The error analysis for degree reduction of Bezier curves

Abstract

The error analysis of Farin's and Forrest's algorithms for generating an approximation of degree n - 1 to an n(th) degree Bezier curve is presented. Algorithms are based on observations of the geometric properties of the Bezier curve which allow the development of detailed error analysis. By combining subdivision with a degree reduction algorithm, a piecewise approximation can be generated, which is within some preset error tolerance of the original curve. The number of subdivisions required can be determined a priori and a piecewise approximation of degree m can be generated by iterating the scheme.