非静态混合细分法  

Non-Stationary Blending Subdivision Scheme

作　　者：闫飞一 郑红婵[1] 

机构地区：[1]西北工业大学理学院应用数学系,陕西西安710129

出　　处：《图学学报》2015年第2期178-185,共8页Journal of Graphics

基　　金：国家自然科学基金资助项目(61070233)

摘　　要：提出了一种含参数b的非静态Binary混合细分法,当参数取0、1时,分别对应已有的非静态四点C1插值细分法及C-B样条细分法。用渐进等价定理证明了对任意(0,1]区间的参数其极限曲线为C2连续的。从理论上证明了细分法对特殊函数的再生性,及其对圆和椭圆等特殊曲线的再生性,并通过实验对比说明了对任意的[0,1]区间的参数,该细分法都能再生圆和椭圆等特殊曲线,而与其渐进等价的静态细分法则不具备该性质。将该细分法推广为含局部控制参数的广义混合细分法,从而可以达到局部调整极限曲线的目的。A non-stationary blending Binary subdivision scheme with a parameter is presented first in this paper.Existing four-point C1 interpolating non-stationary scheme and C-B spline subdivision scheme are special cases of this subdivision when the parameter is 0 and 1 respectively.The limit curve of the scheme is C2 with any parameter in the interval （0,1],which is proved by using the theory of asymptotic equivalence.Then the abilities of the scheme with any parameter in [0,1] to reproduce special functions and some special curves,such as circle and ellipse,are analyzed,and comparisons with the corresponding stationary schemes are also given to better demonstrate it.At last,a generalized non-stationary blending scheme with local control parameter is proposed,which allows local adjustment of the limit curves.

关 键 词：非静态混合细分法 C-B样条 圆 椭圆 局部参数 

分 类 号：TP391.6[自动化与计算机技术—计算机应用技术]