椭圆offset曲线的多项式逼近算法

A Polynomial Approximation Algorithm for Calculating Offsets of Ellipse Curves

首先对椭圆进行必要的细分,然后将每一段椭圆弧的offset曲线用一段Bézier曲线逼近,进而得到G1连续的分段Bézier曲线作为椭圆offset曲线的近似.该算法一方面给出了计算Bézier曲线段控制顶点的表达形式,计算简单;另一方面对offset曲线的逼近误差给出了整体估计,并且利用整体误差估计决定细分椭圆的段数,构造了满足给定容差的近似曲线.

An algorithm to approximate offsets of ellipse curves by piecewise cubic Bézier segments is proposed. After some necessary partition, the offset curve of each elliptic arc is approximated by a cubic Bézier segment. And then the whole offset curve with G^1 is obtained. On one hand, the algorithm is simple to calculate because the control points of the Bézier segment can be expressed explicitly. On the other hand, the global error estimation for the algorithm is given. The error estimation can be used to determine the number of the segments in the partition of the ellipse.é