Shape-preserving interpolation by splines using vector subdivision (Q1774020)

In this paper, spline approximations are studied which are to be computed by subdivision methods. Special attention is given to shape-preservation of these splines which appears here as a local convexity preservation property. Local monotonicity preservation is also addressed. In order to obtain this, cubic splines are used. They are computed by a vector subdivision scheme. The splines are able to satisfy Hermite interpolation conditions, i.e. function values as well as first and second derivatives. The algorithm for computing these splines is given, as well as several numerical and graphical examples.