Offset曲线的区间多项式逼近

用一个较简单的逼近格式去逼近：Bezier曲线的offset曲线，即用一个三次参数曲线去逼近offset曲线．通过分析逼近误差而由此给出了offset曲线的区间多项式逼近，即得到了一个包含offset曲线的区间Bezier曲线．同时给出了区间Beier曲线的区间控制点的大小与Bezier曲线控制顶点之间的关系．最后举出实例说明这种逼近方法可以与细分技术结合达到很好的逼近效果．

Interval Polynomial Curves Approximation of Offset Curves

This paper is devoted to the study of an approximation algorithm of offset curves for the parametric Bézier curves. By considering the error of approximation, we give an interval polynomial approximation of the offset curve and obtain an interval Bézier curve only containing one interval point, the others are degenerate ones. We also develop a relation among the interval control points of the interval Bézier curve. Some examples show that such approximation coupled with the subdivision leads to better approximation effects.