Geometric problems in automated manufacturing

In this paper, the following two classes of problems in automated inspection are considered. In the first class of problems, we are given two sets of points S, T, on two parallel planes. The problem is then to superimpose one plane onto the other so as to obtain the best possible fit between the two sets of points. In the second case, we have two sets of polygonal or circular objects on two parallel planes. The problem is to match the objects on one plane with those on the other plane and superimpose one plane onto the other, so that each object on one plane contains or is contained in its partner on the other plane. We describe a pseudo-polynomial time algorithm for the first class and a polynomial time algorithm for the second class of problems.