Modeling of curves by a design-control approximating refinement scheme

Abstract

This paper introduces a modified method for construction of a new design-control 6-point approximating refinement scheme. The construction of the new scheme is based on translation of the points of 4-point approximating refinement scheme to the new position according to the linear combination of certain displacement vectors. The initial and terminal points of these vectors are the refinement points of two 4-point approximating binary schemes. The new scheme contains three design-control parameters. These parameters increase the efficiency and flexibility of the new scheme. The mathematical and graphical analysis of the refinement scheme show that this scheme is good choice for curve modeling.

Keywords:

• Approximating refinement scheme
• curve
• design-control parameter
• Gibbs oscillation

MSC[2010]:

• 65D07
• 65D10
• 68U07
• 65D17

Disclosure statement

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Data availability

The data used to support the findings of the study is available within this paper.