Abstract
Automatic control of plotters, tool machines, or robots is getting more and more important in industry. Most of the tools to be controlled require a smooth movement at a speed as high as possible, with respect to the materials of tool and work-piece. Often the movement is steered via several joints giving rise to a fairly high dimension of the control space. In this paper, parametric splines are used to handle such problems and a method for the optimal choice of the knot parameters is presented.
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References
Ahlberg, J.H., Nilson, E.N., Walsh, J.L.: The Theory of Splines and Their Applications. New York and London, Aca demic Press 1967
Bär, G. : Parametrische Interpolation empirischer Raumkurven. ZAMM 57(1977), 305–314
Böhm, W.: Cubic B-Spline Curves and Surfaces in Computer Aided Geometric Design. Computing 19(1977), 29–34
Brodlie, K.W.: A Review of Methods for Curve and Function Drawing; in Brodlie, K.W.(editor): Mathematical Methods in Computer Graphics and Design. London, New York, Academic Press 198O, 1–37
Glass, J.M.: Smooth-Curve Interpolation: A Generalised Spline-Fit Procedure. BIT 6(1966), 277–293
Lee, E.H., Forsythe, G.E.: Variational Study of Nonlinear Spline Curves. SIAM Review 15(1973), 120–133
Malcolm, M.A.: On the Computation of Nonlinear Spline Functions. SIAM J.Numer.Anal. 14(1977), 254–282
Mehlum, E.: Curve and surface fitting based on variational criteria for smoothness. Ph.D. dissertation, Dept. of Math. Univ. of Oslo, Norway (1969)
Schmidt, R.: Spline-Prozeduren. Hahn-Meitner-Institut für Kernforschung Berlin GmbH, Bericht Nr. HMI-B 220, 1976
Woodford, C.H.: Smooth Curve Interpolation. BIT 9(1969), 69–77
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© 1982 Birkhäuser Verlag Basel
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Töpfer, HJ. (1982). Models for Smooth Curve Fitting. In: Collatz, L., Meinardus, G., Werner, H. (eds) Numerical Methods of Approximation Theory, Vol.6 / Numerische Methoden der Approximationstheorie, Band 6. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 59. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7186-0_16
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DOI: https://doi.org/10.1007/978-3-0348-7186-0_16
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7188-4
Online ISBN: 978-3-0348-7186-0
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