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中文摘要：
等距曲线广泛应用于数控机床加工过程、机器人行走路线、刺绣针法生成等工业领域中，与基曲线相比，其表示更为复杂，基本不能用有理曲线来精确表示．为了使等距曲线与CAD／CAM系统更好地相容，基于圆弧的Bezier多项式逼近，提出一种Bezier曲线的等距曲线的同次多项式逼近方法．首先利用Tchebyshev多项式逼近圆弧，并由此得到圆弧的任意次数的B6zier多项式逼近；然后利用上述圆弧逼近的方法去逼近等距曲线的基圆，进而推导出了一种Bezier曲线的等距曲线多项式逼近方法，得到等距逼近曲线是与基曲线次数相同的Bezier曲线．最后通过实例与其他基于圆弧逼近的等距曲线逼近方法进行了比较，结果表明，文中方法与其他方法具有相似的逼近效果，但大大降低了逼近次数．
英文摘要：
Offset curves has been widely used process, robot walking route etc. , comparing with and can＇t be represented by rational curve except in CNC （computer numerical control） machining the original curve, offset curves are more complex, for special cases. In order to be compatible with existing CAD/CAM system, based on the Bezier polynomial approximation of circular arcs, a new algorithm is proposed to approximate offset curves of Bezier curves. At first, by use of Tchebyshev polynomial to approximate circular arcs, we present an arbitrary order Bezier polynomial approximation of circle, then use it to derive the approximation for offsets of Bezier curves, which is a new Bezier curve with the same degree of the base curve. Two examples are given finally for comparing with other methods, the results show that the effectiveness of our method similar to other methods, but our method reduces the approximation degree.
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The dual bases for the Bézier -Said- Wang type generalized Ball polynomial bases and their applicati
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