Constrained Control of a Rational Interpolant
In this paper, a rational cubic spline interpolation has been constructed using the rational cubic spline with quadratic denominator and the rational cubic spline based on function values. The spline can preserve monotonicity of the data set. The spline not only belongs to in the interpolating interval, but could also be used to constrain the shape of the interpolant curve such as to force it to be the given region. The explicit representation is easily constructed, and numerical experiments indicate that the method produces visually pleasing curves.
Helen Zhang, Gang Shen and David Jin
M. Tian and H. L. Geng, "Constrained Control of a Rational Interpolant", Advanced Materials Research, Vols. 225-226, pp. 170-173, 2011