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\(C^2\) Rational Interpolation Splines with Region Control and Image Interpolation Application

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Abstract

In this work, we deal with the region control of \(C^2\) interpolation curves and surfaces using a class of rational interpolation splines in one and two dimensions. Simple sufficient data-dependent constraints are derived on the local control parameters to generate \(C^2\) interpolation curves lying strictly between two given piecewise linear curves and \(C^2\) interpolation surfaces lying strictly between two given piecewise bi-liner blending quintic interpolation surfaces. Moreover, we also develop an algorithm concerning the application of the \(C^2\) rational interpolation spline surfaces on image interpolation.

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Acknowledgements

The research is supported by the National Natural Science Foundation of China (Nos. 61802129, 61572527), the Natural Science Foundation Guangdong Province, China (No. 2018A030310381), and the Hunan Science Fund for Distinguished Young Scholars (No. 2019JJ20027).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, People’s Republic of China

    Zhuo Liu & Shengjun Liu

  2. School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Yuanpeng Zhu

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  1. Zhuo Liu
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Correspondence to Yuanpeng Zhu.

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Liu, Z., Liu, S. & Zhu, Y. \(C^2\) Rational Interpolation Splines with Region Control and Image Interpolation Application. J Math Imaging Vis 63, 394–416 (2021). https://doi.org/10.1007/s10851-020-01005-z

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