A New Approach of Constrained Interpolation Based on Cubic Hermite Splines

Abstract

Suppose we have a constrained set of data and wish to approximate it using a suitable function. It is natural to require the approximant to preserve the constraints. In this work, we state the problem in an interpolating setting and propose a parameter-based method and use the well-known cubic Hermite splines to interpolate the data with a constrained spline to provide with a $C^1$ interpolant. Then, more smoothing constraints are added to obtain $C^2$ continuity. Additionally, a minimization criterion is presented as a theoretical support to the proposed study; this is performed using linear programming. The proposed methods are demonstrated with illustrious examples.