A graphics system for tile-by-tile converting of vertex data into output images for displaying on a screen. The vertex data represents objects by a set of polygons and comprises 3D space coordinates for each vertex (q1, q2, . . . , q12) in the image. A polygon is constituted of at least three vertices (q1, q2, . . . , q12). The system comprises a tile processor, for subdividing the image into a plurality of tiles (t21, 22, t23) and for determining polygon strips (q1-q12), comprising a sequence of polygons. The tile processor is also operative to determine sub-strips (q3-q10) for each polygon strip (q1-q12). Each sub-strip (q3-q10) comprises those polygons of the polygon strip (q1-q12) which at least partly overlap a single one of the tiles (t21, 22, t23). For processing a tile (t21, 22, t23), only the sub-strips (q3-q10), i.e. the polygons covering that tile (t21, 22, t23), have to be processed.