Performing graphics rendering without the computational expense of hither plane clipping and with only a minimum of display image clipping. Where a three dimensional polygon crosses to both sides of a hither plane, any vertices on the back side of the hither plane are translated to the hither plane, producing polygons which occupy only the area in front of the hither plane. A display image memory, from which display images are generated, is located within a larger guard memory such that many images which would need to be clipped to fit in the display image memory may be written to the guard memory without clipping.