The function to obtain associated surfaces on coordinate measuring machines (CMM's) is based on the minimization of the distance between measured points and the ideal surface. This function is non-linear for usual surfaces. In many works, to accelerate iterative calculations, the problem is linearized. The aim of this work is to reduce scraps using a transcription optimization of the fitting functionality of mechanical parts in maximum state of matter. An adaptive verification method is suggested. It takes account of the interface properties. A control by a virtual gauge and verification a process is developed to validate the tolerancing according to the previously suggested methodology.