论文标题
具有提高精度的非均匀角切割细分方案
A non-uniform corner-cutting subdivision scheme with an improved accuracy
论文作者
论文摘要
本文的目的是构建一种新的非均匀角切割（NUCC）细分方案，该方案提高了经典（固定和非组织）方法的准确性。改进规则是通过指数多项式的复制属性制定的。指数多项式具有形状参数，因此可以适应给定数据的特征。在这项研究中，我们提出了一种选择形状参数的方法，以便它使相关方案能够实现改进的近似顺序（即{\ em三}），而经典方法则达到了二阶精度。对所提出的方案的收敛性和平滑度进行了分析。所提出的方案证明具有与古典Chaikin的转角切割算法相同的平滑度，即$ C^1 $。最后，提出了一些数值示例，以证明新的角切算法的优势。
The aim of this paper is to construct a new non-uniform corner-cutting (NUCC) subdivision scheme that improves the accuracy of the classical (stationary and nonstationary) methods. The refinement rules are formulated via the reproducing property of exponential polynomials. An exponential polynomial has a shape parameter so that it may be adapted to the characteristic of the given data. In this study, we propose a method of selecting the shape parameter, so that it enables the associated scheme to achieve an improved approximation order (that is, {\em three}), while the classical methods attain the second order accuracy. An analysis of convergence and smoothness of the proposed scheme is conducted. The proposed scheme is shown to have the same smoothness as the classical Chaikin's corner-cutting algorithm, that is, $C^1$. Finally, some numerical examples are presented to demonstrate the advantages of the new corner-cutting algorithm.
