Rational trigonometric cubic spline to conserve convexity of 2D data

Researchers in different fields of study are always in dire need of spline interpolating function that conserve intrinsic trend of the data. In this paper, a rational trigonometric cubic spline with four free parameters has been used to retain convexity of 2D data. For this purpose, constraints on two of free parameters βi and γi in the description of the rational trigonometric function are derived while the remaining two αi and δi are set free. Numerical examples demonstrate that resulting curves using the technique of the underlying paper are C1.