High dimensional B-splines are catching tremendous attentions in fields of Iso-geometry Analysis, dynamic surface reconstruction and so on. However, the actual measured data are usually sparse and nonuniform, which might not meet the requirement of traditional B-spline algorithms. In this paper, we present a novel dynamic surface reconstruction approach, which is a 3-dimensional key points interpolation method (KPI) based on B-spline, aimed at dealing with sparse distributed data. This method includes two stages: a data set generation algorithm based on Kriging and a control point solving method based on key points interpolation. The data set generation method is designed to construct a grided dataset which can meet the requirement of B-spline interpolation, while promisingly catching the trend of sparse data, and it also includes a parameter reduction method which can significantly reduce the number of control points of the result surface. The control points solving method ensures the 3-dimensional B-spline function to interpolate the sparse data points precisely while approximating the data points generated by Kriging. We apply the method into a temperature data interpolation problem. It is shown that the generated dynamic surface accurately interpolates the sparsely distributed temperature data, preserves the dynamic characteristics, with fewer control points than those of traditional B-spline surface interpolation algorithm.
翻译:高维B- Spline 正在Iso- 地理测量分析、 动态表面重建等领域引起大量注意。 然而, 实际测量的数据通常稀少且不统一, 可能不符合传统的 B- Spline 算法的要求。 在本文中, 我们提出了一个全新的动态地表重建方法, 这是一种基于 B- Spline 的三维关键点的内插法(KPI), 旨在处理分散的数据。 这个方法包括两个阶段: 基于 Kriging 的数据集生成算法, 和基于关键点内插的控制点解决方法。 数据集生成方法旨在构建一个能满足 B- Spline 内插算法要求的网格化数据集, 同时有望赶上稀散数据的趋势, 并且还包括一个减少参数的方法, 能够显著减少结果表面表面控制点的数量。 控制点确保三维 B- spline 函数精确地将稀少的数据点进行内插, 同时与 Krigging 生成的数据点相向内流数据流流流数据流流的系统内部分配问题。 它显示的是, 流地平流数据流数据流数据流的系统内流的系统流的系统流流数据流数据流数据流的内流的流流流流流的流数据流数据流的分布。