{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:42:52Z","timestamp":1761964972107,"version":"3.41.2"},"reference-count":24,"publisher":"ASME International","issue":"3","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2018,9,1]]},"abstract":"<jats:p>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 for optimization requires contacting at least two input points. It is also shown that there exist cases where the optimal condition is achieved while contacting only two input points. These problems arise in digital manufacturing, where one is confronted with the task of processing a (potentially large) number of points with three-dimensional coordinates to establish datums on manufactured parts. The optimality conditions reported in this paper provide the necessary conditions to verify if a candidate solution is feasible, and to design new algorithms to compute globally optimal solutions.<\/jats:p>","DOI":"10.1115\/1.4039583","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T22:31:03Z","timestamp":1521585063000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":7,"title":["Optimality Conditions for Constrained Least-Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums"],"prefix":"10.1115","volume":"18","author":[{"given":"Craig M.","family":"Shakarji","sequence":"first","affiliation":[{"name":"Mem. ASME Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vijay","family":"Srinivasan","sequence":"additional","affiliation":[{"name":"Fellow ASME Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2018,6,12]]},"reference":[{"key":"2019100602194235300_bib1","article-title":"Dimensioning and Tolerancing","volume-title":"Y14.5-2009","author":"ASME,","year":"2009"},{"key":"2019100602194235300_bib2","article-title":"Mathematical Definition of Dimensioning and Tolerancing Principles","volume-title":"Y14.5.1-1994","author":"ASME,","year":"1994"},{"key":"2019100602194235300_bib3","article-title":"Geometrical Product Specifications (GPS)\u2014Geometrical Tolerancing\u2014Tolerances of Form, Orientation, Location and Run-Out","volume-title":"ISO 1101:2012","author":"ISO","year":"2012"},{"key":"2019100602194235300_bib4","article-title":"Geometrical Product Specifications (GPS)\u2014Geometrical Tolerancing\u2014Datums and Datum Systems","volume-title":"ISO 5459:2011","author":"ISO","year":"2011"},{"year":"2012","key":"2019100602194235300_bib5","article-title":"The ISO Geometrical Product Specifications Handbook\u2014Find Your Way in GPS"},{"edition":"3rd ed.","volume-title":"Fundamentals of Geometric Dimensioning and Tolerancing","year":"2012","key":"2019100602194235300_bib6"},{"key":"2019100602194235300_bib7","article-title":"Geometrical Product Specification","volume-title":"CIRP Encyclopedia of Production Engineering","author":"Laperri\u00e8re","year":"2014"},{"edition":"4th ed.","volume-title":"Tool and Manufacturing Engineers Handbook: Quality Control and Assembly","year":"1987","key":"2019100602194235300_bib8"},{"key":"2019100602194235300_bib9","doi-asserted-by":"publisher","DOI":"10.1115\/IMECE2015-50654","article-title":"A Constrained L2 Based Algorithm for Standardized Planar Datum Establishment","volume-title":"ASME","year":"2015"},{"key":"2019100602194235300_bib10","doi-asserted-by":"crossref","unstructured":"Shakarji, C. M., and Srinivasan, V., 2016, \u201cTheory and Algorithm for Planar Datum Establishment Using Constrained Total Least-Squares,\u201d 14th CIRP Conference on Computer Aided Tolerancing, Gothenburg, Sweden, May 18\u201320, pp. 232\u2013237.","DOI":"10.1016\/j.procir.2016.02.104"},{"key":"2019100602194235300_bib11","doi-asserted-by":"publisher","DOI":"10.1115\/IMECE2016-67753","article-title":"Computational Investigations for a New, Constrained Least-Squares Datum Definition for Circles, Cylinders, and Spheres","volume-title":"ASME","year":"2016"},{"volume-title":"Practical Optimization","year":"1982","key":"2019100602194235300_bib12"},{"key":"2019100602194235300_bib13","doi-asserted-by":"publisher","DOI":"10.1115\/DETC2017-67143","article-title":"Optimality Conditions for Constrained Least-Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums","volume-title":"ASME","year":"2017"},{"year":"1990","key":"2019100602194235300_bib14","article-title":"The Mathematics of Datums"},{"issue":"1","key":"2019100602194235300_bib15","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/0278-6125(93)90035-R","article-title":"Criteria for Establishing Datums in Manufactured Parts","volume":"12","year":"1993","journal-title":"J. Manuf. Syst."},{"year":"1993","key":"2019100602194235300_bib16","article-title":"Chebyshev Best-Fit Geometric Elements"},{"year":"1994","key":"2019100602194235300_bib17","article-title":"Algorithms for Geometric Tolerance Assessment"},{"issue":"1","key":"2019100602194235300_bib18","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1177\/0954405412464012","article-title":"Reflections on the Role of Science in the Evolution of Dimensioning and Tolerancing Standards","volume":"227","year":"2013","journal-title":"Proc. Inst. Mech. Eng., Part B"},{"issue":"1","key":"2019100602194235300_bib19","doi-asserted-by":"publisher","DOI":"10.1115\/1.3647877","article-title":"On the Enduring Appeal of Least-Squares Fitting in Computational Coordinate Metrology","volume":"12","year":"2012","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"3","key":"2019100602194235300_bib20","doi-asserted-by":"publisher","DOI":"10.1115\/1.4024854","article-title":"Theory and Algorithms for Weighted Total Least-Squares Fitting of Lines, Planes, and Parallel Planes to Support Tolerancing Standards","volume":"13","year":"2013","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"key":"2019100602194235300_bib21","doi-asserted-by":"publisher","DOI":"10.1115\/DETC2013-12372","article-title":"Theory and Algorithms for L1 Fitting Used for Planar Datum Establishment in Support of Tolerancing Standards","volume-title":"ASME","year":"2013"},{"key":"2019100602194235300_bib22","doi-asserted-by":"publisher","DOI":"10.1115\/DETC2014-35461","article-title":"An Improved L1 Based Algorithm for Standardized Planar Datum Establishment","volume-title":"ASME","year":"2014"},{"issue":"4","key":"2019100602194235300_bib23","doi-asserted-by":"publisher","DOI":"10.1115\/1.4031827","article-title":"Datum Planes Based on a Constrained L1 Norm","volume":"15","year":"2015","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"edition":"2nd ed.","volume-title":"Computational Geometry in C","year":"1998","key":"2019100602194235300_bib24"}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4039583\/5997398\/jcise_018_03_031008.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4039583\/5997398\/jcise_018_03_031008.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,6]],"date-time":"2019-10-06T06:19:51Z","timestamp":1570342791000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/doi\/10.1115\/1.4039583\/367945\/Optimality-Conditions-for-Constrained-LeastSquares"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,12]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4039583","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"type":"print","value":"1530-9827"},{"type":"electronic","value":"1944-7078"}],"subject":[],"published":{"date-parts":[[2018,6,12]]},"article-number":"031008"}}