Multidegree Reduction Approximation of H-Bézier Curves

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