Optimal multi-degree reduction of Bezier curves with constraints of endpoints continuity

摘要

Given a Bezier curve of degree n, the problem of optimal multi-degree reduction (degree reduction of more than one degree) by a Bezier curve of degree m 9m < n-1) with constraints of endpoints continuity is investigated. With respect to L_2 norm, this per presents one approximate method MDR by L_2) that gives an explicit solution to deal with it. The method has good properties of endpoints interpolation: Continuity of any r, s (r, s ≥ 0) orders can be preserved at two endpoints respectively.