任意平面曲线的圆弧逼近方法

Approximating a Random Plane Curve by Arc Splines

提出了一种根据给定精度逼近平面任意曲线的方法。该方法可以逼近任意次有理Ｂ样条曲线以及非均匀有理Ｂ样条曲线，尤其克服了双圆弧逼近方法的局限性实现了对封闭曲线的圆弧逼近。该方法独立于坐标系，独立于曲线类型。实际应用结果表明，它是一个适用于ＣＡＤ／ＣＡＭ集成系统任意平面曲线的圆弧逼近通用算法。本文对边界条件确定、误差修正和拐点处理进行了一定的研究，得出了一些价值性高、实用性强的结论，为数控加工任意平面曲线提供了一条简捷、易行、可靠的途径。

The paper describes the method of prosramming to approximate a random plane curve with given accuracy by arc splines. The method may approximate arbitrary Rational Bspline and NURBS (Non-Uniform-Rational-B-spline). It overcomes the limitation of a double arc method and reallies the approximation of a closed curve.It is independent of coordinate system and the type of curves. The result of its application illustrates that the method is a conmon algorithm of are approxunation to a random plane curve,which fits in an integrated CAD/ CAM system.In the paper, the determination of boundary conditions, error eorrection and curve turning point handhg have been discussed and studied. Some valuale and practicable conclusions have been made. The paper provides a simple and easy way for programming machining of a random plane curve.