Subdivision schemes are useful mathematical tools for the generation of curves and surfaces. The linear approaches suffer from Gibbs oscillations when approximating functions with singularities. On the other hand, when we analyze the convergence of nonlinear subdivision schemes the regularity of the limit function is smaller than in the linear case. The goal of this paper is to introduce a corrected implementation of linear interpolatory subdivision schemes addressing both properties at the same time: regularity and adaption to singularities with high order of accuracy. In both cases of point-value data and of cell-average data, we are able to construct a subdivision-based algorithm producing approximations with high precision and limit functions with high piecewise regularity and without diffusion nor oscillations in the presence of discontinuities.

翻译：分层计划是生成曲线和表面的有用数学工具。 线性方法在接近单数功能时会受到 Gibbs 的振动。 另一方面, 当我们分析非线性分层计划的趋同时, 限制功能的规律性比线性要小。 本文的目的是引入一个纠正性地同时针对两种特性的线性跨线性分层计划的实施: 规律性和适应高度精确的奇数。 在点值数据和平均细胞数据的两种情况下, 我们都能构建一个基于分层的算法, 产生高度精确和限制的近似值, 高片性正常性, 在不连续的情况下不扩散或振动。