Key-Point Interpolation: A Sparse Data Interpolation Algorithm based on B-splines

TL;DR

This paper introduces KPI, a novel B-spline surface interpolation algorithm capable of accurately interpolating sparse, non-uniform data by combining Kriging with key-point interpolation, applicable to higher dimensions like dynamic surface reconstruction.

Contribution

The paper presents a two-stage interpolation method that effectively handles sparse, irregular data and extends B-spline interpolation to higher-dimensional applications.

Findings

Accurately interpolates temperature data from weather stations.

Preserves dynamic characteristics of the data.

Extensible to higher-dimensional data interpolation.

Abstract

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.