Bound-preserving interpolation using quadratic splines

In this work, we study a data visualization problem which is classified in the field of shape-preserving interpolation. When   function  is known to be bounded, then it is  natural to expect its interpolant to adhere boundedness. Two spline-based techniques are proposed to handle this kind of problem. The proposed methods   use quadratic splines as basis and involve solving a linear programming or a mixed integer linear  programming problem which gives C^۱ interpolants. An energy minimization technique is employed to gain the optimal smooth solution. The reliability  and  applicability of  the proposed techniques  have been illustrated through examples.

Keywords:

Shape preserving interpolation , Boundedness , quadratic splines , Linear programming