基于广义逆矩阵的有理Bézier曲线降多阶逼近

Approximation of multi-degree reduction of rational Bézier curves by the general inverse matrix

文章利用有理Bézier曲线的齐次坐标表示,参考基于广义逆矩阵的多项式的降多阶逼近方法,给出了基于广义逆矩阵的有理Bézier曲线的降多阶逼近方法。在降阶过程中,分别考虑了不保端点插值和具有端点高阶插值条件的情形,并分别得到了降多阶后的有理Bézier曲线的控制顶点齐次坐标的计算公式。最后,给出数值实例,以显示所给方法的有效性。

Rational Bzier curves are the generation of polynomial Bzier curves. In this paper, an approach for multi-degree reduction of rational Bzier curves is presented, which is based on the coordinate expression of rational Bzier curves and the method of multi-degree reduction of polynomial Bzier curves by the general inverse matrix. The explicit formula of the homogeneous coordinates of the control points of the reduced rational Bzier curves is obtained. In the process of degree reduction, the case with higher order interpolation conditions of endpoints is considered. Finally, some numerical examples are presented to illustrate the effects of this method.