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.%Diskq-Bézier curve is a special representation form of the parametric curve. Using this represen-tation, 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 diskq-Bézier curves with lower degree diskq-Bézier curves, the algorithms for degree reduction of diskq-Bézier curves are proposed. First of all, the degree reduction approximation to the center curves of the original diskq-Bézier curves are found using best uniform ap-proximation methods. The center curves of the degree reduced diskq-Bézier curves are obtained. Then the radius of the degree reduced diskq-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.
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