Optimal multi-degree reduction of Bezier curves with constraints of endpoints continuity
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   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 the stepwise computing. When applied to the multi-degree reduction with endpoints continuity of any orders, the MDR by L-2 obtains the best least squares approximation. Comparison with another method of multi-degree reduction (MDR by L-infinity), which achieves the nearly best uniform approximation with respect to L-infinity norm, is also given. The approximate effect of the MDR by L2 is better than that of the MDR by L-infinity. Explicit approximate error analysis of the multi-degree reduction methods is presented. (C) 2002 Published by Elsevier Science B.V.
degree reduction bezier curve endpoint continuity optimal approximation