1. A hierarchical memory localized triangle rasterization method, comprising the steps of: (a) walking a plurality of tiles of pixels and determining if each tile is valid; (b) breaking each valid tile into a plurality of subtiles and determining if each subtile is valid; (c) breaking each valid subtile into a plurality of quads and determining if each quad is valid; and (d) rendering pixels for each valid quad, wherein steps (a) through (d) are performed in parallel; and wherein the walking step (a) comprises determining a walk direction from each tile according to whether the tile is determined to be valid.