An image generating system and a program enabling scissoring of a polygon in a three-dimensional stage to prevent display failure of a polygon on a screen end or at a short distance from the viewpoint with a reduced computation load. The system performs scissoring processing for a polygon in a three-dimensional stage and generates an image of an object including a new vertex generated by the scissoring. A polygon which is at a short distance from a view point, displaying of which is likely to be missed, is scissored on side surfaces of a quadrangular pyramid forming a view volume, to prevent the display failure of the polygon existing at a short distance from the end of a screen. A polygon arranged in the three-dimensional space is subjected to coordinate transformation into a screen coordinate system, to detect an undrawable vertex, and a polygon containing the detected vertex is scissored at a portion containing the detected vertex, in a predetermined plane.