In this paper, we present a family of circular or square optimal polynomial filters for pre-filtering 2D polygons and images. The criterion of designing polynomial filters is to maximize the energy concentration within a period of the spectra of the filters. The filters are non-negative and can have arbitrary radius and order. For a given radius, the filters converge very fast when the order increases, making low-order filters suffice for high-quality pre-filtering. With polynomial filters, it is convenient to evaluate the integral over the parts of polygons within the filter mask with closedform solutions, or generate look-up tables quickly via analytic evaluation. The experiments demonstrate the excellent anti-aliasing performance of our polynomial filters.