Multi-degree reduction of Bezier curves with higher approximation order

The L₂-norm method is often used in the multi-degree reduction problem of Bezier curves, which achieves an approximation order of m+1 by using polynomials of degree m. This paper presents a tangent method for achieving a higher approximation order, in which a system of linear equations in the unknown control points of the resulting approximation Bezier curve is derived. Given the degrees of the given and the approximation Bezier curves, i.e., n and m, the control points of the approximation curve can be explicitly expressed. In principle, when the given Bezier curve geometrically coincides with a cubic Bezier curve, the new method can exactly recover the cubic Bezier curve. Numerical examples show that the new method can achieve a better approximation effect than that of the L₂-norm method for degree reduction.