Describe C2 monotonic (rational) splines?

[mgeier]

Delbourgo R, Gregory JA. C 2 rational quadratic spline interpolation
to monotonic data. IMA J Numer Anal 1983;3:141-52.

Gregory JA, Delbourgo R. Piecewise rational quadratic interpolation
to monotonic data. IMA J Numer Anal 1982;2:123-30.