代数曲线的近似参数化

Approximate Parametric Representation of Algebraic Curves

给出了一种用分段三次、整体Ｇ１连续的参数曲线逼近一条平面代数曲线的算法．同文［１］的算法相比，该方法具有更好的逼近精度．实例表明，为达到同样的逼近精度，该方法在分割段数与所花费时间上约为［１］中方法的一半．此外，还给出了一种新的逼近意义下的误差估计．

An algorithm is proposed to approximate planar algebraic curves with G1 piecewise cubic parametric curves. Compared with, the proposed algorithm boasts better convergence. Examples show that for the same approximation error, the algorithm presented in this paper only costs half the time and demands half of the subdividing segments required by the algorithm in. Furthermore, a new error bound is provided.