Interacting with detail-in-context presentations

A method for generating a presentation of a region-of-interest in an original image for display on a display surface, the method comprising: establishing a lens for the region-of-interest, the lens having a focal region with a magnification for the region-of-interest at least partially surrounded by a shoulder region across which the magnification varies to provide a continuous transition from the focal region to regions outside the lens; receiving a first signal for selecting the shoulder region; while receiving the first signal, receiving a second signal for selecting the focal region and for adjusting a position of the focal region relative to the shoulder region to define a degree and a direction of a folding of the focal region over the shoulder region for the lens; and, applying the lens to the original image to produce the presentation.