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Interpolation; trigonometric polynomial; regularity; computer vision
It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction. In this paper, we introduce a new kind of 2-period interpolation of functions with period $2\pi $. We find out the necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of practical significance. Our results provide the theoretical basis for using our interpolation in practical problems.
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