On \(G^2\) continuous spline interpolation of curves in \(\mathbb{R}^d\) (Q1864783)

The author studies the problem of \(G^2\) continuous interpolation of curves in \(\mathbb{R}^d\) by polynomial splines of degree \(n\). If \(r\) denotes the number of interior points interpolated by each segment of the spline curve, the case \(n=r+2=d\) is completely studied. The author shows that the problem is uniquely solvable asymptotically. In order to confirm the results, a numerical example for a curve in \(\mathbb{R}^4\) is presented in the last section.