有理曲线曲面的降阶逼近  

Approximate Degree Reduction of Rational Curves and Surfaces

作　　者：覃廉[1] 关履泰[1] 

机构地区：[1]中山大学科学计算与计算机应用系,广州510275

出　　处：《中国图象图形学报》2006年第8期1062-1067,I0001,I0002,共8页Journal of Image and Graphics

基　　金：国家自然科学基金项目(60475042);广东省自然科学基金重点项目(036608)

摘　　要：基于齐次坐标空间,提出了一种NURBS曲线曲面和有理Bezier曲线曲面降阶的简便方法。在齐次坐标空间中,使降阶后的曲线曲面与原曲线曲面的差的L2范数达到极小,将有理曲线曲面降多阶问题转化为二次规划问题求解,并给出了误差估计。实验结果表明,该方法计算速度快,降阶逼近效果好。Based on homogeneous coordinates, this paper presents a convenient algorithm for approximate degree reduction of NURBS and rational Bezier curves and surfaces. In homogeneous coordinates, the difference of the low degree curve/ surface and high degree curve/surface is minimized. The problem of approximate multi-degree reduction of rational curves and surfaces is transformed into quadratic programming. Error estimate is presented. Experimental results show that this algorithm is very efficient.

关 键 词：NURBS 有理BEZIER 降阶 二次规划 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]