Calculating screen coverage

When drawing a 3D object it is sometimes useful to find a rectangle on the screen that completely encloses the object. This can be used to minimize screen-update and z-buffer-clear regions. If the entire object is visible within the screen boundaries, this calculation is easy, you just find the minimum and maximum x and y screen coordinates. If the object extends outside the screen boundaries in one or more coordinates, the calculation is a little trickier. Simply extending the enclosing boundaries to the entire screen dimensions is overly conservative. The paper describes a way to determine a reasonable screen extent enclosing an object even if some points are off the screen or, even worse, behind the viewer's head. It is also a good exercise of your intuition about the homogeneous perspective transformation. Firstly the paper reviews the technique of clip culling.