代数双曲B-样条的几何构造  

Geometric Construction of Algebraic Hyperbolic B-Spline

作　　者：朱平[1] 汪国昭[2] 

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]浙江大学CAD＆CG国家重点实验室,杭州310027

出　　处：《计算机辅助设计与图形学学报》2009年第7期912-917,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60773179);国家“九七三”重点基础研究发展计划项目(2004CB318000)

摘　　要：样条曲线的升阶是CAD系统相互沟通必不可少的手段之一.由于双阶样条的升阶算法具有割角性质,因此具有鲜明的几何意义.以代数双曲B-样条为例,证明了样条曲线经过不断升阶之后,其控制多边形序列会像Bézier曲线一样收敛到初始的代数双曲B-样条曲线.利用文中得到的结果,就可以像Bézier曲线一样,通过几何割角法生成B-样条曲线?双曲线?悬链线等常用曲线.Degree elevation of spline curves is an essential technique for communication between CAD systems. Since degree elevation algorithm by bi-order Spline can be interpreted as corner cutting process, degree elevation of Spline curve has obvious geometric meaning. Taking algebraic hyperbolic B-spline curve as an example, it is proved that Spline curve＇s control polygon sequence will converge to the initial algebraic hyperbolic B-spline curve after degree elevation continually. By this conclusion, common curves including B-spline, hyperbola and catenary curves can be obtained by geometric corner cutting as Bezier curves.

关 键 词：AH B-样条 双阶AHB-样条 升阶 几何收敛 积分估计 几何生成 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]