If your reconstruction function is symmetric, which it should be, then your pixel centers are at 0.5, 0.5. All commonly used resampling algorithms are symmetric

If your reconstruction function is symmetric, which it should be, then your pixel centers are at 0.5, 0.5. All commonly used resampling algorithms are symmetric, except perhaps truncating implementations of point sampling (which are thus inconsistent with the rest and arguably wrong for this reason). It doesn't matter how you choose to reconstruct, samples should still be centered around their reconstruction function. Otherwise, you're shifting the image around every time you reconstruct. This causes errors and can be very hard to reason about.