An improved parameterization method for B-spline curve and surface interpolation

The parameterization method plays a critical role in B-spline interpolation. Some of the well-known parameterizations are the uniform, centripetal, chord length, Foley and universal methods. However, the interpolating results of these methods do not always satisfy all data features. In this study, we propose a new parameterization method which aims to improve the wiggle deviation of the interpolation, especially when interpolating the abrupt data interpolation. This new method is a refined centripetal method. The core of refinement is introducing the osculating circle at each data point. Besides the new parameterization method, we also design a fine wiggle validation method to verify the performance of all methods. In this paper, the proposed method is compared with centripetal, chord length, Foley, uniform and universal methods in both curve and surface cases. As a result, the proposed method has fewer wiggles than the centripetal method and other methods in the cases of abrupt-changing data. In addition, this refined method is stable for all kinds of data types, including free-form data distribution in this paper. The proposed method has fewer drawbacks than other methods, such as wiggles, oscillations, loops, and peaks, among others. More advantage, the proposed method is less influenced by the degree changing.

Figure optionsDownload as PowerPoint slideHighlights
► A well-refined parameterization method for B-spline interpolation.
► Significantly reduces the wiggles of the centripetal method for abrupt data type.
► This refined method performs stably regardless the ordered data distributions.
► The results of the refined method are stable under different interpolating degree.
► Results and deviations comparison to other commonly are demonstrated.