4. Associated geometric elements

Associating an ideal geometric element with a set of points is like solving a mathematical problem of constrained optimization. As real lines and surfaces are never perfect, they are measured by a number of points greater than the minimum required for the mathematical definition of the corresponding geometric element. It is therefore possible to associate with the same set of measured points, several geometric elements of the same type, each meeting a criterion expressing the "best representation" of a technological function that the real geometric element must satisfy.

ISO specification standards provide guidance on the "best representation" of a real surface by an ideal surface. Two criteria can be distinguished, one relating to the shape of the element, the other to the assembly function. Thus, the shape of an element can be characterized by a shape defect t,...