Approximate Multidegree Reduction of -Bézier Curves

Besides inheriting the properties of classical Bézier curves of degree , the corresponding -Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction of -Bézier curves in the -norm. By analysing the properties of -Bézier curves of degree , a method which can deal with approximating -Bézier curve of degree by -Bézier curve of degree is presented. Then, in unrestricted and , constraint conditions, the new control points of approximating -Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement.