Abstract
The task of fairing a curve interpolating a given point data set and potentially given end conditions by minimizing an explicit fairness measure is discussed from the viewpoint of the resulting curve quality. Results are compared for different choices of a fairness criteria applied to a variety of data sets. The improvements achievable by going from integer to rational cubic B-spline curves are examined in particular. Fairness quality can be raised both by lessening the constraints and by increasing the freedoms in curve representation.
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References
Holladay, J. C.: Smoothest Curve Approximation. Math. Tables Aids Computations 11 (1957).
Theilheimer, F., Starkweather: The Fairing of Ship Lines on a High-Speed Computer. David Taylor Model Basin Report No. 1474, Bethesda, MD (1961).
Meier, H.: Differential Geometry Based Design and Analytic Representation of Curvature Continuous Ship Surfaces and Similar Free Form Surfaces. Diss., TU Berlin, VDI-Verlag, Reihe Rechnerunterstützte Verfahren, 20 (5), in German, Düsseldorf (1987).
Meier, H., Nowacki, H.: Interpolating Curves with Gradual Changes in Curvature. Computer Aided Geometric Design 4 (1987), XX-YY.
Hohenberger, W., Reuding, T.: Smooth rational B-Spline curves using the weights in an optimization procedure. Computer Aided Geometric Design 12 (1995) 8, 837–848.
Neider, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7 (1965), 308–313.
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© 1996 B. G. Teubner Stuttgart
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Nowacki, H., Heimann, J., Melissaratos, E., Zimmermann, SH. (1996). Experiences in Curve Fairing. In: Hoschek, J., Kaklis, P.D. (eds) Advanced Course on FAIRSHAPE. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-82969-6_1
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DOI: https://doi.org/10.1007/978-3-322-82969-6_1
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-519-02634-1
Online ISBN: 978-3-322-82969-6
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