Rational C1 cubic Powell–Sabin B-splines with application to representation of ruled surfaces

Abstract

This paper defines rational $C^1$ cubic Powell–Sabin splines and analyses their basic properties. A rational B-spline basis is established and an algorithm for determining the corresponding control points and weights by using the blossoming operator is presented. The capability of the introduced splines to represent rational cubic triangular Bézier patches and quadratic NURPS is discussed and explicit conversion formulas are provided. Moreover, the application of the rational $C^1$ cubic Powell–Sabin splines to representation of ruled surfaces is studied, showing that the cubic splines can give smoother parametrizations than the NURPS.