A formal-numerical approach to solve 3D geometric constraints systems

In computer-aided design, solvers generally use a geometric avatar of the "divide and conquer" paradigm to cope with their complexity. However, this scheme often fails in the case of 3D geometric constraints systems since they are hardly decomposable. We have studied a new method which uses jointly two solvers, a symbolic one and a numerical one, in order to solve a system S: system S is transformed into a parametric system S "almost" equivalent to S and such that system S is symbolically solvable and the numerical solver computes solution of S from solutions of S.