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KPI Method for Dynamic Surface Reconstruction With B-splines based on Sparse Data

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.