A Family of Integer-Point Ternary Parametric Subdivision Schemes

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.

Geometric Modelling of a Family of 4-Point Ternary Approximating Subdivision Scheme U_φ with Visual Performance

“…Mustafa et al a new family of ternary SDS by using integer vertex mesh at every successive refinement level. The integer parameter generates a variety of smooth curves [14]. A new class of combined ternary subdivision techniques for curve design was presented by Mustafa et al…”