A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics

In this paper we propose a non-stationary uniform tension controlled interpolating 4-point scheme which provides users with a single tension parameter that, for any value in the range of definition, generates a C1-continuous limit curve. This curve scheme unifies non-stationary interpolating 4-point rules that are capable of representing elements of the linear space spanned by trigonometric, polynomial and hyperbolic functions. As a consequence, for special values of the tension parameter, such a scheme will be capable of reproducing all conic sections exactly. Additionally, progressively increasing the value of the tension parameter, we will be able to tighten the limit curve to the piecewise linear curve between the data points.