On the mathematical formulation of the problem of reassembling fragmented objects: two new theorems

In this paper two new theorems are proved in association with the problem of matching three dimensional solid bodies. Rigorous mathematical criteria are given in order to test if two such bodies actually match in a certain position. Since this problem finds important application to the actual problem of reassembling fragmented objects e.g. archaeological, special care is taken to account for small gaps between matching fragments and fuzziness of the matching parameters.