1. A method for texturing and shading on a plurality of shading engines, comprising: producing a respective object list for each rectangular area of a plurality of rectangular areas, each rectangular area bounding a respective set of pixels within an image to be rendered, each object list identifying objects that each provide a visible surface for at least one pixel in its rectangular area; allocating each of a plurality of smaller areas, which each bound a subset of the pixels of one of the rectangular areas and collectively bound all the pixels of that rectangular area, to a respective shading engine of the plurality of shading engines; scanning the plurality of smaller areas of a selected rectangular area in a repeating pattern, in which scanning comprises (a) accessing an object from the object list for that selected rectangular area, (b) determining, for the accessed object, and for one or more objects for which the scanning has begun, but not yet completed one iteration of the repeating pattern, which pixels, if any, in a current smaller area each of those objects provides a visible surface, (c) in parallel with the determining, for each previously-accessed object that has now completed one iteration of the repeating pattern, if any, outputting pixel intersection data that identifies each pixel, within the selected rectangular area, in which that object provides a visible surface, and updating the current smaller area to a subsequent smaller area in the repeating pattern, and repeating (a)-(c) at least once for each smaller area within the selected rectangular area, and after a first iteration, at least one object is accessed and at least one object completes each time the current smaller area is updated; and within each of the plurality of shading engines, texturing and shading the pixels within each smaller area allocated to that shading engine that are identified by the outputted pixel intersection data.