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Spline curve approximation and design by optimal control over the knots. (English) Zbl 1078.41012

Optimal control methods over reparametrization for curve design were introduced in M. Alhanaty and M. Bercovier [Comput. Aided Des. 33, 167–182 (2001)]. The advantage of optimal control over global minimization such as in T. Speer, M. Kuppe and J. Hoschek [Comput. Aided Geom. Des. 15, 869–877 (1998; Zbl 0910.68214)] is that it can handle both spline curve approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest curve, minimal approximation error). In this paper, the authors study the optimal control over the knot vectors of non-uniform B-spline curves. 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.

MSC:

41A15 Spline approximation
49N90 Applications of optimal control and differential games
65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)

Citations:

Zbl 0910.68214
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