平面 NURBS 曲线的椭圆弧自适应逼近

给出了用椭圆弧及双椭圆弧自适应逼近平面NURBS曲线的算法。算法所得到的椭圆样条能够G1连续 ,双椭圆样条还能够保形。与现行的圆弧逼近算法相比 ,本算法不需要求解非线性方程组 ,而是由给定的插补误差自动计算参数增量 ,得到椭圆曲线的特征点 ,还可以将误差控制在预期的范围之内 ;与现行的直线插补方法相比 ,不需要额外的时间和空间 ,也适用于CNC环境。本算法在腔体加工、二维轮廓加工等方面有特别的实用价值。

Auto-adaptable Approximation of Planar NURBS Curve with Ellipse Arc

An algorithm to approximate a planar NURBS curve by ellipse arc and bi ellipse arc is presented. The piecewise ellipse arc spline calculated by this algorithm is G 1 continuous, and shape preserving. Compared with the present arc approximation, this algorithm does not need equation solving, and enable an automatic choice of parameter increment responding to the given interpolation tolerance in calculation of the character points of ellipse arc. The algorithm also has advantage in approximation error control, which can control the approximation error to an expected one. Compared with present line approximation mode, this algorithm, which needs no extra time and space in calculation, is applicable to CNC environment. The algorithm is specially valuable in cavity and contour machining.