Spline Curve Approximation and Design by Optimal Control Over the Knots

Rony Goldenthal () and Michel Bercovier ()
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Rony Goldenthal: Hebrew University, School of Computer Science and Eng.
Michel Bercovier: Hebrew University, School of Computer Science and Eng.

A chapter in Geometric Modelling, 2004, pp 53-64 from Springer

Abstract: Abstract In [1] Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in [16] is that it can handle both approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control over the knot vectors of non-uniform B-Splines. Violation of Schoenberg-Whitney condition is dealt naturally within the Optimal Control framework. A geometric description of the resulting null space is provided as well.

Keywords: Knot vector placement; curve fitting; interpolation; optimal control; schoenberg-whitney condition; 41A15; 49N99; 65K10; 65D05; 65D07; 65D10; 65D17 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-0587-0_5

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DOI: 10.1007/978-3-7091-0587-0_5

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