Fitting weighted total least-squares planes and parallel planes to support tolerancing standards

Proceedings of the ASME Design Engineering Technical Conference

Volumn 2, Issue PARTS A AND B, 2012, Pages 449-459

  Shakarji, Craig M ^a   Srinivasan, Vijay ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DESIGN; EIGENVALUES AND EIGENFUNCTIONS; POINT CONTACTS;

A-PLANE; LEAST SQUARE SENSE; LEAST SQUARES FITTING; LEAST-SQUARES PLANE; ORTHOGONAL LEAST SQUARES; PARALLEL PLANES; POINT SAMPLING; SIMPLE++; TOLERANCING; WEIGHTED TOTAL LEAST SQUARES;

SINGULAR VALUE DECOMPOSITION;

EID: 84884641659     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2012-70398     Document Type: Conference Paper

References (16)

1. International Organization for Standardization (ISO), 2010, "ISO 14405-1:2010, Geometrical product specifications (GPS) - Dimensional tolerancing - Part 1: Linear sizes".
2. International Organization for Standardization (ISO), "ISO 1101:(future), Geometrical tolerancing - Tolerances of form, orientation, location and run-out".
3. International Organization for Standardization (ISO), "ISO 14405-3:(future), Geometrical product specifications (GPS) - Dimensional tolerancing - Part 3: Angular sizes".
4. Parratt, S., and Voelcker, H., 1997, "Do You Know How to Tolerance a Hinge?, " mfg., Brown & Sharpe Manufacturing Company, pp. 42-43.
5. Shakarji, C. M., 1998, "Least-squares fitting algorithms of the NIST algorithm testing system, " J. Res. Natl. Inst. Stand. Technol., 103, pp. 633-641.
6. Forbes, A., "Least-squares best-fit geometric elements, " NPL Report, April 1989.
7. Nievergelt, Y., 1994, "Total least squares: State-of-The-Art regression in numerical analysis, " SIAM Review, pp. 258-264.
8. Nievergelt, Y., 2001, "Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares, " Linear Algebra and its Applications, 331, pp. 43-51.
9. de Groen, P., 1996, "An Introduction to Total Least Squares, " Nieuw Archief voor Wiskunde, Vierde serie, deel 14, pp. 237-253.
10. Krystek, M., and Anton, M., 2007, "A weighted total least-squares algorithm for fitting a straight line, " Meas. Sci. Technol., 18, pp. 3438-3442.
11. Srinivasan, V., Shakarji, C. M., and Morse, E. P., 2012, "On the Enduring Appeal of Least-Squares Fitting in Computational Coordinate Metrology, " ASME Journal of Computing and Information Science in Engineering, 12(1).
12. Shakarji, C. M., 2011, "Coordinate Measuring System Algorithms and Filters, " Coordinate Measuring Machines and Systems, R. J. Hocken, and P. H. Pereira, eds., CRC Press, pp. 153-182.
13. Krommer, A. R., and Ueberhuber, C. W., 1998, Computational integration, Society for Industrial and Applied Mathematics, Philadelphia.
14. Stewart, G. W., 1973, Introduction to matrix computations, Academic press, New York.
15. Meyer, C. D., and Stewart, G. W., 1988, "Derivatives and Perturbations of Eigenvectors, " SIAM Journal on Numerical Analysis, 25(3), pp. 679-691.
16. Watkins, D. S., 1991, Fundamentals of matrix computations, John Wiley and Sons, New York.