**Example 2: Shape error verification**

Once the bid is built the customer requires a quality control.

A grid of N points is generated over the mould and compared with the corresponding set of points on the mathematical model.

The goal is to find the displacement that minimizes a certain polynomial error measure.

Therefore one has to solve a system of algebraic equations where the unknowns are the entries of a displacement matrix.

The system has been generically solved (as a function of the coordinates of the N points) using Groebner basis and ad-hoc simplifications.

A patent on the solution is in process.