Approximate Multidegree Reduction of lambda-Bezier Curves

摘要

Besides inheriting the properties of classical Bezier curves of degree n, the corresponding lambda-Bezier 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 lambda-Bezier curves in the L-2-norm. By analysing the properties of lambda-Bezier curves of degree n, a method which can deal with approximating lambda-Bezier curve of degree n + 1 by lambda-Bezier curve of degree m (m <= n) is presented. Then, in unrestricted and C-0, C-1 constraint conditions, the new control points of approximating lambda-Bezier 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.