In this paper, an improved algorithm for pre-filtering 2D polygons is presented. The part of the polygon within the mask of a filter is decomposed into basic component regions whose parameters can be easily computed. Given the parameters, the integral of the filter over the basic component region can be looked up from a table or even be computed with a closed-form solution. The integral or its negative is then added to the accumulation buffer of the pixel according to whether the pixel center is outside the component region or not. After traveling all polygon edges, the accumulation buffers are shifted by integers so that they are all between 0 and 1. In this way, the expensive clipping of the polygons against the filter mask becomes unnecessary.