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Construction of Trigonometric Box Splines and the Associated Non-Stationary Subdivision Schemes

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Abstract

In this paper, we define trigonometric box splines on regular triangular meshes using directional convolution. Using the theory, a non-stationary subdivision scheme for a particular trigonometric box spline is introduced. Later, it is generalized to a non-stationary subdivision scheme for arbitrary triangular meshes. It is also shown that the new subdivision scheme is a non-stationary generalization of the popular stationary Loop scheme.

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Acknowledgements

This research is supported by the Department of Science and Technology, Govt. of India (Regd. No. DST/INSPIRE Fellowship/2016/IF160366). The authors are very much thankful to the anonymous referees and the editor of this paper for their valuable comments and suggestions for the improvement of this paper.

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  1. Department of Mathematics, Veer Surendra Sai University of Technology, Burla, 768018, India

    Hrushikesh Jena & Mahendra Kumar Jena

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  1. Hrushikesh Jena
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Correspondence to Mahendra Kumar Jena.

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Jena, H., Jena, M.K. Construction of Trigonometric Box Splines and the Associated Non-Stationary Subdivision Schemes. Int. J. Appl. Comput. Math 7, 129 (2021). https://doi.org/10.1007/s40819-021-01069-4

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