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COMPUTING
2004

Spline Curve Approximation and Design by Optimal Control Over the Knots

13 years 3 months ago
Spline Curve Approximation and Design by Optimal Control Over the Knots
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 [17] 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. An interesting aspect is that the interpolation or the approximation matrix might become singular due to invalid knot vector values with respect to the current parametrization (violation of Schoenberg-Whitney condition). This situation is dealt naturally within the Optimal Control framework. A geometric description of the resulting null space is provided as well.
Rony Goldenthal, Michel Bercovier
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMPUTING
Authors Rony Goldenthal, Michel Bercovier
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