有理Bézier曲面的降阶逼近  

Degree reduction approximation of rational Bézier surfaces

作　　者：赵前进[1] 

机构地区：[1]安徽理工大学数理系,安徽淮南232001

出　　处：《安徽理工大学学报（自然科学版）》2003年第1期60-62,共3页Journal of Anhui University of Science and Technology:Natural Science

摘　　要：为了减少曲面表示的存储量,提高曲面计算的效率和稳定性,研究有理Bézier曲面的降阶逼近。分析了有理Bézier曲面降阶逼近的新问题,讨论了有理Bézier曲面的退化条件,基于权和控制顶点的扰动,给出了一种有理Bézier曲面降阶逼近的多目标约束优化新方法,利用此方法,将有理Bézier曲面降阶逼近问题转变为求解多目标二次规划问题。为便于求解,采用了分步约束优化方法并给出了数值例子。Degree reduction of rational Bézier surfaces is investigated to reduce the data storage in CAD systems and to increase the stability and efficiency of rational Bézier surfaces calculation. A new problem for degree reduction approximation of rational Bézier surfaces is analysed. At the same time, the degenerating condition of rational Bézier surfaces is discussed based on the perturbations of weights and control points. A new approach of multi-object constrained optimization for degree reduction approximation of rational Bézier surfaces is proposed. By using this method, the problem of approximation of rational Bézier surfaces is changed into one of solving multi-object quadratic programming . In order to solve the problem easily, the approach of stepwisely constrained optimization is discussed and numerical examples are given.

关 键 词：有理BÉZIER曲面 降阶 逼近 退化条件 CAD CAM 计算机辅助设计 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]