中文摘要：

圆域q-Bézier曲线是参数曲线的一种特殊表示形式,这种表示形式在很大程度上解决了CAD系统中浮点运算带来的不稳定性问题.为了用低阶圆域q-Bézier曲线逼近圆域q-Bézier曲线,提出圆域q-Bézier曲线的降阶算法.首先利用最佳一致逼近法构造原圆域q-Bézier曲线的中心曲线的降阶逼近,得到降阶后圆域q-Bézier曲线的中心曲线;然后用扰动法计算降阶后圆域q-Bézier曲线的半径;最后分析了降阶算法的边界误差.数值实例结果表明,该方法是有效的.

英文摘要：

Disk q-Bézier curve is a special representation form of the parametric curve.Using this representation,the problem of instability due to floating-point arithmetic in all state-of-the-art CAD systems can be largely solved.In this paper,to approximate disk q-Bézier curves with lower degree disk q-Bézier curves,the algorithms for degree reduction of disk q-Bézier curves are proposed.First of all,the degree reduction approximation to the center curves of the original disk q-Bézier curves are found using best uniform approximation methods.The center curves of the degree reduced disk q-Bézier curves are obtained.Then the radius of the degree reduced disk q-Bézier curve is computed by using perturbation method.Finally,the bounding errors for the degree reduction algorithm are analyzed.Some numerical examples demonstrate the effectiveness of the proposed methods.