Department of Mathematics, Korea Advanced Institute of Science and Technology Gu-sung Dong, Yu-sung Gu, Taejon, 305-701, Republic of Korea
Abstract:
The error analysis of Farin's and Forrest's algorithms for generating an approximation of degree n ? 1 to an nth degree Bézier curve is presented. Algorithms are based on observations of the geometric properties of the Bézier 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.