Approaches presented herein provide for removal or reduction of anti-aliasing artifacts, such as Moiré patterns or staircasing, in an image to be rendered. In many instances, these artifacts correspond to regular texture patterns with fine detail, and the addition of randomization in sampling position can help to remove the impact of the regularity of the pattern. In at least one embodiment, a first order approximation can be used that introduces a random amount of shifting determined using texture coordinate derivatives. The random amount can account for any jitter offset, and shift the texture coordinates by the determined random amount, such that sample selected for that pixel will select from a sample location that corresponds to the random shift but is constrained to be within the bounds of the pixel.