Admissible slopes for monotone and convex interpolation

In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of various C1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials, C1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions. © 1987 Springer-Verlag.