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.