1. A method in a computer system for generating a presentation of a region-of-interest in an original image for display on a display screen, the original image being a collection of polygons having polygons defined by three or more shared edges joined at vertex points, the method comprising: establishing a lens for the region-of-interest, the lens having a magnified focal region for the region-of-interest at least partially surrounded by a shoulder region across which the magnification decreases, the focal and shoulder regions having respective perimeters; subdividing polygons in the collection of polygons proximate to at least one of the perimeters, as projected with the polygons onto a base plane, by inserting one or more additional vertex points and additional edges into the polygons to be subdivided; and, applying the lens to the original image to produce the presentation by displacing the vertex points onto the lens and perspectively projecting the displacing onto a view plane in a direction aligned with a viewpoint for the region-of-interest.