五点二重逼近细分法

图学学报

五点二重逼近细分法

出版日期:2012-10-31 发布日期:2015-07-28

A five-point binary approximating subdivision scheme for curve design

Online:2012-10-31 Published:2015-07-28

摘要/Abstract

摘要： 提出了一种新的构造曲线的算法——五点二重逼近细分法。利用细分格式
的生成多项式讨论了该细分格式的一致收敛性及Ck 连续性。该细分格式带有一个张力参数
μ, 通过选取不同的μ值，可以分别生成C1~C5 连续的极限曲线。特别是当μ=9/256 时，细
分格式生成的极限曲线可以达到C7 连续。最后给出了五点二重逼近曲线细分的实例，表明
了这种细分格式是有效的。

关键词: 二重逼近细分, 生成多项式, Ck 连续性, 极限曲线

Abstract: A binary five-point approximating subdivision scheme is described. The
generating polynomial method is used to investigate the uniform convergence and Ck -continuity
of this subdivision scheme. The subdivision scheme generates a family of Cn (n=1, 2,3,4,5)
limiting curves for certain range of tension parameter μ and a C7 limiting curves forμ=9/256.
Some examples of the subdivision curve design are given to demonstrate the efficiency of the
scheme.

Key words: binary approximating subdivision, generating polynomial, Ck-continuity;
limiting curves

庄兴龙，檀结庆. 五点二重逼近细分法[J]. 图学学报.

Zhuang Xinglong, Tan Jieqing. A five-point binary approximating subdivision scheme for curve design[J]. Journal of Graphics.