Shape Preserving C2-Spline Histopolation Original Research Article

In this paper, an area matching approximation of histograms is considered under constraints like convexity, monotonicity, or positivity. Using rational-lacunary C2-splines, sufficient conditions for the existence of convex, monotone, or positive histosplines as well as algorithms for constructing them effectively are given. Moreover, the existence criteria are shown to be satisfied for sufficiently large rationality or lacunarity parameters.