How a simple shift can significantly improve the performance of linear interpolation

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. Thanks to a theoretical analysis, we determine the optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and it is close to 1/5. We confirm our theoretical findings by performing a cumulative rotation experiment, which shows a significant increase of the quality of the shifted method with respect to the standard one. Most interesting is the fact that we get a quality similar to that of high-quality cubic convolution at the computational cost of linear interpolation.