This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exactly. Our interpolation is characterized by two real parameters: τ, the location of the generators, and α, related to their dissymmetry. By varying these parameters, we show that it is possible to optimize the quality of the approximation, independently of the function to interpolate. We recover the optimal value of shifted-linear interpolation (τ = 0.21 and α = 1) which requires IIR prefiltering, but we also find a new configuration (τ = 0.21 and α = 0.58) which reaches almost the same quality, while requiring FIR filtering only. This new solution is able to greatly reduce the amount of Gibbs oscillations generated in the shifted-linear interpolation scheme. We validate our finding by computing the PSNR of the difference between multi-rotated images and their original version.