On spline interpolation of space data

In this paper the interpolation by G continuous Bezier spline curves Bn in IR is outlined. Each segment of the spline curve interpolates r interior and two boundary points. The general approach is followed in detail for the case d = 3, n = 3, r = 1. For the single component case, the optimal approximation order is proved, and asymptotic existence established. The interpolation scheme is demonstrated by practical experiments. §