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, \(m<n\).


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