## Circular splines.(English)Zbl 0763.65005

A circular spline is a $$C^ 1$$ curve consisting of circular arcs which join at the knots $$P_ 1,\dots,P_ n$$. The author considers the problem of interpolating a given point set (open or closed) in $$\mathbb{R}^ 2$$ and $$\mathbb{R}^ 3$$ by circular splines with knots at the interpolation points. The circular arcs are presented in terms of Bézier curves. He also presents an algorithm for approximation of point sets in $$\mathbb{R}^ 2$$ consisting of $$n$$ points by circular splines with $$m$$ knots, $$m<n$$.

### MSC:

 65D07 Numerical computation using splines 41A15 Spline approximation 41A05 Interpolation in approximation theory 65D05 Numerical interpolation
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