On the use of the Discrete Fourier Transform in Subdivision Schemes

The article is devoted to the development of the method of geometric modeling based on subdivision schemes and the application of this method to the parametric description of a surface or an area from a point cloud obtained by any method. To find the initial sequence of the scheme of subdivisions, the method of least squares is used, but its direct use is difficult due to the huge size of the matrices. Since subdivision schemes are based on sequence convolutions, a discrete Fourier transform is used to eliminate the matrix size problem, and the method of least squares is not the initial sequence itself, but its Fourier transform.

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