非静态混合细分法

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。

Non-Stationary Blending Subdivision Scheme

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.