An Iterative Algorithm for Degree Reduction of Bézier Curves

In order to improve the stability for degree reduction of Bézier curves,this paper presents an iterative algorithm to minimize the approximation error based on the L₂-norm.Starting with an initial Bézier curve,control points are gradually displaced to obtain the approximate curve with a minimal error.The linear search algorithm is adopted to optimize the displacements of the control points,so that the error is reduced to be locally minimal after each iteration step.Finally,numerical examples demonstrate the fast convergence of the proposed algorithm.