摘要
通过在Hassan的四点三重插值细分法中引入一个偏移变量,推导出了一种逼近细分法,从而使三重逼近细分和插值细分统一到一个细分格式.该方法利用细分格式的生成多项式,在理论上分析了提出的细分格式的一致收敛性和Ck连续性;通过对细分格式中参数u取不同的值,可对生成的极限曲线形状进行控制.数值实验结果表明,文中方法是合理有效的.
This paper presents a new method for constructing approximating subdivision, which is obtained by introducing an offset variable to the interpolating four-point ternary subdivision schemes proposed by Hassan. The new scheme unifies the ternary approximating subdivision and interpolation subdivision. The uniform convergence and Ck smoothness of the limit curve produced by our subdivision scheme are analyzed by means of the Laurent polynomials. It is pointed out that the parameter in the subdivision can be adjusted to control the shape of the limit curve. Numerical experiments show that the proposed method is effective.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2015年第7期1162-1166,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金-广东联合基金重点项目(U1135003)
国家自然科学基金(61472466
61070227)
关键词
插值细分法
逼近细分法
生成多项式
Ck连续性
interpolating subdivision
approximating subdivision
Laurent polynomial
C-continuity
