Apparatus and methods are disclosed which are most advantageously used in conjunction with a digital computer to provide improved graphics capability. These techniques permit the representation and manipulation of any arbitrarily shaped image in terms of "inversion points". Inversion points defining a region are sorted and stored such that the region shape may be regenerated at a later time from the inversion points. Means are provided to compare existing regions and new regions to be displayed, and region operators are provided to specify a precedence between the existing and new regions. Thus, new regions are appropriately "clipped" such that only portions of a new region may actually be displayed to achieve the desired graphic representation.