A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

Abstract

In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C 3 continuity.

A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

“…Ashraf et al analyzed the ternary four-point rational interpolating subdivision scheme's geometric properties [18,19]. More subdivision schemes are studied in [17,[20][21][22].…”

The Family of Multiparameter Quaternary Subdivision Schemes

“…Ashraf et al [6,7] presented and analyzed the geometrical properties of four point interpolating subdivision schemes. Hameed et al [8] presented a 4-point subdivision scheme for regular curves and surfaces design.…”