title: Optimal multi-degree reduction of Bezier curves with constraints of endpoints continuity
abstract: 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 (m<n-1) with constraints of endpoint continuity is investigated. With respect to L/sub 2/ norm, this paper presents an approximate method (MDR by L/sub 2/) that gives an explicit solution to deal with it. The method has good properties of endpoint interpolation: continuity of any r, s (r, s>or=0) orders can be preserved at two endpoints respectively. The method in the paper performs multi-degree reduction at one time and does not need stepwise computing. When applied to multi-degree reduction with endpoint continuity of any order, the MDR by L/sub 2/ obtains the best least squares approximation. Comparison with another method of multi-degree reduction (MDR by L/sub infinity /), which achieves the nearly best uniform approximation with respect to L/sub infinity / norm, is also given. The approximate effect of the MDR by L/sub 2/ is better than that of the MDR by L/sub infinity /. Explicit approximate error analysis of the multi-degree reduction methods is presented
keyphrases: optimal multi-degree reduction Bezier curves approximate method explicit solution endpoint interpolation least squares approximation uniform approximation explicit approximate error analysis endpoint continuity constraints