{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T20:00:37Z","timestamp":1760472037160,"version":"3.41.2"},"reference-count":23,"publisher":"ASME International","issue":"1","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2012,3,1]]},"abstract":"<jats:p>The vast majority of points collected with coordinate measuring machines are not used in isolation; rather, collections of these points are associated with geometric features through fitting routines. In manufacturing applications, there are two fundamental questions that persist about the efficacy of this fitting\u2014first, do the points collected adequately represent the surface under inspection; and second, does the association of substitute (fitted) geometry with the points meet criteria consistent with the standardized geometric specification of the product. This paper addresses the second question for least-squares fitting both as a historical survey of past and current practices, and as a harbinger of the influence of new specification criteria under consideration for international standardization. It also touches upon a set of new issues posed by the international standardization on the first question as related to sampling and least-squares fitting.<\/jats:p>","DOI":"10.1115\/1.3647877","type":"journal-article","created":{"date-parts":[[2011,12,21]],"date-time":"2011-12-21T23:05:01Z","timestamp":1324508701000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":18,"title":["On the Enduring Appeal of Least-Squares Fitting in Computational Coordinate Metrology"],"prefix":"10.1115","volume":"12","author":[{"given":"Vijay","family":"Srinivasan","sequence":"first","affiliation":[{"name":"Fellow ASME Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Craig M.","family":"Shakarji","sequence":"additional","affiliation":[{"name":"Mem. ASME Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edward P.","family":"Morse","sequence":"additional","affiliation":[{"name":"Mem. ASME Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC 28223 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2011,12,21]]},"reference":[{"key":"2019100413475621000_c1","first-page":"79","article-title":"Elements of Computational Metrology","volume-title":"DIMACS Book Series","author":"Srinivasan"},{"key":"2019100413475621000_c2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1115\/1.2424246","article-title":"Computational Metrology for the Design and Manufacture of Product Geometry: A Classification and Synthesis","volume":"7","author":"Srinivasan","journal-title":"Trans. ASME, J. Comput. Inf. Sci. Eng."},{"key":"2019100413475621000_c3","unstructured":"Walker, R.\n          , 1988, Government-Industry Data Exchange Program, GIDEP Alert No. X1-A-88-01, Aug. 22."},{"volume-title":"The History of Statistics: The Measurement of Uncertainty Before 1900","author":"Stigler","key":"2019100413475621000_c4"},{"key":"2019100413475621000_c5","doi-asserted-by":"crossref","first-page":"633","DOI":"10.6028\/jres.103.043","article-title":"Least-Squares Fitting Algorithms of the NIST Algorithm Testing System","volume":"103","author":"Shakarji","journal-title":"J. Res. Natl. Inst. Stand. Technol."},{"volume-title":"Least-Squares Best-fit Geometric Elements","author":"Forbes","key":"2019100413475621000_c6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3442-0_28"},{"issue":"2","key":"2019100413475621000_c7","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1137\/1036055","article-title":"Total Least Squares: State-of-the-Art Regression in Numerical Analysis","volume":"36","author":"Nievergelt","journal-title":"SIAM Rev."},{"edition":"2nd ed.","volume-title":"Computational Geometry in C","author":"O\u2019Rourke","key":"2019100413475621000_c8"},{"key":"2019100413475621000_c9","first-page":"297","article-title":"Line Geometry for 3D Shape Understanding and Reconstruction","volume-title":"European Conference on Computer Vision, Lecture Notes in Computer Science","author":"Pottmann"},{"key":"2019100413475621000_c10","doi-asserted-by":"crossref","unstructured":"Gelfand, N., and Guibas, L. J., 2004, \u201cShape Segmentation Using Local Slippage Analysis,\u201d Proceedings of the Eurographics Symposium on Geometry Processing, pp. 214\u2013223.","DOI":"10.1145\/1057432.1057461"},{"key":"2019100413475621000_c11","unstructured":"Shakarji, C. M.\n          , 2003, \u201cEvaluation of One- and Two-Sided Geometric Fitting Algorithms in Industrial Software,\u201d Proceedings of the American Society of Precision Engineering Annual Meeting, pp. 100\u2013105."},{"issue":"2127","key":"2019100413475621000_c12","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1098\/rspa.2010.0307","article-title":"Free-form Surface Filtering Using the Diffusion Equation","volume":"467","author":"Jiang","journal-title":"Proc. R. Soc. A"},{"issue":"4","key":"2019100413475621000_c13","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1109\/2945.817351","article-title":"The Ball-Pivoting Algorithm for Surface Reconstruction","volume":"5","author":"Bernardini","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"2019100413475621000_c14","doi-asserted-by":"crossref","unstructured":"Jiang, X., Zhang, X., and Scott, P., 2010, \u201cTemplate Matching of Freeform Surfaces Based on Orthogonal Distance Fitting for Precision Metrology,\u201d Meas. Sci. Technol., 21, art. no. 045101.","DOI":"10.1088\/0957-0233\/21\/4\/045101"},{"key":"2019100413475621000_c15","first-page":"511","article-title":"Uncertainty Management for CMM Probe Sampling of Complex Surfaces","volume":"4","author":"Edgeworth","journal-title":"ASME J. Manuf. Sci. Eng., MED"},{"key":"2019100413475621000_c16","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/S0141-6359(99)00004-5","article-title":"Adaptive Sampling for Coordinate Metrology","volume":"23","author":"Edgeworth","journal-title":"Precis. Eng."},{"article-title":"Simulation of Adaptive Sampling in Profile Measurement for Structured Surfaces","volume-title":"Computing and Engineering Researchers\u2019 Conference","author":"Wang","key":"2019100413475621000_c17"},{"key":"2019100413475621000_c18","first-page":"197","article-title":"Robust Global Registration","volume-title":"Proceedings of Eurographics Symposium on Geometry Processing","author":"Gelfand"},{"issue":"4","key":"2019100413475621000_c19","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1109\/TSMCB.2003.814304","article-title":"Estimating the Principal Curvatures and the Darboux Frame From Real 3-D Range Data","volume":"33","author":"Hameiri","journal-title":"IEEE Trans. Syst., Man, Cybern., Part B: Cybern."},{"issue":"2","key":"2019100413475621000_c20","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1115\/1.1887192","article-title":"Verification of Scanned Engineering Parts With CAD Models Based on Discrete Curvature Estimation","volume":"5","author":"Lipshitz","journal-title":"J. Comput. Inf. Sci. Eng."},{"key":"2019100413475621000_c21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05105-4_2","article-title":"Discrete Differential Geometry Operators for Triangulated 2-Manifolds","volume-title":"Proceedings of VisMath \u201902","author":"Meyer"},{"issue":"1","key":"2019100413475621000_c22","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/34.982886","article-title":"ICP Registration Using Invariant Features","volume":"24","author":"Sharp","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"2019100413475621000_c23","doi-asserted-by":"publisher","first-page":"3438","DOI":"10.1088\/0957-0233\/18\/11\/025","article-title":"A Weighted Total Least-Squares Algorithm for Fitting a Straight Line","volume":"18","author":"Krystek","journal-title":"Meas. Sci. Technol."}],"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\/1.3647877\/5532789\/011008_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.3647877\/5532789\/011008_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T17:48:13Z","timestamp":1570211293000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/doi\/10.1115\/1.3647877\/455404\/On-the-Enduring-Appeal-of-LeastSquares-Fitting-in"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,21]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,3,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.3647877","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"type":"print","value":"1530-9827"},{"type":"electronic","value":"1944-7078"}],"subject":[],"published":{"date-parts":[[2011,12,21]]},"article-number":"011008"}}