University of Guilan Journal of Mathematical Modeling 2345-394X 10 3 2022 09 01 Bound-preserving interpolation using quadratic splines 407 419 5323 10.22124/jmm.2021.19496.1676 EN Jamshid Saeidian Faculty of Mathematical Sciences and Computer, Kharazmi University, No. 50, Taleghani Avenue, Tehran, Iran 0000-0003-3991-1701 Muhammad Sarfraz Department of Information Science, College of Life Sciences, Kuwait University, Sabah AlSalem University City, Shadadiya, Kuwait Sajad Jalilian Faculty of Mathematical Sciences and Computer, Kharazmi University, No. 50, Taleghani Avenue, Tehran, Iran Journal Article 2021 05 01 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. https://jmm.guilan.ac.ir/article_5323_ed3559e2689004ef7a3feacb3ed4679e.pdf