Matrix Representation for Optimal Multi-degree Reduction of Bézier Curves with G¹ Constraints

The existing algorithms for multi-degree reduction of Bézier curves with G¹ constraints only provide numerical solutions.To overcome this flaw, an algorithm for optimal degree reduction of Bézier curves with G¹ constraints at the endpoints is presented.By taking the approximation error as the objective function and minimizing this function, the optimal explicit solution to multi-degree reduction of Bernstein polynomials with high-order continuity at the two endpoints is given.And then the optimal explicit solution to multi-degree reduction of Bézier curves with G¹ constraints is also given.The control points of the degree reduced curves and the approximation error are derived from two matrix representations respectively.Numerical examples show that the proposed method is more precise and efficient comparing to previous methods.