Abstract We propose a new approach for meshless multi-level radial basis function (ML-RBF) approximation which offers data-sensitive compression and progressive details visualization. It leads to an analytical description of compressed vector fields, too. The proposed approach approximates the vector field at multiple levels of detail. The low-level approximation removes minor flow patterns while the global character of the flow remains unchanged. And conversely, the higher level approximation contains all small details of the vector field. The ML-RBF has been tested with a numerical forecast data set and 3 D tornado data set to prove its ability to handle data with complex topology. Comparison with the Fourier vector field approximation has been made and significant advantages, i.e. high compression ratio, accuracy, extensibility to a higher dimension etc., of the proposed ML-RBF were proved.

中文翻译：

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径向基函数和多级二维矢量场近似

摘要 我们提出了一种用于无网格多级径向基函数 (ML-RBF) 近似的新方法，该方法提供数据敏感压缩和渐进式细节可视化。它也导致对压缩向量场的分析描述。所提出的方法在多个细节级别上近似矢量场。低级近似消除了较小的流动模式，而流动的全局特征保持不变。相反，更高级别的近似包含向量场的所有小细节。ML-RBF 已经用数值预报数据集和 3D 龙卷风数据集进行了测试，以证明其处理复杂拓扑数据的能力。与傅里叶矢量场近似进行了比较，并具有显着的优势，即高压缩比、准确度、