关键点插值：一种基于B样条的稀疏数据插值算法
Key-Point Interpolation: A Sparse Data Interpolation Algorithm based on B-splines
摘要：
B样条函数由于其优良的性质，在逆向工程和计算机辅助设计等领域有着广泛的应用。传统的B样条曲面插值算法通常假设数据分布是规则的。本文提出了一种新的B样条曲面插值算法：KPI，它可以插值稀疏和非均匀分布的数据点。作为一个两阶段的算法，我们的方法产生的数据集的稀疏数据使用克里格，并使用建议的KPI（关键点插值）方法来生成控制点。该算法可以推广到高维数据插值，如动态曲面重构。并将该方法应用于山西省气温的插值。所生成的动态表面精确地插值气象站提供的温度数据，并且保留的动态特征可以用于气象研究。
英文摘要：
B-splines are widely used in the fields of reverse engineering and computer-aided design, due to their superior properties. Traditional B-spline surface interpolation algorithms usually assume regularity of the data distribution. In this paper, we introduce a novel B-spline surface interpolation algorithm: KPI, which can interpolate sparsely and non-uniformly distributed data points. As a two-stage algorithm, our method generates the dataset out of the sparse data using Kriging, and uses the proposed KPI (Key-Point Interpolation) method to generate the control points. Our algorithm can be extended to higher dimensional data interpolation, such as reconstructing dynamic surfaces. We apply the method to interpolating the temperature of Shanxi Province. The generated dynamic surface accurately interpolates the temperature data provided by the weather stations, and the preserved dynamic characteristics can be useful for meteorology studies.
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