H-Bézier曲线的降多阶逼近

Multidegree Reduction Approximation of H-Bézier Curves

国内外对参数曲线降阶,尤其是对Bézier曲线降阶的研究已渐趋成熟,但尚缺少对超越曲线降阶的研究.为此以能精确表示指数曲线、悬链线等超越曲线的H-Bézier曲线为载体,运用H-Bézier曲线的升阶公式,结合广义逆矩阵理论给出了H-Bézier曲线一次降多阶的逼近方法;同时估计了降阶的误差界,并建立了与Bézier曲线降阶的关系.实验结果表明,采用该方法可取得较好的逼近效果,有效地丰富了H-Bézier曲线的理论体系.

The research on the reduction of parametric curves, especially the Bezier curves,has come of age. But the research on the reduction of transcendental curves is rarely reported in literature. This paper studies H-Bezier curves that can exactly represent transcendental curves such as the exponential curves and the catenaries, and gives an approximation method of multidegree reduction of H-Bezier curves by making use of the elevation property of H-Bezier curves, and the theory of generalized inverse matrix. The degree reduction error bound is estimated, the relationship between the reduction of H-Bezier curves and that of Bezier curves is established, and numerical examples are given to show that the presented method has good approximation effects, and hence the theory of H-Bezier curves is enriched.