a method and apparatus for efficiently rasterizing graphics is provided . the method is intended to be used in combination with a frame buffer that provides fast tile - based addressing . within this environment , frame buffer memory locations are organized into a tile hierarchy . for this hierarchy , smaller low - level tiles combine to form larger mid - level tiles . mid - level tiles combine to form high - level tiles . the tile hierarchy may be expanded to include more levels , or collapsed to included fewer levels . a graphics primitive is rasterized by selecting an starting vertex . the low - level tile that includes the starting vertex is then rasterized . the remaining low - level tiles that are included in the same mid - level tile as the starting vertex are then rasterized . rasterization continues with the mid - level tiles that are included in the same high - level tile as the starting vertex . these mid - level tiles are rasterized by rasterizing their component low - level tiles . the rasterization process proceeds bottom - up completing at each lower level before completing at higher levels . in this way , the present invention provides a method for rasterizing graphics primitives that accesses memory tiles in an orderly fashion . this reduces page misses within the frame buffer and enhances graphics performance .