Construct Polynomial of Degree n by Using Repeated Linear Interpolation

Abstract

In this paper the fundamental concept of repeated linear interpolation and its possible applications in computer-aided geometric design, and start considering basic constructive methods for curves and surfaces. We discuss here a repeated linear interpolation method that we commonly find in computer graphics and geometric modelling. Repeated linear Interpolation means to calculate a polynomial by using several points. For a given sequence of points, this means to estimate a curve that passes through every single point. The purpose of this paper is to construct a polynomial of degree less than or equal to n, by using repeated linear Interpolation.