A system for clipping polygons representing three-dimensional objects to produce a representation of the portion of the objects in a desired viewing space is disclosed. A guardband space at least partially enclosing the viewing space is defined. The polygons are compared to the guardband space to determine which polygons intersect at least one of the guardband planes defining the guardband space. The intersecting polygons are also compared to the viewing space to determine if they intersect at least one of the viewing planes defining the viewing space. Only polygons intersecting both a viewing plane and a guardband plane are clipped.