Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

An improved L1 based algorithm for standardized planar datum establishment

Published

Author(s)

Craig M. Shakarji, Vijay Srinivasan

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 L_1 (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 constrained and unconstrained planar 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 ISO and ASME standardization efforts are actively working to establish datum plane definitions, the timing of such a study is opportune.
Proceedings Title
Proceedings of the ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
Conference Dates
August 17-20, 2014
Conference Location
Buffalo, NY
Conference Title
The ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference

Keywords

algorithm, convex hull, datum, L1, least squares, plane, standard, tolerancing

Citation

Shakarji, C. and Srinivasan, V. (2014), An improved L1 based algorithm for standardized planar datum establishment, Proceedings of the ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Buffalo, NY (Accessed July 3, 2022)
Created October 1, 2014, Updated February 19, 2017