The present invention provides post tile sorting setup in a tiled graphics pipeline architecture. In particular, the present invention determines a set of clipping points that identify intersections of a primitive with a tile. The mid-pipeline setup unit is adapted to compute a minimum depth value for that part of the primitive intersecting the tile. The mid-pipeline setup unit can be adapted to process primitives with x-coordinates that are screen based and y-coordinates that are tile based. Additionally, to the mid-pipeline setup unit is adapted to represent both line segments and triangles as quadrilaterals, wherein not all of a quadrilateral's vertices are required to describe a triangle.