The boundary of a surface can be represented as a series of line segments. A number of polygons are successively superimposed onto the surface. The polygons utilize a common reference point and each of the polygons has an edge that coincides with one of the line segments. Coverage bits are associated with respective sample locations within a pixel. A value of a coverage bit is changed each time a sample location associated with the coverage bit is covered by one of the polygons. Final values of the coverage bits are buffered after all of the polygons have been processed. The values of the coverage bits can be used when the surface is subsequently rendered.