Goldenthal, R.; Bercovier, M. Spline curve approximation and design by optimal control over the knots. (English) Zbl 1078.41012 Computing 72, No. 1-2, 53-64 (2004). 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. Reviewer: Manfred Tasche (Rostock) Cited in 3 Documents 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) Keywords:curve fitting; spline curve; interpolation; approximation; knot vector placement; optimal control; reparametrization; Schoenberg-Whitney condition Citations:Zbl 0910.68214 PDFBibTeX XMLCite \textit{R. Goldenthal} and \textit{M. Bercovier}, Computing 72, No. 1--2, 53--64 (2004; Zbl 1078.41012) Full Text: DOI