
Advances in Engineering Software
Real Time Muscle Deformations using Mass-Spring Systems
CGI '98 Proceedings of the Computer Graphics International 1998
Variational geometry in computer-aided design
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
Solving Geometric Constraints by a Hybrid Method
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
Theories for Mass-Spring Simulation in Computer Graphics: Stability, Costs and Improvements
IEICE - Transactions on Information and Systems
A mass spring model for hair simulation
ACM SIGGRAPH 2008 papers
Combining symbolic and numerical solvers to simplify indecomposable systems solving
Proceedings of the 2008 ACM symposium on Applied computing
A formalization of geometric constraint systems and their decomposition
Formal Aspects of Computing
Using the witness method to detect rigid subsystems of geometric constraints in CAD
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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Current iterative numerical methods, such as continuation or Newton-Raphson, work only on systems for which the corresponding matrix is a square one. The geometric constraint systems need thus either to have no degrees of freedom, or to be a system the software can anchor, i. e. a rigid system. In this article, we propose a new iterative numerical approach which can handle both rigid and under-rigid geometric constraint systems. It is based on the translation of the system under the form of a particle-spring system where particles correspond to the geometric entities and springs to the constraints. We show that consistently over-constrained systems are also solved. We show that our approach is promising by giving results of a prototype implementation. We propose tracks for enhancements of the approach which could tackle its drawbacks (mainly stability).