用重新参数化技术改进有理参数曲线曲面的导矢界  

Improve Derivative Bounds of Rational Parametric Curves and Surfaces Using Reparameterization

作　　者：周联[1,2] 王国瑾[1] 

机构地区：[1]浙江大学数学系计算机图象图形研究所,杭州310027 [2]上海海事大学数学系,上海201306

出　　处：《计算机辅助设计与图形学学报》2010年第7期1104-1109,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60873111);国家自然科学基金重点项目(60933007)

摘　　要：为了改进有理参数曲线曲面的导矢界,利用一类特定分式线性参数变换对有理参数曲线曲面重新参数化.基于导矢界的大小由权因子之间的比值所决定的特点,分别给出2种权因子优化方法:一是以最大权因子和最小权因子之间的比值最小化为目标函数的线性规划解法;二是以对数化后的权因子的方差最小化为目标函数的显式解法.数值实验结果表明,文中方法比已有方法能得到更紧的导矢界,从而进一步提高了曲线曲面绘制和求交的效率.In this paper, to improve derivative bounds of rational parametric curves and surfaces, a linear fractional transformation is used to reparameterize the curves and surfaces. Due to the fact that derivative bounds are determined by the ratio of weights, two weight optimization methods are presented. One is to minimize the maximal ratio of weights in the reparameterized representation, which is solved by a linear programming method. The other is to minimize the variance of the log weights, which is solved explicitly. Numerical experiments show that these two methods can obtain tighter derivative bounds than the other methods, which significantly improve the efficiency of rendering and intersection detection for curves and surfaces.

关 键 词：重新参数化 有理曲线曲面 导矢界 Mbius变换 权因子 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]