Linear interpolation revitalized

We present a simple, original method to improve piecewise-linear interpolation with uniform knots: we shift the sampling knots by a fixed amount, while enforcing the interpolation property. We determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and close to 1/5. We confirm our theoretical findings by performing several experiments: a cumulative rotation experiment and a zoom experiment. Both show a significant increase of the quality of the shifted method with respect to the standard one. We also observe that, in these results, we get a quality that is similar to that of the computationally more costly "high-quality" cubic convolution.