A new family of convex splines for data interpolation

This paper develops a new family of convexity-preserving splines of order n, hereby entitled the CPn-spline, that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term, and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. Numerical results that allow for an assessment of the new spline are provided. In particular, a comparative analysis of the CPn-spline, the cubic spline, and of the Carnicer '92 spline is performed. By varying two parameters, the spline shape can be controlled at the local level, while other conventional means can be used to control the shape at the global level. The CPn-sptine has no singularities in the case where inflection points are present. Additionally, a less general form of the CPn-spline that applies to most practical cases can be implemented with extreme ease. © 1997 Elsevier Science B.V.