A method and system for tessellating a polygon is provided, in which a polygon is divided into bands, each band being bounded by a pair of chains. Each chain is made up of one or more line segments of the polygon. The bands are merged with one another and/or split as needed. Each band is then subdivided into constituent triangles, which may then be sent to a graphics card of a computer. The graphics card then renders the polygon on a monitor by reassembling the constituent triangles.