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Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme

Authors
  • ashraf, pakeeza
  • nawaz, bushra
  • baleanu, dumitru
  • nisar, kottakkaran sooppy
  • ghaffar, abdul
  • ahmed khan, muhammad aqeel
  • akram, saima
Publication Date
Mar 04, 2020
Identifiers
DOI: 10.3390/math8030338
OAI: oai:mdpi.com:/2227-7390/8/3/338/
Source
MDPI
Keywords
Language
English
License
Green
External links

Abstract

Shape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geometry. With an eye on connecting the link between SSs and applied geometry, this paper analyzes the geometric properties of a ternary four-point rational interpolating subdivision scheme. These geometric properties include monotonicity-preservation, convexity-preservation, and curvature of the limit curve. Necessary conditions are derived on parameter and initial control points to ensure monotonicity and convexity preservation of the limit curve of the scheme. Furthermore, we analyze the curvature of the limit curve of the scheme for various choices of the parameter. To support our findings, we also present some examples and their graphical representation.

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