Comonotone shape-preserving spline histopolation

Algorithms are presented for the construction of histopolating splines consisting of linear/linear rational or quadratic polynomial pieces. A unique comonotone histospline of such kind exists for any histogram with weak alternation of data. In general case, without weak alternation of data, a modified comonotone spline histopolation strategy should be used. The method is implemented via the representation with histogram heights and knot values of first derivatives of the spline. Numerical examples are given.