The Precise Measurement of Free-Form Surfaces

[+] Author and Article Information
William Wolovich, Hulya Yalcin

Division of Engineering, Brown University, Providence, RI 02912

Hassan Albakri

Dept. of Engineering, Cornell University, Ithaca, NY 14850

J. Manuf. Sci. Eng 124(2), 326-332 (Apr 29, 2002) (7 pages) doi:10.1115/1.1430677 History: Received April 01, 2000; Revised April 01, 2001; Online April 29, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Farin, Gerald, 1993, Curves and Surfaces for CAGD: A Practical Guide (Third Edition), Academic Press.
Mortenson, Michael E., 1997, Geometric Modeling (Second Edition), Wiley Computer Publishing.
Yamaguchi, Fujio, 1988, Curves and Surfaces in Computer Aided Geometric Design, Springer-Verlag.
Patrikalakis,  N. M., and Bardis,  L., 1991, “Localization of Rational B-Spline Surfaces,” Eng. Comput., 7, pp. 237–252.
Tuohy,  S. T., Maekawa,  T., Shen,  G., and Patrikalakis,  N. M., 1997, “Approximation of Measured Data with Interval B-Splines,” Comput.-Aided Des., 29, No. 11, pp. 791–799.
Wang,  Y., 1992, “Minimum Zone Evaluation of Form Tolerances,” Manufacturing Review, 5, No. 3, pp. 213–220.
Wang,  Y., Gupta,  S., Hulting,  F., and Fussell,  P., 1998, “Manufactured Part Modeling (MPM) for Characterization of Geometric Variations of Automotive Spaceframe Extrusions,” ASME J. Manuf. Sci. Eng., 120 (3), pp. 523–531.
Choi,  W., and Kurfess,  T. R., 1999, “Dimensional Measurement Data Analysis Part I, a Zone Fitting Algorithm,” ASME J. Manuf. Sci. Eng., 121, No. 2, pp. 238–245.
Choi,  W., and Kurfess,  T. R., 1999, “Dimensional Measurement Data Analysis Part II, Minimum Zone Evaluation Design,” ASME J. Manuf. Sci. Eng., 121, No. 2, pp. 246–250.
Sahoo,  K. C., and Menq,  C. H., 1991, “Localization of 3-D Objects Having Complex Sculptured Surfaces Using Tactile Sensing and Surface Description,” ASME J. Ind., 113, pp. 85–92.
Kurfess,  T., and Banks,  D., 1995, “Statistical Verification of Conformance to Geometric Tolerance,” Comput.-Aided Des., 27 (5), pp. 353–361.
Choi,  W., and Kurfess,  T. R., 1998, “Uncertainty of Extreme Fit Evaluation for Three Dimensional Measurement Data Analysis,” Comput.-Aided Des., 30, No. 7, pp. 549–557.
Bispo, Edvaldo, M., and Fisher, Robert B., 1996, “Free-Form Surface Matching for Surface Inspection,” The Mathematics of Surfaces VI, Clarendon Press, pp. 119–136.
Chazelle, Bernard, 1997, “Application Challenges to Computational Geometry,” CG Impact Task Force Report, Department of Computer Science, Princeton University, Princeton, NJ.
Hoffmann, Christoph M., 1989, Geometric & Solid Modeling, Morgan Kaufmann Publishers, Inc.
Sederberg, T. W., Anderson, D. C., and Goldman, R. N., 1984, “Implicit Representation of Parametric Curves and Surfaces,” Computer Vision, Graphics and Image Processing, pp. 72–84, Academic Press.
Bloomenthal, Jules, 1998, Proceedings of Implict Surfaces ’98, The Third International Workshop on Implicit Surfaces, Seattle, Washington, June 15–16.
Tarel, Jean-Phillipe, Wolovich, William A., and Cooper, David B., 1998, “Covariant-Conics Decomposition of Quartics for 2D Object Recognition and Affine Alignment,” Proceedings of the 1998 IEEE International Conference on Image Processing, October 4–7, Chicago, Illinois.
Unel, Mustafa, and Wolovich, William A., 1998, “Complex Representations of Algebraic Curves,” Proceedings of the 1998 IEEE International Conference on Image Processing, October 4–7, Chicago, Illinois.
Unel,  Mustafa, and Wolovich,  William A., 1998, “Pose Estimation and Object Identification Using Complex Algebraic Representations,” Pattern Analysis and Applications, 1, pp. 178–188.
Unel, Mustafa, and Wolovich, William A., 1998, “Fitting Circle Polynomials to Planar Objects,” Proceedings of the First International Workshop on Computer Vision, Pattern Recognition and Image Processing, October 23–28, Research Triangle Park, NC.
Unel, Mustafa, and Wolovich, William A., 1999, “Shape Control Using Primitive Decompositions,” Proceedings of the 1999 International Conference on Shape Modeling and Applications, March 1–4, Aizu-Wakamatsu, Japan.
Wolovich,  William A., and Unel,  Mustafa, 1998, “The Determination of Implicit Polynomial Canonical Curves,” IEEE Trans. Pattern Anal. Mach. Intell., 20, No. 10, pp. 1080–1089.
Wolovich, William A., and Unel, Mustafa, 1998, “Vision-Based System Identification and State Estimation,” The Confluence of Vision and Control, Lecture Notes in Control and Information Systems 237, Springer, pp. 171–182.
Lei,  Z., Blane,  M. M., and Cooper,  D. B., 2000, “The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data,” IEEE Trans. Pattern Anal. Mach. Intell., 22, No. 3, pp. 298–313.
Redding, R. J., and Whatmough, R., 1997, “Fitting Implicit Quartics For Use In Feature Extraction,” Proceedings of the International Conference on Image Processing, Santa Barbara, CA. October.
Tarel, Jean-Phillipe, Civi, Hakan, and Cooper, David B., 1997, “Pose Estimation of Free-Form 3D Objects without Point Matching using Algebraic Surface Models,” Technical Report LEMS-167, September.
Taubin, G., Cukierman, F., Sullivan, S., Ponce, J., and Kriegman, D. J., 1994, “Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting,” IEEE Trans. Pattern Anal. Mach. Intell., 16 , No. 3.
Bosch, John A., 1995, Coordinate Measuring Machines and Systems, Marcel Dekker, Inc.
Taubin,  Gabriel, 1991, “Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation,” IEEE Trans. Pattern Anal. Mach. Intell., 13, No. 11, pp. 1115–1137.
Boissonnat,  J. D., 1988, “Shape Reconstruction from Planar Cross-Sections,” Comput. Vis. Graph. Image Process., 44, pp. 1–29.
Castillo,  Enrique, and Iglesias,  Andres, 1997, “Some Characterizations of Families of Surfaces Using Functionsl Equations,” ACM Trans. Graphics, 16 (3), pp. 296–318.
Muller, H., and Klingert, A., 1993, “Surface Interpolation from Cross Sections,” Focus on Scientific Visualization, Springer-Verlag, pp. 130–189.
Schumaker, Larry L., 1990, “Reconstructing 3D Objects from Cross-Sections,” Computation of Curves and Surfaces, Kluwer Academic Publishers, pp. 275–309.
CRC Standard Mathematical Tables and Formulas, 30th Edition, 1996, CRC Press, pp. 305.


Grahic Jump Location
Determining ≈2-D ⊥ distance errors
Grahic Jump Location
Determining ≈3-D ⊥ distance errors
Grahic Jump Location
Analogous 3-D trajectories
Grahic Jump Location
Red 3L IP fits of blue measured profiles 1 (top), 3 (middle) and 5 (bottom)
Grahic Jump Location
A closer view (model) blade A measurements
Grahic Jump Location
3-D Distance errors to model surface
Grahic Jump Location
Profile 5 perpendicular distances
Grahic Jump Location
Profile 3 perpendicular distances
Grahic Jump Location
Profile 1 perpendicular distances




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In