Abstract
An algorithm for approximation of arbitrary clouds of points with integral tensor product B-spline surfaces is presented. The clouds may be scattered may have holes and may have arbitrary boundaries. The usual methods in Reverse Engineering subdivide the given cloud into rectangular parts and approximate these parts individually. In the presented paper an overall algorithm for tensor product B-spline approximation with free boundary curves is introduced.
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References
Bloor, M. I. G., Wilson, M. J. and Hagen, H.: The smoothing properties of variational schemes for surface design. Computer Aided Geometric Design 12 (1995), 381–394.
Farin, G.: Curves and Surfaces for Computer Aided Geometric Design — A Practical Guide. 3. ed. Academic Press 1993.
Greiner, G.: Variational design and fairing of spline surfaces. Computer Graphics Forum 13:3 (1994), 143–154.
Grossmann, M.: Parametric curve fitting. The Computer Journal 14 (1970), 169–172.
Hadenfeld, J.: Local energy fairing of B-spline surfaces. In M. Daehlen, T. Lyche, and L. L. Schumaker (eds.): Mathematical Methods in CAGD III, (1995), 203–212.
Hagen, H., Schulze, G.: Automatic smoothing with geometric surface patches. Computer Aided Geometric Design 4 (1987), 231–235.
Hoschek, J., Lasser, D.: Grundlagen der geometrischen Datenverarbeitung. 2. Auflage, Teubner 1992.
Hoschek, J., Schneider, F.-J., Wassum, P.: Optimal approximate conversion of spline surfaces. Computer Aided Geometric Design 6 (1989), 293–306.
Hoschek, J., Schneider, F.-J.: Approximate spline conversion for integral and rational Bézier and B-spline surfaces. In R. E. Barnhill (ed.): Geometry Processing for Design and Manufacturing, SIAM (1992), 45–86.
Ma, W., Kruth, J. P.: Parametrization of randomly measured points for least squares fitting of B-Spline curves and surfaces. Computer-Aided Design 27 (1995), 663–675.
Moreton, H. P., Séquin, C. H.: Functional optimization for fair surface design. ACM Computer Graphics 26 (1992), 167–176.
Pratt, M. J.: Smooth parametric surface approximations to discrete data. Computer Aided Geometric Design 2 (1985), 165–171.
Rando, T., Roulier, J.A.: Designing faired parametric surfaces. Computer-Aided Design 23 (1991), 492–497.
Schmidt, R. M.: Fitting scattered surface data with large gaps. Surfaces in CAGD, R. E. Barnhill, W. Boehm (eds.), (1983), 185–189.
Sinha, S. S., Schunck, B. G.: A two-stage algorithm for discontinuity-preserving surface reconstruction. IEEE Transactions on Pattern Analysis and Machine Intelligence 14 (1992), 36–55.
Terzopoulos, D.: Regularization of inverse visual problems involving discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence 8 (1986), 413–424.
Welch, W., Witkin, A.: Variationai surface modeling. ACM Computer Graphics 26 (1992), 157–166.
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© 1996 B. G. Teubner Stuttgart
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Hoschek, J., Dietz, U. (1996). Smooth B-Spline Surface Approximation to Scattered Data. In: Hoschek, J., Dankwort, W. (eds) Reverse Engineering. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-84819-2_12
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DOI: https://doi.org/10.1007/978-3-322-84819-2_12
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-519-02633-4
Online ISBN: 978-3-322-84819-2
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