基于圆弧样条构造NURBS曲线的等距线

Constructing offsets of N U R B S curves via circular spline

利用双圆弧构造 Ｇ１ 圆弧样条逼近原始 Ｎ Ｕ Ｒ Ｂ Ｓ曲线，然后对每段圆弧的法矢进行调整，生成一条光滑的 Ｎ Ｕ Ｒ Ｂ Ｓ曲线，并将其称为等距方向曲线。按等距方向曲线对圆弧样条进行等距操作即可得到原始曲线的逼近的等距线。该方法有以下几个优点：①逼近精度容易控制；②所得等距线具有 Ｎ Ｕ Ｒ Ｂ Ｓ表示，且为一 Ｇ１ 圆弧样条，光滑性可达到工程要求；③算法稳定可靠，适合于任一平面或空间 Ｎ Ｕ Ｒ Ｂ Ｓ曲线，鲁棒性好。

Based on biarcs,a sm ooth N U R B Scurve nam ed offset direction curve is obtained by constructingcircular spline for approxim ating original N U R B Scurve and adjusting norm vectors of every circular arc. Offsetting the circular spline in the offset direction curve can obtain the approxim ating offset curve of origi nal curve. This m ethod has follow ing advantages: 1) Approxim ating tolerance is controlled easily. 2) Ob tained offset curve is a circular spline and has N U R B S representation. M oreover,its sm ooth degree canm eet the dem and of C A D/ C A M ; 3) The algorithm is stable and robust, and fits to any plane or space N U R B Scurve.