Efficient Piecewise Linear Approximation of Bezier Curves with Improved Sharp Error Bound

摘要

This paper presents an efficient algorithm for piecewise linear approximation of Bezier curves with improved sharp error bound. Given a Bezier curve of arbitrary degree, an approximation polygon having the same number of vertices as that of the control polygon is obtained through efficient local refinement of the initial control vertices. The approximation produces improved error bound compared with several existing solutions. With the explicit sharp error bound, it is also possible for prior estimation of necessary subdivisions to meet a pre-defined tolerance. The approximation can also be locally and adap-tively refined for reducing the number of vertices of the piecewise linear approximation while meeting the required tolerance.