6533b835fe1ef96bd129f303
RESEARCH PRODUCT
Numerical decomposition of geometric constraints
Dominique MichelucciJean-paul JurzakSebti Foufousubject
Constraint (information theory)AlgebraSet (abstract data type)symbols.namesakeMathematical optimizationProbabilistic methodJacobian matrix and determinantsymbolsStructure (category theory)CADGas meter proverMathematicsIncidence (geometry)description
Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of incidence constraints, such as collinearities and coplanarities. Jurzak's prover is used to find a similar configuration.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-06-13 | Proceedings of the 2005 ACM symposium on Solid and physical modeling |