The optimized primitive filler is used in a computer system, such as a computer system that displays graphic images. A first step of the method it is determined if a primitive is totally outside a predetermined screen region or at least partially within the predetermined screen region. The primitive is then discarded if the primitive is totally outside the screen region. If the primitive is not totally outside the screen region, at least a portion of the primitive is identified that lies within the screen region. Then only those pixels in the portion of the primitive that is inside the screen region are filled. These steps are executed for each primitive of a plurality of primitives that forms a scene of which the screen region is the portion that the computer system displays. No pixels are filled in primitives which are totally outside the screen region, and no pixels are filled in portions of primitives that are outside the screen region. The optimized primitive filler and its associated method provide a fast and efficient rasterization of primitives.