Univariate approximating schemes and their non-tensor product generalization

Abstract

This article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.

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

“…Mustafa and Bashir [14] dealt with the univariate scheme and its non-tensor product generalization of bivariate SS. The proposed schemes preserved the monotonicity of initial data.…”