基于三次PH 曲线误差可控代数曲线等距线逼近算法

论文提出一种用三次PH 曲线逼近代数曲线的方法及其误差分析。使用该 方法，给出一种用PH 曲线的等距线来逼近原来代数曲线等距线的算法。逼近曲线保持了原 曲线的一些重要几何性质，如单调性、凹凸性、G1 连续性等。数值实验表明，该算法提供 了代数曲线近似参数化的一条有效途径。并在此基础上提出了一种计算代数曲线等距线的有 理参数表示的新方法。

Error controllable algebraic curve offset approximation basedon cubic PH curve

A new algorithm that constructs offsets of a planar algebraic curve by approximating the algebraic curve with piecewise cubic PH curve is proposed. The approximation errors are also estimated. The approximate PH curve keeps some important geometric features of the original algebraic curve such as convexity, monotonicity and G1 continuity. Numerical experiments show that the algorithm provides an efficient approach to approximate parameterization of algebraic curves. The algorithm also provides a new method to calculate rational parameter representation of the algebraic curve offsets.