源于均匀三角B样条的非平稳细分格式
Non-stationary subdivision schemes originated from uniform trigonometric B-spline
AI总结：
提出一种基于均匀三角B样条基函数生成任意m点二进制非平稳细分格式的算法，利用渐近等价理论分析光滑性，该格式能再现圆锥曲线、三角多项式和三角样条。
摘要：
本文提出一种算法，用于生成新颖的m点（m≥2任意整数）二进制非平稳细分格式。该算法利用均匀三角B样条基函数开发，并使用渐近等价理论分析光滑性。结果表明，大多数已知的二进制逼近格式可视为所提算法的非平稳对应物。此外，所提算法开发的格式能够再现或再生圆锥曲线、三角多项式和三角样条。通过选择适当的张力参数0<α<π/3，给出了一些例子以展示其有用性。
英文摘要：
The paper proposes, an algorithm to produce novel m-point (for any integer m>=2) binary non-stationary subdivision scheme. It has been developed using uniform trigonometric B-spline basis functions and smoothness is being analyzed using the theory of asymptotically equivalence. The results show that the most of well-known binary approximating schemes can be considered as the non-stationary counterpart of the proposed algorithm. Furthermore, the schemes developed by the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines as well. Some examples are considered, by choosing an appropriate tension parameter 0<alpha<pi/3, to show the usefulness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
