Shape-Preservation of the Four-Point Ternary Interpolating Non-stationary Subdivision Scheme

• Main Authors: Pakeeza Ashraf, Mehak Sabir, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Ilyas Khan
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2020-01-01
• Series: Frontiers in Physics
• Subjects: interpolating; non-stationary; shape-preservation; subdivision scheme; ternary
• Online Access: https://www.frontiersin.org/article/10.3389/fphy.2019.00241/full

In this paper, we present the shape-preserving properties of the four-point ternary non-stationary interpolating subdivision scheme (the four-point scheme). This scheme involves a tension parameter. We derive the conditions on the tension parameter and initial control polygon that permit the creation of positivity- and monotonicity-preserving curves after a finite number of subdivision steps. In addition, the outcomes are generalized to determine conditions for positivity- and monotonicity-preservation of the limit curves. Convexity-preservation of the limit curve of the four-point scheme is also analyzed. The shape-preserving behavior of the four-point scheme is also shown through several numerical examples.