Reconstruction of radio interferometric images requires the processing of data in Fourier space that dot not have regular coordinates, preventing direct use of the Fast Fourier Transform. The most common solution is to rely on interpolation algorithms, called gridding, that are computationally expensive. In this paper, we propose an algorithmic reinterpretation, named sky to sky method, to reduce the computation cost of the gridding operation and its adjoint, the degridding, when used successively. We analyze the impact of interpolation step size regarding the computation cost and the reconstruction error. We also illustrate this optimization on a full reconstruction with gradient descent and CLEAN algorithm. Finally, we obtain acceleration factors between 1.2 and 16.4 without additional approximation.