Abstract: 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 ...

Abstract: We present the theory and algorithms for fitting a line, a plane, two parallel planes (corresponding to a slot or a slab), or many parallel planes in a total (orthogonal) leastsquares sense to coordinate data that is ...

Abstract: This paper addresses the combinatorial characterizations of the optimality conditions for constrained least-squares fitting of circles, cylinders, and spheres to a set of input points. It is shown that the necessary condition ...

Abstract: This paper addresses some important theoretical issues for constrained least-squares fitting of planes and parallel planes to a set of points. In particular, it addresses the convexity of the objective function and the ...

Abstract: Recent advances in the digitization of manufacturing have prompted ASME and International Organization for Standardization (ISO) standards committees to reexamine the definition of datums. Any new definition of datums ...

Abstract: Constrained least-squares fitting has gained considerable popularity among national and international standards committees as the default method for establishing datums on manufactured parts. This has resulted in the ...