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Keywords:
curves; curvature; prescribed tangent vectors; Lienhard's interpolation
curves; curvature; prescribed tangent vectors; Lienhard's interpolation
Summary:
This paper deals with the constructions of interpolation curves which pass through given supporting points (nodes) and touch supporting tangent vectors given at only some of these points or, as the case may be, at all these points. The mathematical kernel of these constructions is based on the Lienhard's interpolation method. Formulae for the curvature of plane and space interpolation curves are derived.
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References:
[1] H. Lienhard: Interpolation von Funktionswerten bei numerischen Bahnsteuerungen. Undated publication of CONTRAVES AG, Zürich. Zbl 0147.35803
[2] J. Matušů: The Lienhard interpolation method and some of its generalizations. (in Czech). Acta Polytechnica - Práce ČVUT, Prague, 3 (IV, 2), 1978.
[3] J. Matušů J. Novák: Constructions of interpolation curves from given supporting elements (I). The publication is to appear in the 1985 volume of the journal Aplikace matematiky, Prague. MR 0813532
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