基于齐次坐标空间，提出了一种NURBS曲线曲面和有理Bezier曲线曲面降阶的简便方法。在齐次坐标空间中，使降阶后的曲线曲面与原曲线曲面的差的L2范数达到极小，将有理曲线曲面降多阶问题转化为二次规划问题求解，并给出了误差估计。实验结果表明，该方法计算速度快，降阶逼近效果好。

Based on homogeneous coordinates, this paper presents a convenient algorithm for approximate degree reduction of NURBS and rational Bezier curves and surfaces. In homogeneous coordinates, the difference of the low degree curve/ surface and high degree curve/surface is minimized. The problem of approximate multi-degree reduction of rational curves and surfaces is transformed into quadratic programming. Error estimate is presented. Experimental results show that this algorithm is very efficient.