A Family of Integer-Point Ternary Parametric Subdivision Schemes

Ghulam Mustafa,Muhammad Asghar,Ayesha Afzal,Jia-Bao Liu,Shafqat Ali,M M Bhatti

doi:10.1155/2021/9281006

Ghulam Mustafa, Muhammad Asghar + Show 4 more

Open Access

https://doi.org/10.1155/2021/9281006

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Abstract

New subdivision schemes are always required for the generation of smooth curves and surfaces. The purpose of this paper is to present a general formula for family of parametric ternary subdivision schemes based on the Laurent polynomial method. The different complexity subdivision schemes are obtained by substituting the different values of the parameter. The important properties of the proposed family of subdivision schemes are also presented. The continuity of the proposed family is C 2 m . Comparison shows that the proposed family of subdivision schemes has higher degree of polynomial generation, degree of polynomial reproduction, and continuity compared with the exiting subdivision schemes. Maple software is used for mathematical calculations and plotting of graphs.

Highlights

Computer aided geometric design (CAGD) is a field which is related to computational mathematics
We presented a general formula for derivation of parametric family of ternary subdivision schemes
We presented the complete analysis of the proposed family of parametric ternary subdivision schemes

Summary

Introduction

Computer aided geometric design (CAGD) is a field which is related to computational mathematics. In 2002, Hassan et al [1] purposed a family of interpolating 3-point ternary subdivision schemes with C1-continuity. Siddiqi et al [7,8,9] introduced a family of ternary interpolatory and approximating subdivision scheme with one parameter. Ashraf et al [11, 12] presented and analyzed the geometrical properties of the 4-point ternary interpolating subdivision scheme. Hameed et al [15] presented a new method to construct a family of (2N + 2)-point binary subdivision schemes with one tension parameter. E main purpose of this work is to present a generalized formula for derivation of parametric ternary subdivision schemes.

A Family of Integer-Point Ternary Schemes

Comparison with Existing Schemes

Conclusions