Constrained B zier curves' best multi-degree reduction in the L2-norm

• 作 者: ZHANG Renjiang WANG Guojin
• 机 构: Institute of Computer Images and Graphics,State Key Laboratory of CAD&CG,China Institute of Metrolog
• 出 处: 自然科学进展（英文版）
• 发表日期: 2004年期
• 关键词: computer aided design Bézer curve degree reduction L2-norm tolerance

In computer aided geometric design, the degree reduction of the parameter curve is a key technique in data exchange and data compression. The various existing methods of degree reduction cannot decide whether the degree reduction curve satisfying the given tolerance exists beforehand, cannot give approximation of the best multi-degree reduction, or cannot provide explicit expression and error formula of the degree reduction curve. In this paper, we propose an entirely new method, which can hurdle the above flaws completely.tives with the given curve up to (r-1)-th and (s-1)-th orders (r, s≤m＜n) respectively at the endpoints, so the approximating error is less than the given tolerance ε in the L2-norm. If the curve exists, the explicit expression can be given.