Theory and Algorithm for Planar Datum Establishment Using Constrained Total Least-squares

First, we present an efficient algorithm for establishing planar datums that is based on a constrained minimization search based on the L2 norm after forming a convex surface from sampled points. Visualized by Gauss maps, we prove that the problem reduces to a minimization search where the global minimum is localized about the minimizing facet. Second, we highlight advantages of this planar datum, including the major advantage that the datum planes have full mechanical contact with the datum features in stable cases yet are automatically balanced for rocking conditions. These advantages make this definition appealing for standardization.