One embodiment of the present invention includes a method for generating accumulated bounding boxes for graphics primitives. The method includes generating a first bounding box associated with a first graphics primitive. The method further includes, for each graphics primitive included in a first set of one or more additional graphics primitives, determining that the graphics primitive is within a threshold distance of the first bounding box, and adding the graphics primitive to the first bounding box. The method further includes determining not to add a second graphics primitive to the first bounding box. The method further includes generating a second bounding box associated with the second graphics primitive. Finally, the method includes transmitting the first bounding box to a tiling unit via a crossbar. One advantage of the disclosed embodiments is that multiple bounding boxes are combined to generate an accumulated bounding box that is then transferred across the crossbar.