Degree reduction of Bezier curves and its error analysis

Abstract The error analysis of an algorithm for generating an approximation of degree n − 1 to an nth degree Bézier curve is presented. The algorithm is based on observations of the geometric properties of Bézier curves 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.