Monotone linear rational spline interpolation (Q1200991)

A method for interpolating a monotone data sequence (values and derivatives) with a \(C^ 1\) monotone linear rational \(B\)-spline (LRBS) is presented, with some test results. The LRBS accepts any set of monotonic data with compatible derivatives but it cannot handle zero slope which is undesirable in curve parametrization anyway [cf. \textit{J. A. Gregory} and \textit{R. Delbourgo}, IMA J. Numer. Anal. 2, 123-130 (1982; Zbl 0481.65004)]. The LRBS has the advantage that it does not raise the degree of a curve when used for reparametrization. An explicit expression for reparametrization with LRBS was given by \textit{E. T. Y. Lee} and \textit{M. L. Lucian} [Computer Aided Geom. Design 8, 213-215 (1991)].