This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.

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Let$S$denote the class of schlicht functions. D. Bertilsson proved recently that for$f∈S, p<0$and$1<-N<-2|p|+1$the modulus of the$N$th Taylor coefficient of ($f′$)^{$p$}takes its maximal value if$f$is the Koebe function. Here a short proof of a generalisation of this result is presented.

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