AUTHOR=Ashraf Pakeeza , Sabir Mehak , Ghaffar Abdul , Nisar Kottakkaran Sooppy , Khan Ilyas 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 7 - 2019

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00241

DOI=10.3389/fphy.2019.00241

ISSN=2296-424X

ABSTRACT=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.