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 $C^1$ 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.