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非静态混合细分法

  

  • 出版日期:2015-04-30 发布日期:2015-06-03

Non-Stationary Blending Subdivision Scheme

  • Online:2015-04-30 Published:2015-06-03

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。

关键词: 非静态混合细分法, C-B 样条, 圆, 椭圆, 局部参数

Abstract: 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.

Key words: non-stationary blending subdivision scheme, C-B spline, circle, ellipse, local parameter