Datum Planes Based on a Constrained L₁ Norm

This paper has two major goals. First, we present an algorithm for establishing planar datums suitable for a default in tolerancing standards. The algorithm is based on a constrained minimization search based on the $L1$ (L1) norm after forming a convex surface from the original surface or sampled points. We prove that the problem reduces to a simple minimization search between the convex surface and its centroid. The data points in the discrete case do not need to have any corresponding weights provided with them, as appropriate weighting is part of the algorithm itself, thereby making the algorithm largely insensitive to nonuniformly sampled data points. Terse mathematica code is included for the reader. The code is sufficient for primary and secondary planar datum fitting as well as a 3-2-1 datum reference frame generation. The second goal of this paper is to compare this new method with several other possible means for establishing datum planes, ultimately showing several appealing characteristics of the proposed algorithm. Since both the International Organization for Standardization (ISO) and American Society of Mechanical Engineers (ASME) standardization efforts are actively working to establish datum plane definitions, the timing of such a study is opportune.