Shape-Preservation of the Four-Point Ternary Interpolating Non-stationary Subdivision Scheme - Ashraf, Pakeeza; Sabir, Mehak; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Khan, Ilyas (Frontiers in Physics, 2020)
The shape-preserving properties of the ternary four-point interpolating non-stationary subdi4 vision scheme (four-point scheme) are discussed in this paper. Necessary conditions on initial 5 control points which permit to create positivity and monotonicity preserving curves after a finite 6 number of subdivision steps are derived. Moreover, convexity preserving the property of the four7 point scheme is also examined. In addition, the outcomes are generalized to determine conditions 8 for the shape-preservation of the limit curves. Graphical representation of the shape-preserving 9 limit curves of the four-point scheme are illustrated through several examples.